The Tabu Search Heuristic for the Vehicle Routing Problem with Soft

Eingereicht von Arevik Hakobian

Angefertigt am Institut fur Produktions- und Logistik- management

Betreuung Univ.-Prof. Dr. Karl D¨orner

Mitbetreuung Mag. Michael Schilde, PhD

Februar 2017

The Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows Diplomarbeit zur Erlangung des akademischen Grades Magistra der Sozial- und Wirtschaftswissenschaften im Diplomstudium Wirtschaftswissenschaften

JOHANNES KEPLER UNIVERSITAT¨ LINZ Altenbergerstraße 69 4040 Linz, Osterreich¨ www.jku.at DVR 0093696

Acknowledgements

First, I would like to thank Univ.-Prof. Dr. Karl Dörnerand Mag. Michael Schilde, PhD for introducing me in the field of Vehicle Routing Problems and supervising me during the work on this thesis. I also would like to thank Mag. Stefanie Kritzinger, PhD for providing me with her code and helping me whenever questions arose. Further, I wish to thank the Institute of Production and Logistics Management for their support, especially Mag. Gabriele Traugott and Sabine Frank. I also wish to thank my family for their patience and motivating words. Most of all, I would like to thank my parents for always encouraging me in my studies and life decisions. I wish to thank my friends for accompanying me during my studies. When recalling the study years, all I can remember are delicious moments I had with you, specially during lunch and coffee breaks. University would have been quite monotonous without you guys, especially without you Gayaneh! Thanks for being a great friend and a very good listener. I would like to take off my hat to a good friend and cerebrum, Dominik, who deserves to be thanked a lot for helping me without hesitation whenever technical difficulties arose and encouraging me in my work. Finally, I would like to thank the unibrat for crossing my ways with Sebastian, who is not only a very good friend but also my family. Thanks for picking me up.

Eidesstattliche Erkl¨arung

Ich erklärean Eides statt, dass ich die vorliegende Diplomarbeit selbstständigund ohne fremde Hilfe verfasst, andere als die angegebenen Quellen und Hilfsmittel nicht benutzt bzw. die wörtlich oder sinngemäßentnommenen Stellen als solche kenntlich gemacht habe. Die vorliegende Diplomarbeit ist mit dem elektronisch übermittelten Textdokument identisch.

Linz, 09.02.2017

Arevik Hakobian

iii

Abstract

In this work metaheuristics are introduced for the solution of the vehicle routing problem with soft time windows. The tabu search algorithm is implemented in this context along with the iterated local search and tested on different parameter settings and methods. During the tests on tabu search, intensification, diversification and route minimization strategies are gradually developed and implemented. The tabu search algorithm is further tested on different types of soft time windows. Computational test results of benchmark problems are calculated and compared to results from literature. Results show that in comparison with other tabu search algorithms, the tabu search generated in this work could outperform several paper results.

Kurzfassung

Diese Arbeit befasst sich mit Metaheuristiken fürdie Lösungdes Tourenpla- nungsproblems mit weichen Zeitfenstern, welches das Ziel hat kostengünstigste Routen von einem Depot zu geographisch verteilte Kunden zu entwerfen, wobei jeder Kunde innerhalb eines vorgegebenen Zeitintervalls durch ein Fahrzeug bedient werden muss bzw. kann. Als Lösungsverfahren, wird der Tabu Suchalgorithmus zusammen mit der Iterierten Lokalen Suche implementiert und mit verschiedenen Parametern und Methoden getestet. Währendder Tests zur Tabu Suche werden Intensivierungs-, Diversifizierungs- und Routenminimierungsstrategien entwickelt und umgesetzt. Das Tabu Suchver- fahren wird mit verschiedene Arten von weichen Zeitfenstern getestet. Rechnerische Testergebnisse von Benchmark-Problemen werden berechnet und mit Ergebnissen aus der Literatur verglichen, die zeigen, dass der entwickelte Tabu Suchalgorithmus Publikationen zur selben Thematik übertreffen konnte.

vii

Contents

Abstract v

Kurzfassung vii

List of Tables xi

List of Figures xiii

List of Algorithms xv

1. Introduction 1 1.1. Related Work ...... 2 1.2. Structure ...... 4

2. The Vehicle Routing Problem 5 2.1. Introduction ...... 5 2.2. Problem Deﬁnition ...... 6 2.3. Solution Methods ...... 6 2.3.1. Classical Heuristics ...... 7 2.3.2. Metaheuristics ...... 7

3. The Vehicle Routing Problem with Time Windows 11 3.1. Introduction ...... 11 3.2. Problem Deﬁnition ...... 12 3.3. Solution Method ...... 13 3.3.1. Initial Solution ...... 13 3.3.2. Neighborhood Operators ...... 14 3.3.3. Tabu Search ...... 16

4. Computational Experiments 21 4.1. Test Instances ...... 21 4.2. HeuristicLab Experiment ...... 22 4.3. Simulation Software ...... 23 4.3.1. The Iterated Local Search Algorithm ...... 24 4.3.2. The Tabu Search Algorithm ...... 25 4.3.3. Infeasible Solutions ...... 26 4.3.4. Minimizing the Number of Routes ...... 26

ix Contents

4.4. Computational Test Results ...... 27 4.4.1. Tests on Iterated Local Search ...... 27 4.4.2. Tests on Tabu Search ...... 30 4.5. Performance Analysis ...... 46

5. Conclusion 51

Appendices 53

A. Appendix A 55 A.1. VRPTW ...... 55 A.1.1. Problem Deﬁnition ...... 55 A.1.2. An Example ...... 56 A.2. VRPSTW ...... 57 A.2.1. Experiment on Minimizing the Number of Vehicles ...... 57

B. Appendix B 59 B.1. Computational Experiments ...... 59

List of Abbreviations 95

Bibliography 97

x List of Tables

1. Related Work on TS and VRPTW ...... 3

2. Cross Exchange ...... 17

3. Results HL-experiment for the VRPSTW ...... 23 4. Overview Parameters ...... 27 5. Test on Acceptance Strategy with HTW and TO-NNB Heuristic . . 28 6. Test on Acceptance Strategy with HTW and RIS ...... 28 7. Test on Acceptance Strategy with STW and TO-NBB Heuristic . . . 29 8. Test on Acceptance Strategy with STW and RIS ...... 29 9. Overview Tests on ILS ...... 30 10. Overview of Results of TT ...... 31 11. Overview Results of Intensiﬁcation Strategies ...... 32 12. Comparison of TS Implementations of Chiang & Russell [8] . . . . . 33 13. Comparison of TS Implementations ...... 34 14. Comparison Test Results of Minimizing Number of Routes ...... 35 15. Test on Initial Solution ...... 36 16. Comparison of the Results of Type a of VRPSTW ...... 38 17. Comparison of CPU Time on Type a of VRPSTW ...... 39 18. Comparison of the Results of Type b of VRPSTW ...... 40 19. Comparison of CPU Time on Type b of VRPSTW ...... 40 20. Comparison of the Results of Type c of VRPSTW (Pmax = 0) . . . 42 21. Comparison of the Results of Type c of VRPSTW (Pmax = 5) . . . 43 22. Comparison of the Results of Type c of VRPSTW (Pmax = 10) . . 44 23. Comparison of CPU Time on Type c of VRPSTW ...... 45 24. Comparison of the Results of VRPTW ...... 45 25. Comparison to the Optimal Solution ...... 46 26. Comparison ILS and TS Algorithm with Best Known Solutions . . . 48 27. Comparison of Tabu Search Algorithms ...... 49

A1. Average Test Results of toleranceV alue ...... 57

B1. Test on Acceptance Strategy with HTW and TO-NNB Heuristic . . 59 B2. Test on Acceptance Strategy with HTW and RIS ...... 59 B3. Test on Acceptance Strategy with STW and TO-NNB Heuristic . . . 59 B4. Test on Acceptance Strategy with STW and RIS ...... 59 B5. Overview Tests on ILS ...... 60

xi List of Tables

B6. Detailed Results HL-experiment for the VRPSTW ...... 61 B7. Detailed Test Result ILS with TO-NNB Heuristic and FF for the VRPTW ...... 62 B8. Detailed Test Result ILS with TO-NNB Heuristic and BF for the VRPTW ...... 63 B9. Detailed Test Result ILS with RIS and FF for the VRPTW . . . . . 64 B10. Detailed Test Result ILS with RIS and BF for the VRPTW . . . . . 65 B11. Detailed Test Result ILS with TO-NNB Heuristic and FF for the VRPSTW ...... 66 B12. Detailed Test Result ILS with TO-NNB Heuristic and BF for the VRPSTW ...... 67 B13. Detailed Test Result ILS with RIS and FF for the VRPSTW . . . . 68 B14. Detailed Test Result ILS with RIS and BF for the VRPSTW . . . . 69 B15. Overview Tests on TT ...... 70 B16. Detailed Test Result TS with Tabu Tenure =1 ...... 71 B17. Detailed Test Result TS with Tabu Tenure =2 ...... 72 B18. Detailed Test Result TS with Tabu Tenure =3 ...... 73 B19. Detailed Test Result TS with Tabu Tenure =4 ...... 74 B20. Detailed Test Result TS with Tabu Tenure =5 ...... 75 B21. Detailed Test Result TS with Tabu Tenure =6 ...... 76 B22. Detailed Test Result TS with Tabu Tenure =7 ...... 77 B23. Detailed Test Result TS with Tabu Tenure =8 ...... 78 B24. Detailed Test Result TS with Tabu Tenure =9 ...... 79 B25. Detailed Test Result TS with Tabu Tenure =10 ...... 80 B26. Detailed Test Result TS with Tabu Tenure =11 ...... 81 B27. Detailed Test Result TS with Tabu Tenure =12 ...... 82 B28. Detailed Test Result TS with Random Tabu Tenure =[1,10] . . . . . 83 B29. Detailed Test Result TS with Random Tabu Tenure =[11,20] . . . . 84 B30. Detailed Test Result TS on Intensification with Or-Opt ...... 85 B31. Detailed Test Result TS on Intensification with S/F Heuristic . . . . 86 B32. Detailed Test Result TS on Intensification with C/R Heuristic . . . 87 B33. Detailed Test Result TS on Intensification and Diversification . . . . 88 B34. Detailed Test Result TS on Minimizing Number of Routes (toleranceV alue = 1.2) ...... 89 B35. Detailed Test Result TS on Minimizing Number of Routes ...... 90 B36. Detailed Test Result TS on RIS ...... 91 B37. Detailed Test Result TS on VRPTW ...... 92 B38. Detailed Test Result TS-VRPSTW - Type b ...... 93 B39. Detailed Test Result ILS with TO-NNB Heuristic and BF for the VRPSTW (toleranceV alue = 1.2) ...... 94

xii List of Figures

1. The Vehicle Routing Problem ...... 5

2. Soft Time Windows [23] ...... 11 3. 2-Opt and Or-Opt [6] ...... 15 4. 2-Opt* and Relocate Operator [6] ...... 16 5. Cross Operator [6] ...... 16 6. Tabu Search Functioning [80] ...... 17 7. Tabu List ...... 18

8. Test Instances C101, R101, RC101 [78] ...... 21

A1. VRPTW - a simple example ...... 56

xiii

List of Algorithms

1. Basic VNS [35] ...... 8 2. Simple Tabu Search Algorithm [28] ...... 9

3. Best Improvement ...... 15

4. Push Forward Insertion Heuristic [75] ...... 22 5. Basic Structure ...... 24 6. CrossTSBestFit ...... 25 7. Minimizing Number of Routes ...... 26 8. Intensiﬁcation of Schulze & Fahle [67] ...... 32

1. Introduction

In a typical logistics network raw materials are transported from suppliers to manu- facturers, where items are produced at one or more factories, shipped to warehouses and distributed to retailers or customers. Due to the continuous movement of the products from one point of the supply chain to another, effective transportation management can play an important role in terms of cost reduction and service improvement. Good transportation management can minimize distribution costs by optimizing routes leading to shorter distances and less penalty for delayed delivery [74, 70]. The Vehicle Routing Problem with Time Windows (VRPTW) is an extension of the classical Vehicle Routing Problem (VRP), reflecting a real-world problem, where the customers may impose delivery deadlines and earliest delivery times [20, 47]. The objective of the VRPTW is to optimally design routes for a homogenous fleet of vehicles to serve a set of customers, where each customer has a given demand and each vehicle a capacity limit. Each customer is visited once and within a given time interval, called a time window [67, 41, 6]. Common real-world applications for the VRPTW include deliveries to supermar- kets, postal deliveries, school bus routing, industrial refuse collection, JIT (just in time) manufacturing or urban newspaper distribution [41, 6]. Because of its wide applicability to real-life situations, the VRPTW has been intensively researched [72, 6, 7, 41]. Heuristic and exact optimization approaches have been the subject of research efforts. To achieve exact solutions, branch-and-bound algorithms and several exact algorithms based on Lagrangian relaxation and column generation were introduced [20]. Recently, Baldacci et al. [2] were able to solve four of the five open instances of the 56 benchmark instances of Solomon [72], involving 100 customers, exactly. Due to high problem complexity and non-polynomial-hardness (NP-hardness), the majority of research has focused on heuristics, where high-quality solutions can be obtained in reasonable computing times [65, 8, 67, 6, 14]. Metaheuristics, especially tabu search (TS), have shown best performances for tackling the VRPTW [5]. TS is a memory-based local search strategy and was not only successfully applied to VRPTW but also to e.g. graph coloring, P-median problems, JIT production, machine or classroom scheduling [34]. Literature has been treating time windows predominantly as hard constraints, where the time window requirements are strictly enforced. However, in practice these hard time windows are often relaxed as vehicle travel times are usually stochastic and not precisely predictable [9, 23]. The vehicle routing problem with soft time

1 Introduction windows (VRPSTW) is a variation of the VRPTW, where time windows may be violated by paying penalties [1, 23]. The purpose of this work is to describe and implement the TS heuristic for the VRPSTW. Along with the implementation experiments of diﬀerent attributes of the TS heuristic are performed and analyzed. To give a brief insight in this topic, a literature review on VRPTW and TS is following.

1.1. Related Work

Garcia et al. [26] were the first to introduce a (parallel) TS heuristic for the VRPTW. The heuristic uses parallelism to divide neighborhoods, where multiple modifications with neighborhood operators are applied to the particular solution. However, the authors reported that TS commits too early to a specific region of the search space, meaning that the heuristic can get trapped very quickly in a local optimum, from which it is difficult to escape. In the paper of Rochat and Taillard [63], the authors presented a probabilistic technique, which allows diversification and intensification to overcome the weakness of local search methods, i.e. to be trapped in local optima. They introduced the concept of adaptive memory, which is a pool of good solutions. New starting solutions for the TS are provided with the selection and combination of routes from the memory, where the selection is done probabilistically. After improving the selected routes, they are inserted back to the memory [7, 12]. Potvin et al. [60] implemented a similar non-parallel TS for the VRPTW. Taillard et al. [73] used the same TS heuristic as Rochat and Taillard [63] for the vehicle routing problem with soft time windows (VRPSTW). To reduce the complexity and intensify the search in specific regions of the search space, each initial solution is partitioned into disjoint subsets of routes, where TS is applied to. With their algorithm, the authors could generate several best-known solutions for the 56 benchmark instances of Solomon [72]. Chiang and Russell [8] developed a reactive TS, which can be described as a dynamic TS mechanism that changes its tabu list size during the search process. If identical solutions occur too often, the tabu list size is increasing and decreasing, if no feasible solution can be found [7]. In a later paper, Chiang and Russell [9] introduced a TS heuristic, where the algorithm makes use of an advanced recovery approach to initiate searches from a pool of elite solutions. Another parallel implementation of the TS heuristic is proposed by Schulze and Fahle [67]. Like, Rochat and Taillard [63], the authors make use of the concept of a pool, where feasible solutions generated with TS are stored. New solutions are constructed on the routes in the pool with the set covering problem. Tan et al. [74] introduced a candidate list, which is a long-term memory approach, storing the best solutions the algorithm has discovered during the search. Cordeau et al. [13] proposed a simple but efficient TS heuristic, which can be applied to the Periodic VRPTW (PVRPTW) or the Multi-Depot VRPTW (MDVRPTW) too.

2 1.1. Related Work

Lau et al. [49] presented the concept of a holding list, which contains unserviced customers and can be described as a ”phantom” route with the function of relocating and exchanging customers. Ho and Haugland [36] presented a simple TS heuristic for the VRPTW and split deliveries (VRPTWSD), where they reported experimental results of the VRPTW too. The authors could show that the VRPTWSD is capable of getting better results regarding distance and number of vehicles than the VRPTW version. In their paper, Fu et al. [23] introduced a unified TS for the VRPSTW. They describe different types of soft time windows and present a unified penalty function. Qi et al. [62] presented a new tabu list design, where the tabu list memorizes intervals and if a solution is in any of the intervals, it is considered tabu. The length of the tabu list could be reduced this way, making the algorithm work fast and effective. Table 1 summarizes the main features of the TS heuristics, where the initial solution and neighborhood operators used are presented, but also whether the proposed approach used a post optimization method, parallelism or strategies to minimize the number of routes. Further, it contains the problem type, where the TS method was applied to. With the only exception of De Backer et al. [18], all methods in Table 1 are stochastic.

Author Initial Solution Neighborhood Operator Post-Opt. Parallel Route min. Type Garcia et al. (1994) Solomon’s I1 heuristic Or-opt, 2-opt* No Yes Yes VRPTW Rochat & Taillard (1995) Insertion heuristic & 2-opt 2-opt, relocate Yes Yes Yes VRPTW Potvin et al. (1996) Solomon’s I1 heuristic Or-opt, 2-opt* No No Yes VRPTW Taillard et al. (1997) Solomon’s I1 heuristic Cross, GENIUS Yes Yes Yes VRPSTW Chiang & Russell (1997) Parallel insertion heuristic λ-interchange No Yes Yes VRPTW Schulze & Fahle (1999) Solomon’s I1, parallel & Ejection chains, Or-opt No Yes Yes VRPTW savings heuristic De Backer et al. (2000) Savings heuristic 2-opt, Or-opt, relocate, No No Yes VRPTW cross, exchange Cordeau et al. (2001) Random insertion heuristic Relocate, GENIUS Yes No Yes VRPTW, PVRPTW, MDVRPTW Tan et al. (2001) PFIH λ-interchange, 2-opt* No No No VRPTW Lau et al. (2003) Insertion heuristic Exchange, relocate No No Yes VRPTW Chiang & Russell (2004) Parallel insertion heuristic λ-interchange, k-opt No Yes Yes VRPTW, VRPSTW Ho & Haugland (2004) Nearest neighbor heuristic Relocate, relocate split, Yes No Yes VRPTW, exchange, 2-opt*, US VRPTWSD Fu et al. (2008) Random insertion heuristic Relocate, exchange, 2-opt No No Yes VRPSTW Qi et al. (2008) Greedy insertion heuristic Swap, 2-opt, relocate, exchange No No Yes VRPTW

Table 1.: Related Work on TS and VRPTW

A hierarchical ordering of the objective function, where the solution quality is measured by e.g. minimizing the number of vehicles and afterwards by the total travel cost is very common for the VRPTW [8, 67, 62]. Authors like Chiang and Russell [9] include in their lexicographic objective function the penalty function for TW too, where minimizing the number of vehicles is denoted by the ﬁrst priority level, total travel distance and schedule time by the second one and the total time window violation penalty by the third priority level. However, some scientiﬁc papers use an alternative way of reducing the number of routes by including route-saving-functions, where customers of small routes are moved into other routes [26, 60, 36]. Furthermore, there are several TS heuristics not designed to minimize the number of vehicles.

3 Introduction

Taillard et al. [73], De Backer et al. [18] and Cordeau et al. [13] use the number of vehicles of the best solution reported in the literature as the number of available vehicles.

1.2. Structure

The remainder of this work is structured the following way. Chapter 2 gives a small introduction into the VRP and its solution methods, focusing on classical and metaheuristics. Chapter 3 concentrates on the VRPTW, especially soft time windows. In addition to the problem description of the VRPSTW, a uniﬁed penalty function for soft time windows is deﬁned. The solution methods used in this work can be found in 3.3, where the Time-Oriented Nearest Neighbor heuristic is presented as an initial solution, followed by neighborhood operators used in the TS algorithm. The computational experiments are described in Chapter 4, where the simulation software is described and used to test the TS algorithm. Furthermore, a performance analysis, where the competitiveness of the TS algorithm is tested on heuristics from the literature, is presented. A conclusion of this work is given in Chapter 5.

4 2. The Vehicle Routing Problem

2.1. Introduction

The Vehicle Routing Problem (VRP) or rather ”The Truck Dispatching Problem” was first introduced by Dantzig and Ramser [17] to optimally route a fleet of gasoline delivery trucks between a bulk terminal and a number of service stations. Building up on that paper several variants of that problem have been introduced and it represents today one of the most studied combinatorial optimization problems [76, 14]. The VRP, as illustrated in Figure 1, can be simply defined as the problem of designing a set of minimum-cost vehicle routes, starting and ending at one or more (central) depots, for a fleet of vehicles that delivers a set of geographically scattered customers [76, 72, 47].

Figure 1.: The Vehicle Routing Problem [56]: the left ﬁgure illustrates an undirected complete graph with customers and a depot. By solving the VRP a set of vehicle routes is generated, where each customer is visited once and where the routes start and end at the depot (right ﬁgure).

The road network, which is used for the transportation of the goods, is illustrated through a graph where the arcs describe road sections and vertices the road junctions (depot and customer locations). Depending on whether the arcs can be traversed in only one (e.g. One-way streets) or both directions, they are directed or undirected [76]. Because of its practical relevance the VRP oﬀers solutions for the delivery and/or collection of goods in diﬀerent real-life applications. Typical real-life characteristics of customers are for instance time windows, in which the customer can be served or unloading and loading times, that are required to deliver or collect goods at the customer. Further real-life constraints concern the capacity of vehicles, maximum duration of driving periods or given working periods during the day. Accordingly, several variants of the problem exist and therefore the VRP is viewed more as a 5 The Vehicle Routing Problem class of problems [47]. The Capacitated Vehicle Routing Problem (CVRP), the most studied variant of the VRP, is described in the following section.

2.2. Problem Deﬁnition

In the CVRP [40], the distribution of goods occurs from a single depot, denoted with 0 to a set of n customers, where N = {1, 2, . . . , n}. Each customer i ∈ N is associated with a non-negative demand di, which has to be satisfied. The fleet of K = {1, 2, . . . , k} identical vehicles of capacity Q > 0 is available at the depot. A vehicle that services a subset of customers starts at the depot, visiting once each of the customers and returns back to the depot, where a vehicle moving from i to j causes a travel cost cij. The CVRP can be defined on a directed or undirected graph. V = {0} ∪ N = {0, 1 . . . , n} is the vertex (node) set and for the depot d0 := 0 is defined. The symmetric CVRP is defined on a complete undirected graph G = (V,E), where E = {e = {i, j} = {j, i} : i, j ∈ V ; i 6= j} is the edge set with edge costs cij for {i, j} ∈ E. If at least one pair of nodes i, j ∈ V has asymmetric costs cij 6= cji, then the underlying graph is considered to be a complete digraph G = (V,A) with arc set A = {(i, j) ∈ V × V : i 6= j} and arc costs cij for {i, j} ∈ A. When considering S ⊆ V being an arbitrary subset of vertices, then for undirected graphs the subset δ (S) = {{i, j} ∈ E : i ∈ S, j∈ / S} is the set of edges with one endpoint in S. For directed graphs G = (V,A), the indegree and outdegree of S are notated with δ− (S) = {(i, j) ∈ A : i∈ / S, j ∈ S} and δ+ (S) = {(i, j) ∈ A : i ∈ S, j∈ / S}, where A (S) = {(i, j) ∈ A : i, j ∈ S} is the set of arcs connecting vertices in S. A route (tour) can be described as a sequence r = (i0, i1, i2, . . . , is, is+1), where i0 = is+1 = 0 and where the set S = {i1, . . . , is} ⊆ N of customers is visited. The Ps cost function of route r is c (r) = p=0 cip,ip+1 and the CVRP is solved when there are |K| feasible routes, one for each vehicle k ∈ K. The solution of the CVRP is feasible if the routes r1, r2, . . . , r|K| and corresponding clusters S1,S2,...,S|K| form a partition of N. The objective of the CVRP is to minimize the total cost, while the demands of all the customers delivered are deterministic and non-divisible. The CVRP generalizes the Traveling Salesman Problem (TSP) and is NP-hard [76, 47]. NP-hardness indicates that it is difficult to solve even small instances of a problem optimally with reasonable computational effort. Hence, when solving real-life problems, one should concentrate on finding an acceptable solution within an acceptable amount of computational time [42].

2.3. Solution Methods

Generally, solution methods for the VRP are divided in exact algorithms and heuristics (classical and metaheuristics). As exact algorithms can only solve instances with approximately 100 vertices and as real-world problems or customers often exceed this 6 2.3. Solution Methods size, most solution methods used in practice are heuristics or rather metaheuristics [47, 14]. Regarding exact algorithms the literature diﬀers mainly between branch- and-bound, set-covering-based and branch-and-cut algorithms.1

2.3.1. Classical Heuristics Classical heuristics were developed mostly between 1960 and 1990 with the idea to quickly obtain feasible solutions [12]. These methods are partially pure constructive, but most of them include improvement procedures as well. They perform only in a relatively limited search area and deliver plausible solutions within modest computing times [48]. According to Laporte and Semet [48] classical VRP heuristics are classified into three categories, constructive heuristics, which build gradually a solution without containing an improvement phase per se. These methods typically start from an empty solution and iteratively build routes by inserting one or more customers at each iteration, until all customers are routed [14] (e.g. the savings algorithm from Clarke and Wright [10]). In two-phase heuristics the problem is divided in two subproblems, clustering and routing. In clustering, the vertices are determined to a route and in routing, the sequence of the vertices within each route is constructed. Hereby, two possibilities arise: cluster-first-route-second, where vertices are first grouped into clusters and the routes are determined considering the clusters (e.g. the sweep algorithm [30] or the Fisher and Jaikumar algorithm [22]). In route-first-cluster-second a giant TSP tour is built including all vertices and divided into feasible vehicle routes afterwards [14, 12]. Improvement methods are used to improve initial solutions generated by other heuristics. They try to upgrade any given solution by applying simple modifications like movement of the vertices or arc exchanges with the aim to gain better neighbor solutions. Improvement methods can be divided in intra-route moves, when operating on each route separately, and inter-route moves, when considering more than one route simultaneously. The λ-opt heuristic of Lin [52] for the TSP is an example for intra-route moves. Here a tour is λ-opt, if it is impossible to obtain a tour with smaller cost by replacing any λ edges by any other ones. When finding an improvement solution, it becomes the current one and the process iterates, else a local minimum is identified [14, 47, 12].

2.3.2. Metaheuristics Metaheuristics are general solution procedures, which explore the solution space to ﬁnd good solutions. Compared to classical heuristics, metaheuristics can allow deteriorating and even infeasible solutions during the search process. They can be seen as improvement methods, where the best ones are quite robust and perform in

1More information can be found in [76].

7 The Vehicle Routing Problem a good way even if initiated from a low-quality solution [27, 14, 47]. They can be divided into three classes.

Local Search Algorithms start from an initial solution x0 and explore the solution space by iteratively moving from a solution xt at iteration t to a solution xt+1 in the neighborhood NB (xt) of xt until a stopping condition is satisfied. If f (x) denotes the cost of x, then f (xt+1) does not necessarily need to be smaller than f (xt). To avoid cycling mechanisms have to be implemented [27, 47]. In local search algorithms the definition of the neighborhood and the mechanism to explore it, play an important role. Typically, local search algorithms perform inter-route moves with intra-route reoptimizations [47]. Classical examples of local search algorithms include Simulated Annealing (SA), Deterministic Annealing (DA), Variable Neighborhood Search (VNS) or Tabu Search (TS) [47]. In SA the current solution xt is modified by randomly selecting a modification defined in the neighborhood NB (xt) at iteration t. The current solution and the newly selected solutions are compared, while improving costs are always accepted. However, with an acceptance probability an increase in solution costs can be obtained too, making an escape from local optima possible. The probability of accepting non-improving costs depends on a temperature parameter [57, 29]. DA operates in a similar way, with the exception that a deterministic rule is used for the acceptance of a move [27]. The basic VNS is presented in Algorithm 1. In the initialization phase a set of neighborhood structures is selected NBk, k = 1, . . . , kmax. In the main step a random solution x0 is generated (shaking step) and local search is applied until local optimum is found x00 . If the solution obtained is better, then x = x00 and the search in the current neighborhood is continued, otherwise the neighborhood is changed [55, 35].

Algorithm 1 Basic VNS [35]

1: BVNS(x, kmax, tmax) 2: t ← 0 3: Search: 4: while t < tmax do 5: k ← 1 6: repeat 0 7: x ← Shake (x, k) {random solution} 00 0 8: x ← BestImprovement x {local search}

00 9: x, k ← NeighborhoodChange x, x , k {change neighborhood}

10: until k = kmax 11: end while 12: return x

TS is another local search metaheuristic, introduced by Glover [31], which allows local search methods to overcome local optima. By allowing non-improving moves and forbidding certain moves, cycling back to previously visited solutions is prevented with the use of short-term memories, tabu lists, which record only a fixed and limited 8 2.3. Solution Methods quantity of information [28, 27, 31].2 A template for a simple TS is illustrated in Algorithm 2, where T denotes the tabu list and x∗ the best-known solution. Termination criterion in the search process can be a fixed amount of CPU time or a fixed number of iterations [28].

Algorithm 2 Simple Tabu Search Algorithm [28] 1: Initialization: ∗ 2: Construct an initial solution x0. Set: x ← x0, x ← x, T ← ∅ 3: Search: 4: while not StoppingCondition () do 5: for x in NB (x) {Determine complete neighborhood of x} do 6: if x not in T & x > x∗ {Choose best non-tabu solution} then 7: x∗ ← x {Switch over to new solution} 8: end if 9: end for 10: Record T 11: if T > Tmax then 12: remove oldest entry 13: end if 14: end while 15: return x

Population Search Algorithms work with several generations of solution popu- lations. An example are genetic algorithms, which operate on a population of encoded solutions (chromosomes). At each iteration of the algorithm, some parent solutions are taken out from the current population (selection phase), randomly modiﬁed (mutation phase) and recombined to create the next generation, which should replace the weakest or worst elements of the population in order to provide improvements. Genetic algorithms applied for the VRP have been in combination with local search, where the oﬀspring were improved through local search algorithms [47, 14, 11, 56].

Learning Mechanisms include neural networks and ant colony optimization. Neural networks are computational models derived from artiﬁcial intelligence and composed of interconnected units through weighted links (e. g. neurons in the brain, where a signal is sent from one unit to another, modulated through the associated weight). They operate on a set of deformable templates illustrated through rings or rather vehicle routes, where a vertex is assigned to a tour through a learning process. Ant colony optimization describes an analogy with ants, which lay pheromones on their paths while foraging for food. The quantity of the pheromones depends on the length of the path and the quality of the food source. With time more pheromones are located on the more frequented paths, illustrating the shortest paths traversed by more ants. Hence edges, which appear frequently in good solutions, are giving more weight in the ant colony optimization algorithm [47, 14, 11].

2TS is described more detailed in later Chapter 3. 9

3. The Vehicle Routing Problem with Time Windows

3.1. Introduction

The Vehicle Routing Problem with Time Windows (VRPTW) is an extension of the CVRP, where the customers may impose delivery deadlines and earliest delivery times [20]. Hence, the service at a customer must start within a given time interval, also called time window. Time windows can be distinguished in soft and hard ones. Whereas, the arrival of vehicles after the latest time to begin service, is not allowed when considering hard time windows, soft time windows allow violations in return for penalty costs [72, 41, 12, 20]. In this work the focus will be on soft time windows. According to Fu et al. [23] there are diﬀerent ways of allowing time window violations, which lead to diﬀerent types of soft time windows as shown in Figure 2.

Figure 2.: Soft Time Windows [23] of Types a to f are presented. The horizontal axes represent time and the vertical axes the penalty cost. The penalty costs are linear depending on the length of the time violation. Outer time window and waiting time may restricted to Pmax and Wmax.

In Type a, if a vehicle arrives at the customer i after bi, a penalty incurs for tardiness. Arriving before ai is allowed but in this case it has to wait until ai and no penalty incurs. Contrary to Type b, where both early and late service at the customer is allowed by paying appropriate penalties. In Type c a maximum allowable violation of the time windows Pmax is deﬁned. The outer time window of customer i can be enlarged to [ai − Pmax, bi + Pmax] and time to start service at customer i must be within the outer time window and preferably within the inner time window [ai, bi]. Furthermore, it is assumed that there is a maximum waiting time Wmax.

11 The Vehicle Routing Problem with Time Windows

Type d is based on Type a, where Pmax deﬁnes the maximum allowable lateness at the customer. Type e is based on Type b, where Pmax describes the maximum allowable violation of the time windows and Type f is based on Type c, without the limitation of the maximum allowable waiting time.

3.2. Problem Deﬁnition

The VRPSTW is defined on the directed graph G (V,A), where the depot is represented by the vertices 0 and n + 1 (source and sink). Given N = {1, 2, . . . , n} represent the set of customers. For vertices 0 and n + 1, zero demands and zero service times are defined, d0 = dn+1 = s0 = sn+1 = 0 and their time windows are associated with [a0, b0] = [an+1, bn+1], where the vehicles have to leave the depot at a0 and return at bn+1 at the latest. The set of arcs is described with A and for each arc (i, j), where i 6= j the distance dij, the cost cij and time ti,j are associated. There are no arcs ending at vertex 0 and originating from n + 1. A homogeneous fleet of vehicles K is also defined, where each vehicle has a capacity Q. Each customer i has a demand of di, which has to be satisfied within a time window of [ai, bi].

k k Two sets of decision variables exist, xij and wi . For each arc (i, j) ∈ A, where k i 6= j, i 6= n + 1, j 6= 0 and each vehicle k ∈ K, xij is deﬁned following ( 1, if vehicle k drives directly from i to j xk = ij 0, otherwise

k wi is deﬁned for each vertex i ∈ V and vehicle k ∈ K and indicates the time at which vehicle k starts servicing i.

If we consider Emax and Lmax in place of Pmax, representing the maximum allowable violation of time windows before ai and after bi, then a unified penalty k function P wi for the different types of soft time windows [23] from Figure 2, can 1 be described the following way, where λ and α are penalty coefficients . ∞ (infeasible) if wk < a − E − W  i i max max  k  λEmax if ai − Emax ≤ wi < ai − Emax   k k  λ ai − wi if ai − Emax ≤ wi < ai k  P wi = k (3.1)  0 if ai ≤ wi ≤ bi   k k  α wi − bi if bi < wi ≤ bi + Lmax   k  ∞ (infeasible) if wi > bi + Lmax

1 Type a: Wmax = ∞, Emax = 0, Lmax = ∞. Type b: Wmax = 0, Emax,Lmax = ∞. Type c: Wmax > 0, Emax < ∞, Lmax < ∞. Type d: Wmax = ∞, Emax = 0, 0 < Lmax < ∞. Type e: Wmax = 0, Emax > 0, Lmax < ∞. Type f: when Wmax = ∞, Emax > 0, Lmax < ∞. VRPTW: Wmax = ∞, Emax,Lmax = 0.

12 3.3. Solution Method

Mathematically formulated as multi-commodity network ﬂow model with time window and capacity constraint, the VRPSTW is illustrated the following way.2   X X k X X k min  xijcij + P wi  (3.2) k∈K (i,j)∈A k∈K i∈V

X X k s. t. xij = 1 ∀i ∈ N (3.3) k∈K j∈δ+(i) X k x0j = 1 ∀k ∈ K (3.4) j∈δ+(0) X k X k xij − xji = 0 ∀j ∈ N, k ∈ K (3.5) i∈δ−(j) i∈δ+(j) X k xi,n+1 = 1 ∀k ∈ K (3.6) i∈δ−(n+1) X X k di xij ≤ Q ∀k ∈ K (3.7) i∈N j∈δ+(i) k k k xij(wi + si + tij − wj ) ≤ 0 ∀ (i, j) ∈ A, k ∈ K (3.8) k ai ≤ wi ∀i ∈ V, k ∈ K (3.9) k xij ∈ {0, 1} ∀ (i, j) ∈ A, k ∈ K (3.10)

In the objective function (3.2) the minimization of the total routing cost is described, followed by a number of constraints (3.3)–(3.10). In (3.3) each customer is visited exactly once. The equations (3.4)–(3.6) illustrate the vehicle flow; (3.4) states that each vehicle has to leave the depot 0; after arriving at a customer, the vehicle has to leave to another stop (3.5); and finally all vehicles end the tour at the depot n+1 (3.6). Constraint (3.7) describes the capacity restriction, as a vehicle can be loaded only up to its capacity. Constraint (3.8) guarantees schedule feasibility and in (3.9) the start of service is only restricted by the earliest start of service at the customer. In (3.10) the binary condition of the decision variable is satisfied.

3.3. Solution Method

3.3.1. Initial Solution Most heuristic search strategies start by ﬁnding an initial solution to further improve it by using local or global optimization techniques. To generate an initial solution for the VRPSTW the Time-Oriented Nearest Neighbor (TO-NNB) heuristic of Solomon [72] is introduced here.

2The Problem Deﬁnition of the VRPTW and a small example are presented in Appendix A.1.

13 The Vehicle Routing Problem with Time Windows

The TO-NNB heuristic is a sequential, tour-building algorithm and starts every route by ﬁnding the ”nearest” unvisited customer to the depot. At every following iteration the heuristic searches for the next unrouted customer which is ”nearest” to its predecessor. Without violating the feasibility, this search is performed for all the customers, that can be added to the end of the emerging route. A new route starts when the feasibility is not given, unless there are no more unvisited customers. The feasibility of adding an unrouted customer is veriﬁed with respect to time windows, vehicle arrival time at the depot and capacity constraints. If we consider a route, where i is the last customer and j an unrouted customer, that could be visited next, then ncij denotes the cost from i to j. The cost function ncij measures the ”nearest” customer in the following way.

Tij =aj − (ai + si) (3.11)

vij =bj − (ai + si + tij) (3.12)

ncij =δ1dij + δ2Tij + δ3vij, where δ1 + δ2 + δ3 = 1, δ1 ≥ 0, δ2 ≥ 0, δ3 ≥ 0 (3.13)

Equation (3.11) calculates the time diﬀerence between the realization of service at i and the beginning of service at j. In (3.12) the urgency of delivery to customer j is described. Finally in (3.13) the cost function regarding the calculation of the nearest neighbor is deﬁned, where dij measures the direct distance between the two customers.

3.3.2. Neighborhood Operators Neighborhood operators can be described as classical local search methods, based on the idea of iteratively improving the solution to a problem by exploring neighboring ones [6]. As already described,3 neighboring solutions are created by changing one attribute (e.g. arcs) or a combination of attributes of a given solution. A better neighboring solution replaces the current solution and the search continues with the ”new” current solution. Regarding acceptance strategy, the first improvement (first fit) and best improvement (best fit) are known. First improvement selects the first neighbor that satisfied the acceptance criterion. Best improvement, as illustrated in the following algorithm (Algorithm 3), explores the whole neighborhood and selects the best solution among it. Iterative improvement methods applied to vehicle routing problems are mostly edge-exchange algorithms. The concept of edge-exchange neighborhoods is based on the replacement of k edges within a route (intra-route) or between routes (inter- route). A tour is k-optimal when it is not possible to improve it by a k-exchange. k-optimality requires O nk computation time [6]. Figure 3a and 3b illustrate the 2-exchange (2-opt) and Or-exchange (Or-opt) operator. The depots are figured as squares and the customers as circles.

3See Chapter 2, Improvement Methods.

14 3.3. Solution Method

Algorithm 3 Best Improvement 1: Initialization: ∗ 2: Construct an initial solution x0. Set: x ← x0, x ← x 3: Search: 4: while not local optimum do 5: Determine complete neighborhood of x in NB (x∗) 6: if f (x) > f (x∗) then 7: x←x∗ 8: end if 9: end while 10: return x∗

(a) 2-Opt (b) Or-Opt

Figure 3.: 2-Opt and Or-Opt [6]: Figure (a) illustrates the 2-opt, where 2 edges are removed and inserted elsewhere in the route. Figure (b) illustrates the Or-opt, where a subpath is relocated by replacing 3 edges in the same route.

In 2-opt (intra-route) the tour is improved iteratively by replacing two of its edges (i, i + 1) and (j, j + 1) by two other edges (i, j) and (i + 1, j + 1), reversing the orientation of the path [65, 6, 20]. An improvement is given, when the (sub-) travel cost of the new route is smaller [65] 4:

ci,i+1 + cj,j+1 > ci,j + ci+1,j+1 (3.14) In Or-opt (intra-route) a subpath (i, i + 1) is relocated to a diﬀerent position in a route. Here, three edges are replaced in the original tour by three new ones, where the orientation of the route is preserved. In Figure 3b arcs (i − 1, i), (i + 1, i + 2) and (j, j + 1) are removed and replaced by (i − 1, i + 2) , (j, i) and (i + 1, j + 1) [6, 20]. The Or-opt exchanges are a subset of 3-opt exchanges, which consider only those 3-interchanges that would result in a sequence of one, two or three consecutive vertices, inserted between two other vertices. Or-opt is O n2 complex [58, 65].

In 2-opt* (inter-route), the edges (i, i + 1) and (j, j + 1), from diﬀerent routes, are removed and replaced by (i, j + 1) and (j, i + 1). The 2-opt* is similar to the 2-opt, but in this case two routes are modiﬁed instead of one and opposed to the 2-opt the orientation of the routes is preserved [6, 20, 61].

4 In the case of symmetric costs (cij = cji for all (i, j) ∈ A).

15 The Vehicle Routing Problem with Time Windows

The relocate operator (inter-route) moves a vertex from one route to another by replacing the edges (i − 1, i) , (i, i + 1) and (j, j + 1) by (i − 1, i + 1) , (j, i) and (i, j + 1). Here vertex i is placed from the original route to another one [6]. The 2-opt* and relocate operators are illustrated in Figures 4a and 4b. In the cross operator (inter-route) two subpaths are selected and exchanged. In Figure 5 two edges are removed from the ﬁrst tour, (i − 1, i) , (k, k + 1) and two edges are removed from the second tour (j − 1, j) , l, l + 1 and the segments i − k and j − l, which can contain an arbitrary number of customers, are swapped. [6, 73].

(a) 2-Opt* (b) Relocate Operator

Figure 4.: 2-Opt* and Relocate Operator [6]: Figure (a) illustrates the 2-opt*, where two edges from two diﬀerent routes are removed and inserted elsewhere in the routes. Figure (b) illustrates the relocate operator, where a vertex is moved from one route to another.

Figure 5.: Cross Operator [6]: two subpaths from two diﬀerent routes are exchanged.

3.3.3. Tabu Search TS is a memory-based search algorithm, guiding the local search method to continue its search beyond local optimum [74]. TS explores the solution space by moving at each iteration from the current solution x to the best solution in a subset of its neighborhood NB (x), where the current solution may deteriorate from one iteration to the next [7]. Poorer solutions are accepted with the idea to escape local optima and to explore a larger fraction of the search space. To prevent cycling, solutions with speciﬁc attributes of recently explored solutions are temporarily declared tabu and stored in the tabu list. The duration an attribute remains tabu is called tabu tenure (TT) [7, 60]. The tabu restriction can be overridden, if a tabu solution is better than any previously seen solution (aspiration criterion) [7].

Basic Tabu Search Cross or other neighborhood operators can be used to construct diﬀerent neighborhood solutions, identifying moves that lead from one solution to the next. With each

16 3.3. Solution Method exchange a move value is associated, which represents the change on the objective function value and is used to evaluate the quality of a move. To prevent the search from repeating exchange combinations, the most recent moves are declared tabu [46]. Figure 6 illustrates the general functioning of TS, where different moves of a neighborhood generator lead to different neighborhood solutions. The best solution, if not in the tabu list, is selected, defined as new solution and set tabu.

Figure 6.: Tabu Search Functioning [80]: given an old solution, a neighborhood generator is used, where different moves are generated leading to different neighbor solutions. The best neighboring solution is selected, if not in the tabu list and defined as new solution. The move is set tabu and the search starts from the new solution.

If we consider Route 1= [0,1,2,0] and Route 2=[0,3,4,0] as current or old solution, then Table 2 illustrates neighboring solutions generated with the cross exchange.

Neighbor Curr.Sol. Edge Index Edge Remov. Edge Added New Sol. 1 [0,1,2,0] 1, 2 [0,1][1,2] [0,3][3,2] [0,3,2,0] [0,3,4,0] 1, 2 [0,3][3,4] [0,1][1,4] [0,1,4,0] 2 [0,1,2,0] 1, 2 [0,1][1,2] [0,3][4,2] [0,3,4,2,0] [0,3,4,0] 1, 3 [0,3][4,0] [0,1][1,0] [0,1,0] 3 [0,1,2,0] 1, 3 [0,1][2,0] [0,3][3,0] [0,3,0] [0,3,4,0] 1, 2 [0,3][3,4] [0,1][2,4] [0,1,2,4,0] . . .

Table 2.: Cross Exchange

Tabu List The tabu list is a short-term (recency-based) memory for cycle-prevention, holding a limited amount of information. Its function is not to prevent a move being repeated, but from being reversed [31]. The tabu list only records the modification steps (moves) which have been recently applied. The idea is to store the reverse of the respective move and not whole solutions as this would involve huge amounts of 17 The Vehicle Routing Problem with Time Windows data, which is computationally inefficient [80]. Different types of move attributes for defining tabu restrictions are possible [46], e.g. Zäpfelet al. [80] simply set the removed edges tabu (without any route consideration). Contrary to Chiang and Russell [8] or Cordeau et al. [13], who define for each solution x ∈ X an attribute set B (x) = {(i, k) : customer i is visited by vehicle k}. In this way TABU(i, k) records the tabu status of customer i in route k. When considering the mentioned cross-example in Table 2, where customer 1 of route 1 was exchanged with customer 3 of route 2 (Neighbor 1) and assuming that this solution was the best one in the neighborhood, then the matrix of Figure 7 illustrates the tabu definition of Chiang and Russell [8], where the switch of customer 1 from route 1 to route 2 is recorded TABU (1,1). Therefore, customer 1 cannot switch back to route 1 for the next TT iterations. The same is true for customer 3, here TABU (3,2).

Figure 7.: Tabu List: customer 1 in route 1 and customer 3 in route 2 are set TABU for the next TT iterations.

Diversiﬁcation and Intensiﬁcation

As short-term memory can often be insufficient to produce high quality solutions, long- term (frequency-based) memory is used to complement the short-term memory and to achieve regional intensification and global diversification of the search [32, 33, 34, 74]. According to Glover and Laguna [33, 34] intensification and diversification strategies depict two highly important components of TS. Diversification strategies encourage the search process to explore unvisited regions, while intensification focuses more deeply in regions that have generated effective solutions [63, 8, 33, 34]. Schulze and Fahle [67] use an intensification technique to enforce the search in the region around the current solution by minimizing the vehicle fleet (routes containing up to three customers are moved into other routes) and applying a modified Or-opt heuristic, which allows the insertion of customers in the same route (intra-route exchange) and in other routes (inter-route exchange). Tan et al. [74] also use a

18 3.3. Solution Method neighborhood operator, 2-opt (best fit strategy), to intensify and Taillard et al. [73] intensify the search by reordering the customers within the best routes with Solomon’s I1 insertion heuristic [72]. The intensification strategy Chiang and Russell [8, 9] implemented is designed to reduce the waiting time of the customers. If the waiting time of a customer is eliminated after a switch, then intensification is done by keeping this move INTENS(i, k) for a specific number of iterations. Regarding diversification authors like Chiang and Russell [8, 9], Taillard et al. [73], Schulze and Fahle [67], Cordeau et al. [13] or Cordeau and Maischberger [15] make use of a frequency-based penalty, which is added to the objective function to penalize frequently switched customers.5 The diversification strategy introduced here is derived from these papers and is formulated the following way: X p(x0) = µ fr(i,k) (3.15) (i,k)∈B(x0)

Let fr(i,k) denote the number of insertions of customer i in route k and let µ be a value randomly chosen between [0,0.5], then any solution x0 ∈ N (x) is penalized by p(x0).

5This thesis also makes use of a frequency-based penalty. The ﬁctive penalty is however added to the evaluation value and not the objective value.

4. Computational Experiments

4.1. Test Instances

A common way in the literature to compare heuristics related to the VRPTW are Solomon’s 56 benchmark problems [72, 6]. These problems include 100 customers generated within a 100 × 100 square area, where the x and y coordinates of the customers is known. They further include a central depot, capacity constraints, number of available vehicles, time windows and service times. Six diﬀerent sets are deﬁned, i.e. C1, C2, R1, R2, RC1 and RC2; each one containing between 8 and 12 instances. As you can see from the examples in Figure 8 in C1 and C2 the customers are placed in clusters and in R1 and R2 the geographical data of the customers is randomly generated. The RC1 and RC2 test-sets contain a mix of both random and clustered customers.

Figure 8.: Test Instances C101, R101, RC101 [78]: the ﬁgures show the customer positions of the ﬁrst problems (C101, R101, RC101) of the respective problem sets C1, R1 and RC1. The depots are presented with blue dots.

The problem sets of type 1 (R1, C1, RC1) have a short scheduling horizon, which allows only a few customers to be serviced by the same vehicle. Contrary to type 1, the sets of type 2 have a long scheduling horizon, coupled with large vehicle capacities, where routes with more than 30 customers are feasible.

21 Computational Experiments

4.2. HeuristicLab Experiment

HeuristicLab (HL) [78] is a software environment for heuristic and evolutionary algorithms and is developed by members of the Heuristic and Evolutionary Algorithms Laboratory (HEAL) since 2002. In addition to a user-friendly graphical interface and extensibility on the basis of plugins, HL oﬀers several well-known (meta-)heuristics and optimization problems. Because of these reasons, HL was chosen for a ﬁrst approach to solve the VRPSTW with a TS heuristic. The initial solution for the HL-experiment was generated with the Push Forward Insertion Heuristic (PFIH) [75] with the parameters α = 0.7, αVariance = 0.5, β = 0.1, βVariance = 0.07, γ = 0.2, γVariance = 0.14. The PFIH creates routes sequentially, using a two-step process at every iteration to insert a new customer u into the current route. The algorithm can be described the following way (Algorithm 4).

Algorithm 4 Push Forward Insertion Heuristic [75] 1: Construct an empty route. Set r = 1 2: Insert a seed customer 3: for all unrouted customers u do 4: for all edges i, j in the current route do 5: Compute the cost of inserting each of the unrouted customers between i and j. 6: end for 7: Select the best customer u∗ at edge i(u∗), j(u∗) 8: if insertion of u∗ between i(u∗) and j(u∗) is feasible then 9: Insert u∗ between i(u∗) and j(u∗) and update the capacity of r 10: else 11: Begin a new route from the depot. Set r = r + 1 12: end if 13: end for 14: return PFIH solution

To generate the neighborhood of the solutions, the ”MultiVRPMoveGenerator” was chosen, which randomly selects and applies its move generators (neighborhood operators). The list of move generators includes relocation, exchange, rearrange, shift and 2-Opt* operators.1 The rearrange operator rearranges customers within the same route to the best positions to minimize the value of the objective function and the shift operator moves customers from one route to another [51]. The neighborhood size was restricted to 100 and the best neighbor among these was chosen. The TT was set to 10 and after 1000 iterations the algorithm stopped. The ”Tardiness Penalty” was set to 100 as we deal with soft time windows (of Type a).

1For the problem set R1 the exchange operator was deactivated, because of an error.

22 4.3. Simulation Software

Following the results from the HL experiment compared to optimal solutions2 found in literature [41, 2], are presented. To get average solutions, the algorithm was tested for 10 runs. The experiment was performed with the HL Software on an Intel(R) Core(TM) i5-4200U CPU (1.60 GHz).

Table 3.: Results HL-experiment for the VRPSTW

Best Solution HL Avg. Solution HL Optimal Solution Best Gap

Problem NV Cost Time NV Cost Time NV Cost

C1-Avg. 10.44 870.04 22.41 10.62 908.90 27.27 10.00 826.70 5.24% R1-Avg. 14.08 1229.62 28.74 14.38 1259.67 30.68 13.25 1173.61 4.77% RC1-Avg. 13.75 1427.39 22.97 14.15 1460.22 27.34 12.63 1334.49 6.96%

C2-Avg. 3.25 597.02 20.90 3.69 617.04 23.46 3.00 587.38 1.64% R2-Avg. 4.91 922.37 14.20 4.62 956.23 23.03 5.27 872.53 5.71% RC2-Avg. 5.63 1056.39 21.12 5.50 1096.60 23.28 6.25 1000.73 5.56%

Table 3 illustrates the average results3 of the six problem sets of Solomon’s benchmark instances [72], where the number of vehicles (NV), costs (objective value) and time (CPU time in seconds) are given for the best and average HL solutions. Furthermore, the average optimal solutions and best gaps are presented. As illustrated in Table 3, problem set C2 shows the lowest best gap, in 5 of 8 instances the best gap reported is under 1 percent (see Appendix-Table B6). The best gap describes the gap in percent from the costs of the best solutions with HL, compared to the costs of the optimal solutions. Further, problem sets R2 and RC2 show lower NV than the average results of the optimal solution. Because of the limitation of the neighborhood the running time of HL is about one hour. The problem sets with short scheduling horizon (C1, R1, RC1) tend to require more calculating time than the problem sets with long scheduling horizon (C2, R2, RC2).

4.3. Simulation Software

Beside the HL experiment, algorithms like iterated local search (ILS) and TS were implemented in C++ and tested on Solomon’s benchmark instances [72]. All algorithms were tested within a basic structure, which is shown in Algorithm 5. After calculating an initial solution, the algorithm randomly chooses an intra-route and an inter-route operator. If no other initial solution is mentioned, then the initial solution is performed with the TO-NNB heuristic. Termination criterion can be if a specific threshold is not exceeded, e.g. if the best cost minus the current cost is not exceeding a specific value, or if a specific number of iterations (or counter level) is reached.

2The exact methods use a speciﬁc rounding criterion, which was not applied on the experiments in this work. Thus, the results diﬀer in small amount (e.g. C101 in Table B6). 3Detailed results of the experiment can be found in Table B6.

23 Computational Experiments

4.3.1. The Iterated Local Search Algorithm

ILS is a simple metaheuristic, where the search behavior is characterized by iteratively building a sequence of solutions. ILS can be deﬁned as follows: starting from an initial solution x0, the algorithm applies local search to obtain an improved solution x0 . Iteratively, solution x0 is perturbed to gain a new solution x00 , which is again improved with local search to obtain a solution x∗. If x∗ satisﬁes an acceptance criterion, then x0 is replaced by x∗ and the next perturbation is applied, otherwise the search returns to x0 . According to Lourcen¸coet al. [53] the algorithm is very malleable and many implementation choices are being left to the developer. The

Algorithm 5 Basic Structure 1: Step 0: Initialization 2: Read Parameters 3: Step 1: Local Search 4: while run < maxRun do 5: Calculate Initial Solution 6: Evaluate Solution 7: Set: currCost ← evalV alue, bestCost ← currCost, T ← ∅, iter = 0 8: repeat 9: bestCost = currCost 10: switch (Random - Intra-Route Operator) 11: case 1: Or-Opt 12: case 2: 2-Opt 13: end switch 14: Evaluate Solution and set: currCost ← evalV alue, T ← ∅ 15: switch (Random - Inter-Route Operator) 16: case 1: Cross 17: case 2: Relocate 18: case 3: 2-Opt* 19: end switch 20: Evaluate Solution and set: currCost ← evalV alue 21: iter++ 22: until bestCost − currCost < threshold or iter > maxIterations 23: run++ 24: end while 25: return bestCost

ILS algorithm, tested in this thesis, makes use of the basis structure of Algorithm 5, where tests are made on (random) initial solution, time windows (hard and soft) and acceptance strategy (first fit and best fit). The intra and inter-route operator functions are modified depending on acceptance strategy. The aim of these tests is to find out, which acceptance strategy performs best in combination with the initial solution and time window. In the further analysis, the aim is to find out if ILS performs better than TS. 24 4.3. Simulation Software

4.3.2. The Tabu Search Algorithm The TS algorithm is also based on Algorithm 5 including different functions. As mentioned before the neighborhood operators are modified regarding their acceptance strategy and for the TS algorithm the operators also include TS functions. An example of a modified neighborhood operator is presented in Algorithm 6. The CrossTSBestFit algorithm is, as the name says, a cross operator with TS functions with the acceptance strategy best fit (best improvement). As cross is an inter-route operator, one needs to pass two routes to the function (in Algorithm 6 described with R1 and R2). In the TS algorithm the cross operator is applied on R1 and R2, where help routes HR1 and HR2 are generated. In the next step, frequently exchanged customers are penalized and good solutions intensified, as described Subsection 3.3.3, with the idea to diversify and intensify the search. The best non-TABU and non- INTENS solution in the neighborhood is memorized until the complete neighborhood is determined. If the neighborhood solution is better than the best found so far, then a new best solution is taken and the moved customers are set tabu. The tabu list is decremented and improvement is recorded, so the loop starts from the beginning again by crossing customers from R1 and R2 until no more improvement is possible.

Algorithm 6 CrossTSBestFit 1: Initialization 2: Evaluate routes {e.g.R1, R2} 3: Set: bestCost ← evalV alue, currCost ← bestCost, bestNeighbor ← bestCost 4: Step 1: Local Search 5: Tabu Search 6: while improvement do 7: for x in NB (x) {Determine complete neighborhood of x} do 8: Cross customers of routes {R1 and R2} 9: Evaluate help routes {HR1, HR2} and set: currCost ← evalV alue 10: Diversify the search 11: Intensify the search 12: if Moved customers are not T ABU & not INTENS & bestNeighbor − currCost > 0 then 13: Set: bestNeighbor ← currCost, HR1NB ← HR1, HR2NB ← HR2 14: end if 15: end for 16: if bestCost − bestNeighbor > 0 then 17: Set: bestCost ← bestNeighbor, R1 ← HR1NB, R2 ← HR2NB 18: Set: Moved customers = TABU 19: Decrement Tabu List 20: end if 21: end while 22: return bestCost

25 Computational Experiments

4.3.3. Infeasible Solutions Infeasible solutions occur when capacity, route duration or time window constraints are relaxed. The TS (also ILS) algorithm allows infeasible solutions, which are penalized in the objective function. Similar to Cordeau et al. [13], Cordeau and Maischberger [15] or Kritzinger et al. [45] this thesis makes use of the augmented objective function, which consists of:

f (x) = obj (x) + βq (x) + γd (x) (4.1) where obj (x) describes the objective function of Equation 3.2 and q (x), d (x) denote the violation of capacity and duration, multiplied by non-negative penalty parameters β and γ.

4.3.4. Minimizing the Number of Routes As mentioned in the beginning of this work, different authors use different strategies to minimize the number of routes. In this algorithm, a destroy and repair operator is used (Algorithm 7), where routes (with the route size up to 20)4 are destroyed and the customers are inserted in random routes on random positions.5 Subsequently, local search methods (CrossFF, OrOptFF, RelocateFF, OrOptFF) are applied. If a better solution is found or a solution, which does not exceed a specific tolerance value, then the solution is accepted and the counter is set 0. The algorithm accepts non-improving solutions to minimize number of routes.

Algorithm 7 Minimizing Number of Routes 1: while counter ≥ 5 and counter ≤ counterLimit do 2: Destroy small routes 3: Insert customers in random routes on random positions 4: Local search 5: if better solution found then 6: set: counter = 0 7: else if solution < toleranceV alue * bestEval then 8: set: counter = 0 9: else 10: counter + + 11: end if 12: end while

4The value of 20 is chosen based on an analysis of the initial solutions with TO-NNB heuristic with the idea to ﬁnd the smallest route with the most customers. 5The destroy and repair operator is called when the bestCost has not changed for 5 iterations. This is measured with counter. 26 4.4. Computational Test Results

4.4. Computational Test Results

This section includes a number of tests on the ILS and TS algorithm with the purpose to find out what the determinants for a good solution are. During the tests, parameters and methods are analyzed. The following Table 4 defines parameters are defined, used in the algorithms. All tests were performed on an Intel(R) Core(TM) i5-4200U CPU (1.60 GHz) and over 10 runs.

Table 4.: Overview Parameters Parameter Explanation 6 δ1 = 0.2, δ2 = 0.7, δ3 = 0.1 Parameter for the TO-NNB heuristic threshold = 0.0001 Threshold as termination criterion α = 1, 000, 000 Penalty parameter for hard TW α = 100 Penalty parameter for soft TW β = γ = 100,000 Penalty parameters for duration and load violation maxIterations = 50, 000 Maximal number of iterations counterLimit = 20 Counting parameter toleranceV alue = 1.1 Tolerance parameter to minimize number of routes

4.4.1. Tests on Iterated Local Search During the tests on ILS, the acceptance strategy was tested on different initial solutions and time window combinations. The tests include the destroy operator described in Algorithm 7. Apart from these tests, Tables B1-B5 include tests on ILS without the destroy operator, compared to the optimal solution [41, 2] on VRPTW. The ILS algorithm terminates when the threshold cannot be exceeded, and when the maximum number of iterations or the counting limit is reached. The Tables 5 to 8 illustrate the average best results of Solomon’s benchmark problem sets. The first tests are made on hard time windows (HTW), where the acceptance strategies are tested on the TO-NNB heuristic and random generated initial solutions. The same tests are performed on soft time windows (STW) too. The tables include the results of the first fit (FF) and best fit (BF) strategy of the respective tests. For comparison reasons the tables further contain best known solutions on the VRPTW from the literature [71] and the average best gaps calculated with both acceptance strategies. The results reported as best known solutions have a hierarchical objective function, where the number of vehicles is minimized first and the total distances (here cost) as second. In the tests on ILS the objective function described in Equation 4.1 was used. The ILS results were sorted by the minimum number of vehicles first and the objective function second. The detailed results of the tests are attached in the appendix (B7-B14).

6Parameters taken from [21].

27 Computational Experiments

Test on Hard Time Windows

Table 5 illustrates the average results of the ILS algorithm, calculated with the TO- NNB heuristic and HTW on the acceptance strategy FF and BF. The BF acceptance strategy outperforms only in two of six problem sets, C1 and C2. Furthermore, compared to the FF strategy, BF results in higher cumulative number of vehicles (CNV) and cumulative total cost (CTC) as shown in Table 9. Taking the Tables B7 and B8 from the appendix into consideration, then it can be seen that the majority of the problems in the problem sets C1 and C2 do not diﬀer from the best known solutions. For some problems in R1, RC1, R2 and RC2 even negative best gaps are calculated, which may be explained by the NV used. Considering the problem R103 in Table B7 then it is apparent that R103 results in a best gap of -3.74%. However, it is also apparent that the NV for R103 is one greater than the NV of the best known solution. As most heuristics resulted in the best known solutions [71] have an objective function, where the NV is minimized ﬁrst, the best known solutions tend to have lower NV. As HTW are considered, Tables B7 and B8 show no violations of TW or load and length constraints.

Table 5.: Test on Acceptance Strategy with HTW and TO-NNB Heuristic

Best Solutions ILS-FF Best Solutions ILS-BF Best Known Sol. Best Gap Best Gap

Problem NV Cost Time NV Cost Time NV Cost ILS-FF ILS-BF

C1-Avg. 10.00 863.75 4.78 10.00 852.11 5.22 10.00 828.38 4.28% 2.87% R1-Avg. 12.83 1254.90 6.08 13.00 1247.47 3.83 11.92 1210.34 3.86% 3.25% RC1-Avg. 12.88 1412.70 2.38 12.88 1429.88 2.63 11.50 1384.16 2.51% 3.58%

C2-Avg. 3.00 597.00 78.88 3.00 592.92 46.50 3.00 589.86 1.21% 0.52% R2-Avg. 3.09 996.72 51.55 3.00 1010.72 111.09 2.73 951.03 4.86% 6.69% RC2-Avg. 3.38 1194.12 46.88 3.38 1199.55 58.63 3.25 1119.24 7.39% 7.67%

According to Lourcen¸coet al. [53] improvements in cost can be achieved by random restarting the search, as every solution generated is independent and with the use of multiple trials, low cost search areas can be reached. For this reason random initial solutions (RIS) are generated by sequentially ﬁlling empty routes with randomly chosen customers, where the number of available vehicles is set to the number of vehicles calculated with the TO-NNB heuristic. The average results of the tests on the ILS with HTW and both acceptance strategies, where the initial solution is generated randomly is represented in Table 6.

Table 6.: Test on Acceptance Strategy with HTW and RIS

Best Solutions ILS-FF Best Solutions ILS-BF Optimal Solution Best Gap Best Gap

Problem NV Cost Time NV Cost Time NV Cost ILS-FF ILS-BF

C1-Avg. 10.00 842.86 4.67 10.00 855.57 5.89 10.00 828.38 1.75% 3.29% R1-Avg. 12.83 1239.01 8.00 12.83 1237.98 4.75 11.92 1210.34 2.53% 2.41% RC1-Avg. 13.00 1424.03 6.13 12.75 1420.59 6.63 11.50 1384.16 3.31% 3.11%

C2-Avg. 3.00 596.49 56.75 3.00 594.94 65.13 3.00 589.86 1.12% 0.86% R2-Avg. 3.09 1004.28 121.18 3.00 1009.74 102.64 2.73 951.03 5.75% 6.09% RC2-Avg. 3.38 1202.19 77.38 3.38 1212.18 74.88 3.25 1119.24 7.94% 8.92%

28 4.4. Computational Test Results

Comparing the average best gaps of FF and BF then Table 6 shows that BF performs for the tests on HTW with RIS, in three of six problem sets better than the FF strategy. Furthermore, a comparison of the average NV in problem sets C1, R1, C2 and RC2 show the same value for both acceptance strategies. However, taking Table 9 into account, then the results of the BF strategy are regarding CNV lower than the results with the FF strategy. Considering Tables B9 and B10 then the average solutions for the problems tend to be quite high, which is associated with the allowance of infeasible solutions. Even though the search starts from an infeasible solution, it always results in a feasible one as shown in the best solutions of the Tables B9 and B10.

Tests on Soft Time Windows Tables 7 and 8 represent the tests on STW, where both the initial solutions and acceptance strategies are tested again. Considering Table 7, where the tests are performed on the TO-NNB heuristic, it can be seen that the average best gaps of the FF strategy result in ﬁve of six problem sets better than the BF strategy. Further considering the average NV, then the results in Table 7 show that the BF strategy achieves better solutions. Table 9 even shows that the TO-NNB heuristic results of the BF strategy could reach CNV of 427, which is the lowest CNV along the tests on ILS. Looking at the detailed results of Table 7 in the Tables B11 and B12, then it can be seen that small violations of TW took place in the problem sets R1, RC1, R2 and RC2 related to the FF strategy and TW violations of R1 and RC1 related to the BF strategy. As the penalty parameter for STW violations is α =100 (compared to α = 1,000,000 for HTW), it can be assumed that it is more likely that TW are violated.

Table 7.: Test on Acceptance Strategy with STW and TO-NBB Heuristic

Best Solutions ILS-FF Best Solutions ILS-BF Best Known Sol. Best Gap Best Gap

Problem NV Cost Time NV Cost Time NV Cost ILS-FF ILS-BF

C1-Avg. 10.00 838.86 6.11 10.00 842.86 5.33 10.00 828.38 1.27% 1.75% R1-Avg. 12.92 1250.14 3.58 12.67 1265.92 5.75 11.92 1210.34 3.47% 4.97% RC1-Avg. 12.75 1435.81 5.13 12.63 1480.85 4.00 11.50 1384.16 4.18% 7.43%

C2-Avg. 3.00 596.46 72.25 3.00 597.21 49.25 3.00 589.86 1.12% 1.25% R2-Avg. 3.00 1000.19 77.73 3.00 1012.59 68.73 2.73 951.03 5.04% 6.25% RC2-Avg. 3.38 1217.63 71.63 3.38 1200.38 53.38 3.25 1119.24 9.75% 7.85%

Table 8.: Test on Acceptance Strategy with STW and RIS

Best Solutions ILS-FF Best Solutions ILS-BF Best Known Sol. Best Gap Best Gap

Problem NV Cost Time NV Cost Time NV Cost ILS-FF ILS-BF

C1-Avg. 10.00 853.76 7.89 10.00 852.78 8.44 10.00 828.38 3.07% 2.95% R1-Avg. 12.67 1258.44 4.50 12.92 1235.75 5.33 11.92 1210.34 4.13% 2.14% RC1-Avg. 12.50 1440.26 8.88 12.75 1419.06 3.88 11.50 1384.16 4.39% 2.85%

C2-Avg. 3.00 594.57 64.38 3.00 594.29 105.75 3.00 589.86 0.80% 0.75% R2-Avg. 3.18 984.42 71.64 3.00 999.74 80.73 2.73 951.03 3.56% 4.98% RC2-Avg. 3.50 1193.23 65.00 3.38 1208.61 60.38 3.25 1119.24 7.58% 8.56%

29 Computational Experiments

Considering Table 8 regarding the results of RIS, then a comparison of the average best gaps shows that the BF strategy performs in 4 of 6 problem sets better than the FF strategy. Good solutions could be achieved in the problem set C2 for both acceptance strategies. The Tables B9 and B10 show no gaps in 6 of 8 problem instances of problem set C2. Violation of TW occurred in the test on the FF strategy for problems R102, R106 and RC102. Compared to the BF strategy, where only one TW violation occurred for R101.

Table 9.: Overview Tests on ILS TW Initial Sol. Accep. Str. CNV CTC Hard TO-NNB First Fit 432.00 59,426.99 Hard TO-NNB Best Fit 433.00 59,535.36 Hard RIS First Fit 433.00 59,282.71 Hard RIS Best Fit 430.00 59,484.78 Soft TO-NNB First Fit 431.00 59,552.56 Soft TO-NNB Best Fit 427.00 60,142.81 Soft RIS First Fit 429.00 59,438.26 Soft RIS Best Fit 431.00 59,276.90 Best Known Solution 405.00 57,186.86

Taking all the tests made on ILS into consideration, then it is apparent that the test on STW with TO-NNB heuristic and the BF acceptance strategy performed best, with a CNV of 427 and CTC of 60,142.81 (Table 9). Generally, it can be stated that the tests on STW result in lower CNV, with an exception on the test with RIS and BF strategy. Considering the computational time of the tests, then the CPU times of the best solutions on FF are lower than for the BF strategy. Implementing RIS on the two diﬀerent TW and acceptance strategies, could improve the CTC for each of the respective tests, e.g. when considering the results generated with HTW and FF strategy, then it can be seen that the CTC for RIS is lower than the result generated with TO-NNB heuristic. However, only cost improvements could be reached with the implementation of RIS but the NV could not be minimized in every case. Comparing the test results of initial solutions, then the statement of Lourcen¸coet al. [53] on RIS applies here only for the BF strategy with HTW and FF strategy with STW. Lower CNV and CTC could be reached here with RIS compared to the TO-NNB heuristic illustrated in Table 9. Comparing the results of the diﬀerent TW, then it can be stated that STW tend to result in lower CNV. An exception is given for the tests on RIS and BF, where the CNV results in one more vehicle than the HTW.

4.4.2. Tests on Tabu Search In this section tests on TS are performed, where methods presented in former sections (see 3.3.3) are implemented successively. The tests start by ﬁnding a cost eﬀective

30 4.4. Computational Test Results

TT to be used in further tests. Based on this results, tests on intensification and diversification are performed. For comparison reasons, tests on minimizing the NV are implemented. Furthermore, tests on the initial solution and time windows are realized, where different types of soft TW are tested.

Tests on Tabu Tenure

TT is the number of iterations a customer is kept tabu-active [33]. Accordingly, the ﬁrst tests on TS, have the aim to ﬁgure out which TT performs best within the TS algorithm. The tests were made on TT=1 to TT=12 and on random generated TT with TT=[1,10] and TT=[11,20]7. The tests are run on Algorithm 5, without including the destroy and repair operator to reduce the running time. The algorithm terminated when the threshold was not exceeded and when the counterLimit was reached. An overview of the average results of the instance sets for each test can be found in Table B15 and the detailed results are in the Tables B16-B29.

Table 10.: Overview of Results of TT CNV CTC Optimal Solution: 482.00 54,502.10 TT=11 515.00 57,973.39 TT=10 515.00 58,024.24 TT=8 519.00 58,050.70 TT=9 520.00 58,064.27 TT=12 520.00 58,142.22 TT=4 506.00 58,178.45 TT=[11,20] 524.00 58,193.07 TT=3 519.00 58,202.52 TT=7 518.00 58,257.75 TT=5 515.00 58,269.72 TT=6 511.00 58,296.79 TT=[1,10] 514.00 58,313.04 TT=2 517.00 58,357.42 TT=1 511.00 58,422.50

Table 10 lists the cumulative number of vehicles (CNV) and the cumulative total cost (CTC) of the optimal solution and the tests on TT, sorted by CTC. As Algorithm 5 does not include any route minimization strategies, the heuristic generates routes in a high amount, where all tests have over 500 CNV. The minimum CNV could be found with TT=4 and the minimum CTC with TT=11. As the focus of this work is

7TT=[11,20] states that each time the random generator is called a random number between 11 and 20 is generated.

31 Computational Experiments to approach solutions close to the optimal solution, TT=11 is chosen as basis for further tests.

Tests on Intensification The intensification strategy of Schulze and Fahle [67] and Chiang and Russell [8, 9] are tested in this section with the purpose to find out, which intensification strategy matches best with the TS algorithm of this work. Algorithm 8 describes the intensification approach from Schulze and Fahle [67], where small routes are relocated and improved with an Or-opt operator. In the algorithm of Chiang and Russell [9] intensification is done by reducing the waiting time of the customers. The tests on intensification are made in the same testing environment as the tests on TT.

Algorithm 8 Intensiﬁcation of Schulze & Fahle [67] 1: if bestV alue − bestNeighbor > 0 then 2: bestV alue ← bestNeighbor 3: setMoveTabu 4: if route < 6 then 5: RelocateBestFit {SL=3} 6: end if 7: OrOptBestFit {SL=3} 8: end if

In Table 11 an overview of the tests, made on intensiﬁcation, is presented. For comparison reasons an intensiﬁcation strategy with OrOptBestFit was tested too8. The table is divided in three parts, where the average best results of Solomon’s [72] problem sets of the respective methods and their CNV and CTC can be found.

Table 11.: Overview Results of Intensiﬁcation Strategies

Best Solutions Or-Opt Best Solutions S/F Best Solutions C/R

Problem NV Cost Time NV Cost Time NV Cost Time

C1-Avg. 10.11 843.84 4.67 10.00 849.29 2.11 10.22 847.05 3.11 R1-Avg. 14.67 1260.87 0.83 14.75 1257.41 1.17 14.67 1255.78 3.08 RC1-Avg. 14.25 1448.37 0.88 14.13 1445.85 2.50 14.50 1444.77 1.63

C2-Avg. 3.50 607.31 40.13 3.13 605.43 39.88 3.50 607.42 71.63 R2-Avg. 4.82 946.50 27.45 4.91 949.84 24.36 4.91 939.58 41.55 RC2-Avg. 6.25 1083.28 15.75 5.88 1093.00 16.00 6.00 1070.10 14.88

CNV/CTC 512.00 58,248.11 506.00 58,334.85 514.00 58,006.53

When comparing the results of the intensiﬁcation strategies, then it is apparent that the method of Schulze and Fahle (S/F) [67] results in the lowest CNV, but simultaneously in the highest CTC, contrary to the method of Chiang and Russell [8] (C/R). Furthermore, when comparing the CNV of the Or-opt strategy with the

8To fasten the search the sequence length (SL) of Or-OptBestFit was set to SL=3.

32 4.4. Computational Test Results one of S/F, then the results show that with the use of the relocate operator in the second case, the CNV could be reduced. The average best cost for the method of C/R is, except for C1 and C2, lower than the average best results for the other two intensification methods, but the differences are not very big. However, a comparison of running time shows more significant differences. When comparing the best (average)9 running times of S/F with the ones of C/R, then the latter is in sum approximately 60 % (30 %) higher. Despite, the intensification strategy of C/R is chosen for further tests as it displays the lowest CTC (Table 11).

Test on Diversiﬁcation

In the paper of Chiang and Russell [8], the authors test the effectiveness of various implementations on their TS heuristic, where four different versions were developed. For comparison reasons Table 12 shows the average results10 on Solomon’s [72] benchmark problem sets of the first three versions. As presented in Table 12, in the first version, the results of the short term memory are illustrated (SIMPLE), in the second, intensification (INT) and in the third, diversification (INT/DIV) is included. As this work implemented the intensification strategy of Chiang and Russell [8, 9] and a similar frequency-based diversification strategy, Table 13 is displayed to perform a comparison of the average results calculated within this thesis with the ones of Chiang and Russell [8].

Table 12.: Comparison of TS Implementations of Chiang & Russell [8]

SIMPLE INT INT/DIV

Problem NV Cost Time NV Cost Time NV Cost Time

C1-Avg. 10.00 836.02 7.16 10.00 846.00 7.57 10.00 834.29 7.29 R1-Avg. 12.42 1287.97 9.00 12.50 1271.28 10.00 12.42 1243.50 9.95 RC1-Avg. 12.25 1472.83 7.11 12.13 1445.77 7.82 12.00 1417.08 7.78

C2-Avg. 3.00 638.21 13.51 3.13 725.57 12.63 3.00 604.97 11.19 R2-Avg. 2.83 1079.45 16.08 2.83 1034.20 16.64 2.83 1053.59 16.57 RC2-Avg. 3.38 1336.75 15.20 3.38 1355.36 15.30 3.38 1235.83 15.58

CNV/CTC 419.00 62,276.00 420.00 63,305.00 417.00 60,083.00

When considering the average results of Table 12, then adopting an intensification strategy did not improve the search process of TS. In the paper of Chiang and Russell [8] the objective function tries to reduce the number of vehicles first and the total distance second. Therefore, in four of six problem sets the intensification was less effective than the simple implementation of TS. The authors assume that the intensification strategy (without diversification) focuses on specific areas of the search and limits the search process too much. By adding a diversification strategy the

9The detailed results can be found in the appendix, Tables B30-B32. 10The table includes the average number of vehicles required, average total distance and average CPU time in minutes on a Pentium-166 PC.

33 Computational Experiments average results could be improved in all problem sets, without signiﬁcantly increasing CPU time.

Table 13.: Comparison of TS Implementations

Best Solutions SIMPLE Best Solutions INT Best Solutions INT/DIV

Problem NV Cost Time NV Cost Time NV Cost Time

C1-Avg. 10.11 841.03 1.78 10.22 847.05 3.11 10.00 838.40 5.00 R1-Avg. 14.33 1258.22 1.50 14.67 1255.78 3.08 14.58 1258.57 5.00 RC1-Avg. 14.25 1446.55 1.88 14.50 1444.77 1.63 14.25 1435.03 5.25

C2-Avg. 3.13 602.14 30.75 3.50 607.42 71.63 3.38 609.12 79.50 R2-Avg. 5.55 937.33 36.27 4.91 939.58 41.55 5.64 934.32 41.82 RC2-Avg. 6.50 1075.66 18.00 6.00 1070.10 14.88 6.88 1071.41 25.63

CNV/CTC 515 57,973.39 514 58,006.53 523 57,850.41

The test results of the TS algorithm in this work are illustrated in Table 13, where the first version (SIMPLE) illustrates the average best test results of TT, the second version the results of intensification (INT) and the third the results of the diversification strategy (INT/DIV)11. When comparing the results from Table 12 with the results in Table 13, then it is apparent that the CNV in Table 13 are significantly higher and the CTC lower. The simple implementation of Chiang and Russell’s TS requires in total 96 less vehicles than the simple TS implementation in this work and can be explained through the objective function. As mentioned before the TS algorithm of Chiang and Russell [8] minimizes the number of vehicles first, which is not the case in the TS algorithm here. Generally, it can be stated from Table 12 and 13 that both algorithms behave in a very similar way depending on the particular test or version. Similar to Table 12 the CTC of Table 13 rises when adding an intensification method and falls in a higher amount when including a diversification method. Considering the CTC of the SIMPLE version as basis, then the CTC for INT is 1.65% higher (0.06%) and for INT/DIV 3.52% (-0.27%) lower for the results in Table 12 (Table 13).

Tests on Minimizing the Number of Vehicles As stated in the introduction12 of this work, most TS solved VRPTW papers use a lexicographic order of the objective function or include a route saving phase to minimize the number of routes. The previous tests on TS pursued the goal of calculating optimal solutions, disregarding the minimization of routes. This subsection focuses on minimizing the number of vehicles by including the destroy and repair operator described in Algorithm 7. For comparison reasons the same termination criteria is used like in the tests on ILS. Before testing the TS algorithm regarding the minimization of vehicle numbers, a small experiment was made on diﬀerent toleranceV alues. The experimental results

11Described in Subsection 3.3.3. 12See Chapter 1.

34 4.4. Computational Test Results are illustrated in Appendix-Table A1. Based on the experimental results, the following test was performed with toleranceV alue = 1.2. Table 14 illustrates the average best results of Solomon’s [72] benchmark instances solved with the TS heuristic on diﬀerent papers 13, where the objective function is to minimize the distance and where the minimization of routes occurs in a route- savings-phase like the TS heuristic described in this section. The ﬁrst column in Table 14 represents the authors and the columns C1-Avg. to RC2-Avg. represent the average number of vehicles and average total distance (or total cost) with respect to the six problem groups of Solomon [72]. Additionally, the last column indicates the CNV and CTC over all 56 test problems. Detailed test results can be found in Table B35.

Table 14.: Comparison Test Results of Minimizing Number of Routes

Author C1-Avg. R1-Avg. RC1-Avg. C2-Avg. R2-Avg. RC2-Avg. CNV/CTC

Garcia et al. (1994) 10.00 12.92 12.88 3.00 3.09 3.75 436 877.10 1317.70 1473.50 602.30 1222.60 1527.00 65,977

Potvin et al. (1996) 10.00 12.50 12.63 3.00 3.09 3.38 426 850.20 1294.50 1456.30 594.60 1154.40 1404.80 63,530

Ho & Haugland (2004) 10.00 14.00 13.63 3.00 3.64 4.00 463 844.99 1259.89 1450.76 614.27 1014.56 1227.89 60,228

TS-VRPSTW 10.00 12.50 12.50 3.00 2.91 3.38 423 852.84 1295.02 1413.81 596.81 1011.20 1220.40 60,187

The TS algorithm in Garcia et al. [26] and Potvin et al. [60] are quite similar, even though Potvin et al. [60] report better results regarding CNV and CTC. When assuming that there is a tradeoff between the number of iterations and solution quality [13], then a possible explanation for the performance of Potvin et al. [60] could be that their algorithm stops after 7500 iterations, whereas the algorithm of Garcia et al. [26] terminates after 200 iterations. The TS algorithm of Ho and Haugland [36] includes a three-step process, where a feasible initial solution is generated first then improved by TS and post-optimized. The route-savings phase is performed every fifth iteration and the algorithm terminates when 100 consecutive iterations are performed without any improvement to the best cost. There are some similarities to the TS algorithm (TS-VRPSTW) used in this work, as similar neighborhood operators and termination criteria is used. However, there is a significant difference in the CNV, which can be explained by the route saving size. Ho and Haugland [36] consider vehicle routes with three or less customers for the route savings phase, whereas this work considers vehicle routes up to the size of 20. Considering the CNV, then Table 14 shows that the TS algorithm of this work (TS-VRPSTW) results in the lowest CNV, closely followed by Potvin et al. [60]. Comparing the CNV of the TS-VRPSTW with the two other results, then the difference is 3.1% for Garcia et al. [26] and 9.5% for Ho and Haugland [36]. The

13A review on the papers can be found in the Introduction in Chapter 1.

35 Computational Experiments lowest CTC are calculated with the TS-VRPSTW and the diﬀerences to the other methods are 0.1% for Ho and Haugland [36], 5.6% for Potvin et al. [60] and 9.6% for Garcia et al. [26]. Comparing the problem sets, then Table 14 shows that the TS-VRPSTW could achieve better results in RC1, R2 and RC2 compared to the other methods. In Table B34 the TS-VRPSTW is compared with the best known solutions from literature [71]. The problem sets C1, C2, R2 and RC2 could achieve good results regarding average NV compared to the best known solutions. Further, the problem sets C1, RC1 and C2 show average best gaps smaller than 3%. The highest best gap is calculated with problem instance R102, where the NV is lower than for the best known solution. By violating the TW in R102, a vehicle could be saved in exchange for higher total costs, resulting from high penalty. TW violations occurred only in 3 of 56 problem instances of the best solutions, namely R101, R102 and RC101.

Test on Initial Solution Any TS algorithm requires an initial solution to start the local search process [23]. According to Lau et al. [49] a construction heuristic should produce good initial locations so that the improvement heuristic can start in a region where good solutions are achievable. In a heuristic analysis of TS for the VRP, Van Breedam [77] also states that there is a high degree of dependency of the TS heuristic on the good quality of the initial solution. However, in the tests on initial solutions for ILS it could be shown that randomly generated initial solutions can lead to better final solutions. Furthermore, Fu et al. [24] studied the influence of the initial solution generated randomly or by the farthest first heuristic (FFH) and could show that there was not much influence of the initial solution on final solutions in the TS algorithm for the Open-VRP. The purpose of the next test is to find out what influence the initial solution has regarding the final solution calculated on the TS algorithm in this work.

Table 15.: Test on Initial Solution

Best Solutions TO-NNB Best Solutions RIS Best Known Sol. Best Gap

Problem NV Cost Time NV Cost Time NV Cost NNB RIS

C1-Avg. 10.00 847.40 28.56 10.00 858.16 24.78 10.00 828.38 2.30% 3.60% R1-Avg. 12.75 1296.50 25.33 12.67 1296.07 13.83 11.92 1210.34 6.55% 6.64% RC1-Avg. 12.50 1442.25 28.00 12.75 1467.40 14.50 11.50 1384.16 4.55% 5.89%

C2-Avg. 3.00 596.59 421.00 3.00 596.20 371.25 3.00 589.86 1.14% 1.07% R2-Avg. 3.00 998.19 474.09 3.00 1001.31 294.27 2.73 951.03 5.21% 5.71% RC2-Avg. 3.38 1195.81 350.00 3.38 1206.71 195.63 3.25 1119.24 7.25% 8.33%

CNV/CTC 427.00 60,041.79 428.00 60,453.13 405.00 57,186.86

In Table 15 the average test results regarding initial solution is presented. Test solutions of TO-NNB heuristic 14 and RIS compared to the best known solutions from literature [71] are found, where the best gaps on both tests (NNB and RIS) is illustrated too. Comparing the test results of the TO-NNB heuristic with the ones of RIS, then Table 15 shows that the best gaps of RIS are for all problem sets,

14With toleranceV alue = 1.1. 36 4.4. Computational Test Results with exception of C2, higher. Regarding, CNV and CTC it can be seen that the CNV for the method with RIS is one higher compared to the TO-NNB heuristic and comparing both CTC results with the best known solution from literature [71] then the CTC for RIS are 5.7% and the CTC for TO-NNB heuristic 5% higher. Further, comparing the running time of both methods, then it is apparent that for every problem set, the average best time of the RIS results are lower than the results of TO-NNB heuristic. The detailed test results in Table B36 show that TW violations occur in 4 of 56 problem instances (R101, R102, RC101, RC102) compared to the test results of the TO-NNB heuristic in Table B35, where TW violations also occur in 4 problems (R101, R102, R111, RC101). Taking the statements of Lau et al. [49] and Van Breedam [77] into account, then it can be agreed that there is a positive correlation between initial solution and objective function, but like in the work of Fu et al. [24] it is shown that the initial solution does not have a large inﬂuence on the ﬁnal result in the proposed TS heuristic, as the CNV and CTC results of the RIS method are only 0.2% and 0.7% higher than the results generated wit the TO-NNB heuristic.

Tests on Time Windows According to Fu et al. [23] different ways of allowing TW violations lead to different types of VRPSTW. Therefore, this subsection analyzes different types of VRPSTW. The TS algorithm here is tested on hard, and soft TW of Type a, Type b and Type c15, considering benchmark problems found in literature. During multiple STW experiments, Fu et al. [23] compared their best solutions with other approaches in the literature, where the criteria for the quality of the solution is in following order of importance: (1) the total number of vehicles used, (2) the total deviation of TW to start service, and (3) the total vehicle travel distance. For comparison reasons, the approach of Fu et al.[23] is applied in this subsection. Taillard et al. [73] were the first ones designing a TS heuristic of Type a for the VRPSTW. As the percentage of non-violated TW was 100%, their results reported for the 56 benchmark problems were feasible solutions to the VRPTW, too. The following test uses the same penalty parameters like Taillard et al. [73] and Fu et al. [23]. The results of both papers for the 56 Solomon [72] benchmark problems are illustrated in Table 16, where the number of routes, total travel distance (or cost) and percentage of non-violated TW can be found. Table 16 further reports the best solutions produced by the TS algorithm in this work (TS-VRPSTW) and the CNV/CTC for all methods.16 The best solutions of TS-VRPSTW are compared to those calculated by Taillard et al. [73] and Fu et al. [23], where a single asterisk * means a tie with the best result produced by Taillard et al. [73] and Fu et al. [23]. A single asterisk with a T (*T) or F (*F), indicates that the TS-VRPSTW outperforms the best result of Taillard et al. [73] or Fu et al. [23]. In 3 (1) of 56 problem instances, the TS-VRPSTW could outperform the best results of Taillard et al. [73] (Fu et al. [23]) and on 12

15Described in Chapter 3. 16In the paper of Fu et al. [23] results are reported on the total travel distance of the problem instances, but not on the total cost. Therefore, no CTC could be calculated. 37 Computational Experiments test problems the best solutions of Taillard et al. [73] and Fu et al. [23] could be achieved. Table 16.: Comparison of the Results of Type a of VRPSTW

Taillard et al. (1997) Fu et al. (2008) TS-VRPSTW

Problem NV Cost n.-v. TW NV Distance n.-v. TW NV Cost n.-v. TW

C101 10.00 828.94 100% 10.00 828.94 100% 10.00 828.94 100% * C102 10.00 828.94 100% 10.00 828.94 100% 10.00 828.94 100% * C103 10.00 828.06 100% 10.00 831.03 100% 10.00 950.29 100% C104 10.00 824.78 100% 10.00 824.78 100% 10.00 922.73 100% C105 10.00 828.94 100% 10.00 828.94 100% 10.00 828.94 100% * C106 10.00 828.94 100% 10.00 828.94 100% 10.00 828.94 100% * C107 10.00 828.94 100% 10.00 828.94 100% 10.00 828.94 100% * C108 10.00 828.94 100% 10.00 828.94 100% 10.00 828.94 100% * C109 10.00 828.94 100% 10.00 828.94 100% 10.00 828.94 100% *

C1-Avg. 10.00 828.38 10.00 828.71 10.00 852.84

R101 19.00 1650.79 100% 14.00 1535.24 75% 18.00 1731.38 98% *T R102 17.00 1487.60 100% 13.00 1416.84 89% 16.00 2184.90 97% *T R103 13.00 1294.24 100% 11.00 1267.28 96% 14.00 1260.41 100% R104 10.00 982.72 100% 9.00 983.50 99% 10.00 1029.95 100% R105 14.00 1377.11 100% 13.00 1441.24 98% 14.00 1419.05 100% R106 12.00 1259.71 100% 11.00 1355.25 97% 13.00 1306.53 100% R107 10.00 1126.69 100% 10.00 1147.59 100% 11.00 1100.96 100% R108 9.00 968.59 100% 9.00 978.69 100% 10.00 987.27 100% R109 11.00 1214.54 100% 11.00 1264.22 100% 12.00 1222.20 100% R110 11.00 1080.36 100% 11.00 1083.99 100% 11.00 1140.93 100% R111 10.00 1104.83 100% 10.00 1138.47 100% 11.00 1145.84 100% R112 10.00 964.01 100% 10.00 963.22 100% 10.00 1010.78 100%

R1-Avg. 12.17 1209.27 11.00 1214.63 12.50 1295.02

RC101 14.00 1696.94 100% 13.00 1654.30 92% 15.00 1676.01 100% RC102 12.00 1554.75 100% 12.00 1593.71 100% 13.00 1562.02 100% RC103 11.00 1264.27 100% 11.00 1321.71 100% 12.00 1358.16 100% RC104 10.00 1135.83 100% 10.00 1175.23 100% 10.00 1171.65 100% *F RC105 13.00 1643.38 100% 12.00 1654.07 92% 14.00 1630.65 99% RC106 11.00 1448.26 100% 11.00 1422.72 99% 13.00 1426.91 100% RC107 11.00 1230.54 100% 11.00 1237.64 100% 12.00 1306.08 100% RC108 10.00 1139.82 100% 10.00 1184.55 100% 11.00 1178.98 100%

RC1-Avg. 11.50 1389.22 11.25 1405.49 12.50 1413.81

C201 3.00 591.56 100% 3.00 591.56 100% 3.00 591.56 100% * C202 3.00 591.56 100% 3.00 591.56 100% 3.00 591.56 100% * C203 3.00 591.17 100% 3.00 591.17 100% 3.00 600.54 100% C204 3.00 590.60 100% 3.00 590.60 100% 3.00 616.33 100% C205 3.00 588.88 100% 3.00 588.88 100% 3.00 609.36 100% C206 3.00 588.49 100% 3.00 588.49 100% 3.00 588.49 100% * C207 3.00 588.29 100% 3.00 588.29 100% 3.00 588.29 100% * C208 3.00 588.32 100% 3.00 588.32 100% 3.00 588.32 100% *

C2-Avg. 3.00 589.86 3.00 589.86 3.00 596.81

R201 4.00 1254.80 100% 3.00 1500.36 89% 4.00 1272.20 100% R202 3.00 1214.28 100% 3.00 1205.79 100% 3.00 1310.01 100% R203 3.00 951.59 100% 3.00 950.36 100% 3.00 1006.16 100% R204 2.00 941.76 100% 2.00 854.30 100% 2.00 921.91 100% *T R205 3.00 1038.72 100% 3.00 1001.75 100% 3.00 1107.53 100% R206 3.00 932.47 100% 3.00 917.94 100% 3.00 983.92 100% R207 3.00 837.20 100% 2.00 903.01 100% 3.00 867.09 100% R208 2.00 748.01 100% 2.00 738.27 100% 2.00 754.77 100% R209 3.00 959.47 100% 3.00 909.89 100% 3.00 995.23 100% R210 3.00 980.90 100% 3.00 948.20 100% 3.00 1049.60 100% R211 2.00 923.80 100% 2.00 953.18 100% 3.00 854.83 100%

R2-Avg. 2.82 980.27 2.64 989.37 2.91 1011.20

RC201 4.00 1413.79 100% 4.00 1409.88 100% 4.00 1543.14 100% RC202 4.00 1164.25 100% 3.00 1435.56 100% 4.00 1239.91 100% RC203 3.00 1112.55 100% 3.00 1062.38 100% 3.00 1177.49 100% RC204 3.00 831.69 100% 3.00 799.98 100% 3.00 897.22 100% RC205 4.00 1328.21 100% 3.00 1656.80 93% 4.00 1439.79 100% RC206 3.00 1158.81 100% 3.00 1186.80 100% 3.00 1384.95 100% RC207 3.00 1082.32 100% 3.00 1127.83 100% 3.00 1172.82 100% RC208 3.00 847.90 100% 3.00 846.10 100% 3.00 907.89 100%

RC2-Avg. 3.38 1117.44 100% 3.13 1190.67 100% 3.38 1220.40

CNV/CTC 410 57521.79 390 423 60187.14

Comparing the CNV and CTC of the three methods in Table 16, then it is apparent that Fu et al. [23] have the lowest CNV with 390, followed by Taillard et al. [73] 38 4.4. Computational Test Results with 20 and the TS-VRPSTW with 33 more vehicles. The reason why Fu et al. [23] could obtain significant savings in the CNV is given on the one hand by the objective function, which minimizes the total number of vehicles with the highest priority and on the other hand by the allowance of STW. As illustrated in Table 16 in 10 of 56 problem instances the percentage of non-violated TW is under 100% and in almost all of this cases17 the NV are lower than the ones of Taillard et al. [73]. Unlike Fu et al. [23], Taillard et al. [73] set the available NV to the best solution reported in literature for the VRPTW for each problem instance, without minimizing it in objective function. This could indicate why Taillard et al. [73] calculate 5.1% more CNV than Fu et al. [23] and why no TW violation occurred for each of the problem instances. The CNV of this work differs 8.5% from the results of Fu et al. [23] and 3.2% from Taillard et al. [73]. As stated before, the objective function of the TS-VRPSTW algorithm minimizes only the total routing cost. The minimization of routes is done in a route savings phase, therefore resulting in a into higher CNV. The CTC of TS-VRPSTW differs 4.6% from Taillard et al. [73].

Table 17.: Comparison of CPU Time on Type a of VRPSTW Fu et al. (2008) TS-VRPSTW Problem Set CPU Time in Second CPU Time in Second C1-Avg. 68.41 34.89 R1-Avg. 786.34 33.08 RC1-Avg. 697.25 31.75 C2-Avg. 56.97 350.50 R2-Avg. 528.30 659.64 RC2-Avg. 548.73 334.13

In Table 17 the CPU time in seconds of the average problem sets of the TS heuristic of Fu et al. [23]18 and the TS-VRPSTW is presented. It is apparent that the method of Fu et al. [23] results in higher computational time, with exception of C2-Avg. and R2-Avg., than the TS-VRPSTW. The CPU time diﬀerence is quite high, especially for problem sets R1, RC1 and C2.

Koskosidis et al. [43] introduced an optimization-based method based on the Generalized Assignment Heuristic of Fisher and Jaikumar [22], solving Type b of the VRPSTW. Their algorithm was tested on randomly generated problems and on 21 of 56 Solomon’s [72] benchmark problems. Fu et al. [23] tested Type b of the VRPSTW with their TS algorithm too, setting the penalty coeﬃcients α = λ = 100 for the 21 instances listed. For the following test the same penalty coeﬃcients like Fu et al. [23] are used based on Equation 3.1. As Koskosidis et al. [43] calculate the

17With exception of RC106. 18The authors use a 600 MHz Pentium-II PC with 184 MB RAM.

39 Computational Experiments penalty coeﬃcients diﬀerently by using weighting factors, a comparison is not given.

Table 18.: Comparison of the Results of Type b of VRPSTW

Fu et al. (2008) TS-VRPSTW

Problem NV Distance non-vio. TW NV Distance non-vio. TW

C101 10.00 828.94 100% 10.00 828.94 100% * C102 10.00 828.94 100% 10.00 1266.26 100% C103 10.00 918.08 100% 10.00 1631.99 100% C104 10.00 899.00 100% 10.00 1253.79 100% C105 10.00 828.94 100% 10.00 828.94 100% * C106 10.00 828.94 100% 10.00 828.94 100% * C107 10.00 828.94 100% 10.00 828.94 100% * C108 10.00 828.94 100% 10.00 828.94 100% * C109 10.00 828.94 100% 10.00 870.78 100%

C1-Avg. 10.00 846.63 10.00 1018.61

R101 14.00 1872.94 56% 16.00 2168.03 60% R102 13.00 1732.54 71% 14.00 1846.08 71% R103 12.00 1542.79 91% 13.00 1621.91 92% R104 10.00 1107.18 100% 11.00 1229.40 100% R108 10.00 968.34 100% 10.00 1075.13 100% R109 11.00 1379.87 96% 13.00 1474.06 96%

R1-Avg. 11.67 1433.94 12.83 1569.10

RC101 13.00 1851.22 74% 14.00 1992.39 74% RC102 13.00 1772.42 99% 14.00 1939.28 95% RC103 11.00 1416.81 100% 12.00 1594.45 99% RC104 10.00 1262.55 100% 11.00 1271.50 100% RC106 12.00 1531.57 99% 12.00 1571.24 94% RC108 11.00 1224.72 100% 11.00 1266.48 100%

RC1-Avg. 11.67 1509.88 12.33 1605.89

Table 18 compares the results of Type b, where the NV, total travel distance and the percentage of non-violated time windows is illustrated. The TS-VRPSTW algorithm has not improved any of the 21 instances listed and tied ﬁve solutions, indicated by *. A comparison of computational times of the test on Type b shows in Table 19 that the algorithm of Fu et al. [23] results in much higher CPU times than TS-VRPSTW. For instance, the problem set R1 takes in average 47 times more computational time for calculation than TS-VRPSTW.

Table 19.: Comparison of CPU Time on Type b of VRPSTW Fu et al. (2008) TS-VRPSTW Problem Set CPU Time in Second CPU Time in Second C1-Avg. 315.10 24.56 R1-Avg. 993.10 21.67 RC1-Avg. 810.50 30.17

40 4.4. Computational Test Results

Regarding the tests on Type c of the VRPSTW, Balakrishnan [1] defined functions to calculate the penalty if service of customer i begins before ai or after bi, where the penalty payable is limited to Pmax and waiting time to Wmax. A vehicle arriving at customer i before ai has the possibility of paying the relevant penalty, serving that customer immediately and driving to the next customer. However, if the penalty exceeds Pmax, the vehicle has the further possibility to wait for a certain period of time (up to Wmax) before serving that customer. Pmax and Wmax are expressed as percentages of the maximum allowable route time duration, varying in combinations of 0, 5 and 10%. Balakrishnan [1] implemented three simple heuristics (nearest neighbor, savings and space-time heuristic) and tested them on eight problems from the R1 and RC1 problem sets of Solomon’s [72] benchmark instances. Chiang and Russell [9] developed a TS metaheuristic with an advanced recovery strategy to initiate searches from a pool of good solutions. The authors compared the solution quality of the TS heuristic to the best heuristic solutions generated by Balakrishnan [1]. Fu et al. [23] applied a unified TS algorithm on Type c of the VRPSTW, too by solving the benchmark problems of Balakrishnan [1]. For Type c of the TS-VRPSTW a new function is included in the TS algorithm, which checks the TW feasibility. After a neighborhood operation, an evaluation function in Algorithm 6 examines if the move is TABU or INTENS and additionally k if ai − Pmax − Wmax ≤ wi ≤ bi + Pmax is satisfied for every customer i. To be consistent with Balakrishnan [1], Chiang and Russell [9] and Fu et al. [23], the penalty coefficients are set to α = λ = 1. The computational results of Type c for the TS-VRPSTW (TS) and the comparison with the best solutions found by Balakrishnan’s [1] simple heuristic (SIM), Chiang and Russell’s [9] TS with advanced recovery (AR) and Fu et al.’s [23] unified TS algorithm (UTS) are presented in Tables 20, 21 and 22. The tables contain the values for Wmax and Pmax and the results of the benchmark problems, including the number of vehicles used, the total route distance and percentage of non-violated windows. As presented in Table 20, the TS heuristic could not generate feasible solutions for Pmax = 0 and Wmax = 0, which is difficult to solve as the vehicle has to arrive 19 between ai and bi . Considering the other scenarios of Table 20, then it can be seen that feasible solutions for R109, RC103 and RC106 could be found. However, it is apparent that AR could achieve feasible solutions for all the instances and outperforms SIM and TS in all test problems in terms of NV and total route distance traveled. The reason why TS results in infeasible solutions is related the objective function. Based on the initial solution, which is infeasible for every problem instance in Table 20, the TS-algorithm tries to minimize the total cost restricted by the TW feasibility. Therefore, a move, which would be feasible but would increase the total cost, is not accepted as a deterioration of the initial solution is not allowed.20

19In this scenario no waiting time and violation of TW is allowed. 20A deterioration of the solutions is only allowed when the destroy and repair operator is applied and the tolerance limit is not exceeded. 41 Computational Experiments 13 14 12 12 14 100 100 100 100 100 1304 1109 1409 1414 1596 = 0) 19 19 19 19 17 17 13 12 1216 14 15 15 14 13 14 12 11 12 15 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 max SIM AR UTS TS 1915 1692 1695 1890 1511 1490 1492 1165 1158 1396 2012 1651 1685 1808 1530 1502 1679 1284 1331 1689 P of VRPSTW ( 13 14 12 12 100 100 100 100 1370 1234 1409 1420 Type c 19 19 20 19 17 17 13 12 1216 14 15 15 14 13 14 12 11 12 15 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 SIM AR UTS TS 2043 1808 1757 1877 1600 1470 1482 1172 1159 1509 2012 1643 1704 1807 1560 1617 1676 1296 1358 1743 SIM AR UTS TS : 0 0 0 : 0 5 10 max max P W Table 20. : Comparison of the Results of Distance% n.-v. TWDistance% 2439 n.-v. TW 100 Distance% 1958 n.-v. TW 100 1685 100 Distance% 1475 n.-v. TW 100 1381 1567 100 1219 100 Distance 1206 100% n.-v. TW 100 2200 100 1764Distance 1913 100% n.-v. TW 100 Distance% 1627 n.-v. TW 100 1675 1885 100 1362 100 Distance 1428 100% n.-v. TW 100 1664 100 1424 1492 100 100 Problem R101 NVR102 NVR103 NV 22 R109 NV 19RC101 19 NV 14RC102 13 14 NV 12 16RC103 12 NV 5 16 RC106 NV 14 13 14 11 12 13 12 13

42 4.4. Computational Test Results = 5) 17 147215 14 24 1283 16 45 ** 13 12 47 54 1186 13 61 ** 13 11 59 61 1195 12 73 ** 14 11 60 76 1356 12 75 ** 13 13 39 84 1188 14 6412 12 58 70 *B 1082 14 8112 11 69 88 1171 12 86 11 61 93 *B 13 81 89 SIM AR UTS TS 1885 1370 1438 1930 1636 1265 1339 1602 1452 1066 1168 1521 1445 1084 1168 1382 1839 1424 1529 1822 1850 1375 1413 1804 1469 1183 1254 1464 1496 1223 1336 1505 max P of VRPSTW ( Type c 17 147215 14 29 1280 15 37 ** 13 12 44 37 1084 14 60 ** 12 11 60 56 1180 12 81 ** 15 11 58 77 1394 13 8214 13 44 89 1193 15 7213 11 61 71 1097 13 74 ** 13 11 69 88 1198 12 89 ** 11 58 92 13 77 88 SIM AR UTS TS 1903 1392 1456 1882 1693 1259 1348 1693 1530 1134 1232 1447 1363 1093 1140 1396 1972 1425 1554 1908 1776 1357 1475 1700 1680 1186 1251 1481 1699 1233 1325 1557 SIM AR UTS TS Table 21. : Comparison of the Results of :: 0 5 5 5 10 5 max max P W Distance% n.-v. TW 1917 1483Distance 55 1628% n.-v. TW 25 2113 1754 1364Distance 69 42 1389% n.-v. TW 39 1804 46 1436 1126Distance 77 61 1189% n.-v. TW 60 1506 59 1383 1123Distance 73 78 1158% n.-v. TW 62 1361 75 1835 1522Distance 68 82 1594% n.-v. TW 47 2025 89 1679 1368Distance 84 72 1523% n.-v. TW 60 1775 72 1605 1229Distance 88 79 1265% n.-v. TW 79 1462 76 1620 1269 95 90 1329 71 1528 93 *B 82 90 Problem R101 NVR102 NVR103 16 14 NVR109 14 15 12 NV 17 RC101 13 12 NV 11 14 RC102 12 11 NV 11 12 14RC103 ** 11 12 NV 13 13 13RC106 12 NV 15 12 12 10 13 13 11 11 12 11 13

43 Computational Experiments = 10) 15 126214 12 8 1081 14 31 ** 13 11 33 38 1083 13 51 ** 12 10 58 67 1090 11 76 ** 15 11 47 77 1162 12 8214 12 27 82 1181 13 54 ** 13 11 56 67 1083 12 74 ** 12 11 65 76 1090 12 90 ** 11 49 87 12 81 81 SIM AR UTS TS 1832 1212 1376 1696 1569 1173 1287 1475 1657 1013 1185 1373 1431 1005 1183 1254 1832 1275 1457 1763 1569 1222 1367 1575 1657 1119 1275 1414 1431 1160 1337 1503 max P of VRPSTW ( Type c 15 126214 12 11 1178 15 3713 11 39 47 1082 13 56 ** 12 10 56 69 1090 11 75 ** 14 11 47 69 1161 12 8213 12 36 86 1183 13 59 ** 12 11 56 69 1092 13 7813 11 63 84 *B 1097 11 87 ** 11 50 88 *F 12 73 ** 82 SIM AR UTS TS 1832 1216 1364 1757 1790 1147 1272 1572 1575 1008 1197 1310 1431 1019 1176 1320 1795 1288 1474 1712 1719 1218 1458 1612 1530 1123 1266 1387 1620 1158 1303 1474 SIM AR UTS TS :: 0 10 5 10 10 10 Table 22. : Comparison of the Results of max max P W Distance% n.-v. TW 1737 1266Distance 44 1399% n.-v. TW 14 1720 1507 1167Distance 63 33 1324% n.-v. TW 35 1465 31 1363 1028Distance 68 55 1209% n.-v. TW 57 1346 64 1311 *B 1017Distance 67 76 1161% n.-v. TW 54 1272 72 1784 1305Distance 60 85 1502% n.-v. TW 25 1796 86 2060 1249Distance 97 59 1503% n.-v. TW 55 1667 75 1571 *B 1137Distance 92 69 1258% n.-v. TW 65 1439 87 1620 1191 97 86 1301 47 1552 87 77 82 Problem R101 NVR102 NVR103 14 12 NVR109 13 12 11 NV 14 RC101 12 11 NV 10 13 RC102 11 10 NV 10 11 14RC103 ** 11 11 NV 12 14 12RC106 11 NV 14 12 11 10 13 ** 13 10 10 12 11 12 **

44 4.4. Computational Test Results

The TS-VRPSTW heuristic (TS) could solve all problem instances listed in the Tables 21 and 22. Comparing the results of Table 21 and 22 with the best solutions of the simple heuristic (SIM), then there are 24 cases (indicated with **), where the TS heuristic (TS) results in lower NV and seven cases (indicated with *B and *F), where TS produces more non-violated TW for the same NV. Comparing the percentage of non-violated TW in Tables 21 and 22, then it can be stated that the TS heuristic satisﬁes a higher percentage of the original hard TW than AR for all problems and scenarios.

Table 23.: Comparison of CPU Time on Type c of VRPSTW CPU Time in Seconds Problem Set SIM AR UTS TS R1 18.9-79.1 448.2-692.4 170.0-1586.3 7.3-34.0 RC1 17.6-55.1 595.8-844.8 193.1-1899.7 6.2-29.5

In Table 23 the CPU times of the heuristics of the tests on Type c of VRPSTW are presented, showing the range of time in seconds for the problem sets R1 and RC1. The computational requirements for AR21 and UTS are signiﬁcantly higher than SIM22 and TS. The TS-VRPSTW heuristic of this work results in the lowest CPU times23.

Table 24.: Comparison of the Results of VRPTW AR TS Best Known Sol. Problem NV Cost NV Cost NV Cost C1-Avg. 10.00 828.38 10.00 848.24 10.00 828.38 R1-Avg. 12.08 1219.06 12.83 1248.72 11.92 1210.34 RC1-Avg. 11.88 1376.57 12.75 1415.20 11.50 1384.16 C2-Avg. 3.00 589.86 3.00 596.27 3.00 589.86 R2-Avg. 2.73 972.95 2.82 1026.36 2.73 951.03 RC2-Avg. 3.38 1113.87 3.38 1194.78 3.25 1119.24 CNV/CTC 411 57,428.92 428 59,558.66 405 57,186.86

Chiang and Russell [9] tested the robustness of their AR algorithm on hard TW problems solving Solomon’s [72] benchmark instances by setting Pmax = 0 and Wmax = ∞. The TS implementation (AR) of Chiang and Russell [9] achieved good results compared to the best known solutions from literature [71], diﬀering only 1.5% and 0.4% regarding CNV and CTC. The TS heuristic in this work (TS) resulted

21Chiang and Russell [9] tested the advanced recovery strategy on a 2.25 GHz Athlon computer. 22Balakrishnan [1] tested its simple heuristics on a 25 MHz 80386/387 computer. 23Values are given as averages over 10 runs of the problems.

45 Computational Experiments in the test on hard TW, in higher CNV and CTC. Compared to the best known solutions, the CNV diﬀers 5.7% and the CTC 4.1% from the TS heuristic (TS). In the problem sets C1, C2 and RC2 the same average NV is calculated for AR and TS.

4.5. Performance Analysis

In this section, the best solutions produced by the TS algorithm in this work are compared with heuristic and exact approaches from the literature. The ﬁrst part refers to approaches, that solely concentrate on the minimization of total travel cost (distance) and the second part focuses on heuristics, where the number of vehicles is considered as primary optimization criterion.

Table 25.: Comparison to the Optimal Solution

Author C1-Avg. R1-Avg. RC1-Avg. C2-Avg. R2-Avg. RC2-Avg. CNV/CTC

Tan et al. (2001) 10.00 13.83 13.63 3.25 3.82 4.25 467 870.87 1266.37 1458.16 634.85 1080.24 1293.38 62008

HeuristicLab 10.44 14.08 13.75 3.25 4.91 5.63 498 870.04 1229.62 1427.39 597.02 922.37 1056.39 57378

ILS-VRPTW 10.56 14.67 14.75 3.75 6.27 7.13 545 873.82 1256.38 1459.44 614.95 942.13 1073.64 58489

TS-VRPSTW 10.00 14.58 14.25 3.38 5.64 6.88 523 838.40 1258.57 1435.03 609.12 934.32 1071.41 57850

Kritzinger et al. (2011) 10.0 13.3 12.6 3.0 5.3 6.3 483 826.7 1173.6 1334.5 587.4 873.9 1000.7 54517

Optimal Solution 10.00 13.25 12.63 3.00 5.27 6.25 482 826.70 1173.61 1334.49 587.38 872.53 1000.73 54502

Table 25 illustrates average best results of Solomon’s [72] benchmark problem sets of diﬀerent algorithms compared to the optimal solution [41, 2]. Apart from results of TS algorithms, the table contains results of the ILS24 calculated in this work. The TS algorithms refer to the results of Tan et al. [74]25, the HL experiment26 and the TS-VRPSTW27 solved with Algorithm 6. For comparison reasons, the results of Kritzinger [44] are included too, where the VRPSTW is solved with VNS 28. Although, the authors use the same tardiness parameter as Taillard et al. [73] (soft TW of Type a), they end up with no time window violations at the customer locations. The VNS algorithm is not designed to minimize the number of vehicles, instead the algorithm starts with 20% more vehicles than the optimal solution.

24See Table B5. 25See Chapter 1.1. 26See Chapter 4.2. 27See Chapter 4.4.2., Test on Diversification. 28As some parts of the code of Kritzinger [44] are included in the Basic Algorithm 5, the results of the VNS are illustrated with the aim to find out, what the differences in performance are. Kritzinger [44] uses the same rounding criteria as the methods for the optimal solution.

46 4.5. Performance Analysis

Comparing the average best solutions of Table 25, then it is apparent that Tan et al. [74] result in the highest CTC, differing 13.7% from the optimal solution on VRPTW. The lowest CTC gap is achieved with the VNS heuristic of Kritzinger [44], which is under 0.0% from the optimal solution. The ILS algorithm shows the highest CNV and differs regarding CTC 1.1% from the TS-VRPSTW and 7.3% from the optimal solution. The HL experiment could outperform the TS-VRPSTW in five of six problem sets (R1, RC1, C2, R2, RC2) and shows a better CTC result, differing -0.8% from the TS-VRPSTW and 5.3% from the optimal solution. The TS-VRPSTW could only outperform the TS heuristic of Tan et al.[74] and the ILS heuristic regarding CTC, differing 6.1% from the optimal solution.

The implementation of the ILS algorithm beard the idea in mind to see how heuristics other than the TS perform, given the same basic algorithm (see Algorithm 5). The following performance analysis concentrates on the ILS and TS heuristic, where the minimization of vehicle numbers is relevant.29 Apart from that the algorithms are compared to the best known solutions. Table 26 illustrates the best results from the ILS and TS algorithm on the VRPSTW, compared to the best known solutions on the 56 Solomon [72] benchmark instances. The table includes the NV, Cost and additionally the percentage of non-violated TW for the soft TW. Two asterisks (**) indicate that the TS or ILS heuristic produced a better solution than the best known solution (shorter total travel distance or lower NV). As the best known solution refer to hard TW problems, the ILS or TS algorithm are only then compared to the best known solution when the percentage of non-violated TW is 100%. A single asterisk * indicates a tie with the best known solution whereas an asterisk with a T (*T) indicates that the TS heuristic performed better than the ILS algorithm, using the same judging criteria for the solution quality described in the tests on time windows.30 Furthermore, the CNV and CTC is given for the methods and best known solution. In 12 (11) of 56 problem instances the TS (ILS) algorithm produced the best known solution, locatable in the problem sets C1 and C2. Neither the TS nor the ILS algorithm could improve the best known solutions for the VRPTW. Comparing the CNV of both methods with the best known solution, then the diﬀerence for the ILS is 5.4% (22 vehicles) and 4.2% (18 vehicles) for the TS algorithm. Considering the CTC, then the gap is 4.8% for ILS and 5.2% for TS, compared to the CTC of the best known solution. The performance analysis of the ILS and TS heuristic shows that in 24 of 56 problem instances the TS could achieve better solutions than the ILS, mostly in the problem sets R1, RC1 and R2 as illustrated in Table 26. With a CNV gap of -0.9% the TS algorithm performed better than the ILS algorithm.

29For the TS algorithm the results of Table B34 are considered here. As the TS algorithm uses a toleranceV alue = 1.2, the same parameter test was performed on the best ILS test result, see Table 9 and B39. 30See Chapter 4.4.2., Tests on Time Windows.

47 Computational Experiments

Table 26.: Comparison ILS and TS Algorithm with Best Known Solutions

VRPTW VRPSTW (Type a)

Best Known Solution ILS Algorithm TS Algorithm

Problem NV Cost Ref. NV Cost n.-v. TW NV Cost n.-v. TW

C101 10.00 828.94 [63] 10.00 828.94 100% 10.00 828.94 100% * C102 10.00 828.94 [63] 10.00 834.64 100% 10.00 828.94 100% * C103 10.00 828.06 [63] 10.00 953.83 100% 10.00 950.29 100% *T C104 10.00 824.78 [63] 10.00 851.69 100% 10.00 922.73 100% C105 10.00 828.94 [63] 10.00 828.94 100% 10.00 828.94 100% * C106 10.00 828.94 [63] 10.00 828.94 100% 10.00 828.94 100% * C107 10.00 828.94 [63] 10.00 828.94 100% 10.00 828.94 100% * C108 10.00 828.94 [63] 10.00 828.94 100% 10.00 828.94 100% * C109 10.00 828.94 [63] 10.00 828.94 100% 10.00 828.94 100% *

C1-Avg. 10.00 828.38 10.00 845.98 10.00 852.84

R101 19.00 1650.80 [37] 18.00 1670.60 99% 18.00 1731.38 98% R102 17.00 1486.12 [63] 18.00 1512.23 99% 16.00 2184.90 97% *T R103 13.00 1292.68 [50] 14.00 1267.29 100% 14.00 1260.41 100% *T R104 9.00 1007.31 [54] 10.00 1070.98 100% 10.00 1029.95 100% *T R105 14.00 1377.11 [63] 15.00 1413.64 100% 14.00 1419.05 100% *T R106 12.00 1252.03 [54] 12.00 1331.53 100% 13.00 1306.53 100% R107 10.00 1104.66 [68] 11.00 1132.91 100% 11.00 1100.96 100% *T R108 9.00 960.88 [4] 10.00 973.26 100% 10.00 987.27 100% R109 11.00 1194.73 [38] 12.00 1252.93 100% 12.00 1222.20 100% *T R110 10.00 1118.84 [54] 12.00 1169.07 100% 11.00 1140.93 100% *T R111 10.00 1096.72 [64] 11.00 1123.26 100% 11.00 1145.84 100% R112 9.00 982.14 [25] 10.00 1007.54 100% 10.00 1010.78 100%

R1-Avg. 11.92 1210.34 12.75 1243.77 12.50 1295.02

RC101 14.00 1696.94 [73] 16.00 1726.11 100% 15.00 1676.01 100% *T RC102 12.00 1554.75 [73] 13.00 1662.03 100% 13.00 1562.02 100% *T RC103 11.00 1261.67 [69] 12.00 1344.50 100% 12.00 1358.16 100% RC104 10.00 1135.48 [13] 10.00 1184.36 100% 10.00 1171.65 100% *T RC105 13.00 1629.44 [4] 15.00 1632.21 100% 14.00 1630.65 99% *T RC106 11.00 1424.73 [4] 12.00 1604.20 100% 13.00 1426.91 100% RC107 11.00 1230.48 [68] 11.00 1514.48 100% 12.00 1306.08 100% RC108 10.00 1139.82 [73] 11.00 1201.67 100% 11.00 1178.98 100% *T

RC1-Avg. 11.50 1384.16 12.50 1483.70 12.50 1413.81

C201 3.00 591.56 [63] 3.00 591.56 100% 3.00 591.56 100% * C202 3.00 591.56 [63] 3.00 591.56 100% 3.00 591.56 100% * C203 3.00 591.17 [63] 3.00 600.21 100% 3.00 600.54 100% C204 3.00 590.60 [63] 3.00 614.88 100% 3.00 616.33 100% C205 3.00 588.88 [63] 3.00 609.36 100% 3.00 609.36 100% C206 3.00 588.49 [63] 3.00 588.49 100% 3.00 588.49 100% * C207 3.00 588.29 [63] 3.00 588.29 100% 3.00 588.29 100% * C208 3.00 588.32 [63] 3.00 588.32 100% 3.00 588.32 100% *

C2-Avg. 3.00 589.86 3.00 596.58 3.00 596.81

R201 4.00 1252.37 [38] 4.00 1298.04 100% 4.00 1272.20 100% *T R202 3.00 1191.70 [64] 4.00 1127.32 100% 3.00 1310.01 100% *T R203 3.00 939.50 [79] 3.00 985.22 100% 3.00 1006.16 100% R204 2.00 825.52 [3] 2.00 944.09 100% 2.00 921.91 100% *T R205 3.00 994.42 [64] 3.00 1095.09 100% 3.00 1107.53 100% R206 3.00 906.14 [66] 3.00 987.03 100% 3.00 983.92 100% *T R207 2.00 890.61 [59] 3.00 906.59 100% 3.00 867.09 100% *T R208 2.00 726.82 [54] 2.00 829.94 100% 2.00 754.77 100% *T R209 3.00 909.16 [37] 3.00 1019.98 100% 3.00 995.23 100% *T R210 3.00 939.37 [54] 3.00 1035.06 100% 3.00 1049.60 100% R211 2.00 885.71 [79] 3.00 843.00 100% 3.00 854.83 100%

R2-Avg. 2.73 951.03 3.00 1006.49 2.91 1011.20

RC201 4.00 1406.94 [54] 4.00 1549.61 100% 4.00 1543.14 100% *T RC202 3.00 1365.65 [19] 4.00 1252.13 98% 4.00 1239.91 100% *T RC203 3.00 1049.62 [16] 3.00 1164.01 100% 3.00 1177.49 100% RC204 3.00 798.46 [54] 3.00 846.68 100% 3.00 897.22 100% RC205 4.00 1297.65 [54] 4.00 1409.18 100% 4.00 1439.79 100% RC206 3.00 1146.32 [37] 3.00 1327.31 99% 3.00 1384.95 100% RC207 3.00 1061.14 [3] 3.00 1196.09 99% 3.00 1172.82 100% *T RC208 3.00 828.14 [39] 3.00 950.34 100% 3.00 907.89 100% *T

RC2-Avg. 3.25 1119.24 3.38 1211.92 3.38 1220.40 100%

CNV/CTC 405 57187 427 59948 423 60187

48 4.5. Performance Analysis

In Table 27 the best results of the TS algorithms described in the introduction31 are summarized with the purpose to monitor the performance of the TS algorithm calculated in this work (TS-VRPSTW). The ﬁrst column illustrates the authors and the following six columns report the average best results of Solomon’s [72] problem sets for the respective paper. The last column illustrates the CNV and CTC32 over all 56 problem instances. All methods consider the number of vehicles, and total travel cost or time as optimization criterion.

Table 27.: Comparison of Tabu Search Algorithms

Author C1-Avg. R1-Avg. RC1-Avg. C2-Avg. R2-Avg. RC2-Avg. CNV/CTC

Garcia et al. (1994) 10.00 12.92 12.88 3.00 3.09 3.75 436 877.10 1317.70 1473.50 602.30 1222.60 1527.00 65,977

Rochat & Taillard (1995) 10.00 12.25 11.88 3.00 2.91 3.38 415 828.38 1208.50 1377.39 589.86 961.72 1119.59 57,231

Potvin et al. (1996) 10.00 12.50 12.63 3.00 3.09 3.38 426 850.20 1294.50 1456.30 594.60 1154.40 1404.80 63,530

Taillard et al. (1997) 10.00 12.17 11.50 3.00 2.82 3.38 410 828.38 1209.35 1389.22 589.86 980.27 1117.44 57,523

Chiang & Russell (1997) 10.00 12.17 11.88 3.00 2.73 3.25 411 828.38 1204.19 1397.44 591.42 986.32 1229.54 58,502

Schulze & Fahle (1999) 10.00 12.25 11.75 3.00 2.82 3.38 414 828.94 1239.15 1409.26 589.93 1066.68 1286.05 60,346

De Backer et al. (2000) 10.00 12.50 12.13 3.00 3.00 3.38 421 828.71 1205.93 1392.03 589.86 946.51 1129.16 57,229

Cordeau et al. (2001) 10.00 12.08 11.50 3.00 2.73 3.25 407 828.38 1210.14 1389.78 589.86 969.57 1134.52 57,556

Lau et al. (2003) 10.00 12.17 12.25 3.00 3.00 3.38 418 832.13 1211.55 1418.77 589.86 1001.12 1170.93 58,477

Chiang & Russell (2004) 10.00 12.08 11.88 3.00 2.73 3.38 411 828.38 1219.06 1376.57 589.86 972.95 1113.87 57,429

Ho & Haugland (2004) 10.00 14.00 13.63 3.00 3.64 4.00 463 844.99 1259.89 1450.76 614.27 1014.56 1227.89 60,228

TS-VRPSTW 10.00 12.50 12.50 3.00 2.91 3.38 423 852.84 1295.02 1413.81 596.81 1011.20 1220.40 60,187

According to Table 27 the TS algorithm of Cordeau et al. [13] produced the best results in terms of solution quality with CNV of 407. Further well-performing approaches include the TS methods of Taillard et al. [73] or Chiang and Russell [8, 9], where the diﬀerence in CNV is under 1%. The algorithm of Ho and Haugland [36] illustrates the highest CNV.33 Comparing TS-VRPSTW algorithm with the results of Cordeau et al. [13], then the CNV gap is 3.9% and the CTC gap remains in 4.6%. The TS algorithm of De Backer et al. [18] results in 2 vehicles less than the TS-VRPSTW, calculating the lowest CTC of all TS algorithms in Table 27 and diﬀering 5.2% from the CTC of TS-VRPSTW.

31See Chapter 1.1. Related Work. Fu et al. [23] are not included because the authors give no information on the cost of the VRPSTW. Qi et al. [62] did not report results of all problem instances of Solomon [72]. 32The CTC are rounded to integers as some values taken from Br¨aysyand Gendreau [7] are reported in that format. 33See also 4.4.2., Tests on Minimizing the Number of Vehicles.

49 Computational Experiments

Considering the problem sets C1 and C2 in Table 27, then all methods could generate the same average NV. The TS-VRPSTW algorithm could achieve good results in the problem sets R2 and RC2 regarding average NV, in 9 of 12 cases of RC2, the TS-VRPSTW could generate lower or equal NV.

Summing up the TS algorithm implemented in this work could achieve, without any minimization of vehicle numbers, better results than the TS-algorithm of Tan et al. [74] and the ILS algorithm illustrated in Table 25. Prioritizing the vehicle numbers, then the TS algorithm could again generate better results than the ILS algorithm. In comparison with other TS algorithms, the TS algorithm generated in this work could outperform three paper results, illustrated in Table 27.

50 5. Conclusion

In this work a TS algorithm is developed to solve the VRPSTW. Along with the implementation the TS algorithm is tested on different methods and parameters with the aim to find good solutions. Additionally to the TS algorithm, the ILS heuristic is introduced and tested on the same basic algorithm. For a first experimental approach the TS algorithm is performed on a software environment (HL). The initial solution for solving the VRPSTW is generated with the TO-NNB heuristic. To search the solution space, the TS algorithm makes use of of neighborhood operators like 2-opt, Or-opt, 2-opt*, relocate and cross, where the best improvement acceptance strategy is applied to. Additionally, intensification and diversification strategies are used to enhance the search. First tests are executed on the ILS algorithm, where the acceptances strategy is tested on initial solutions and TW combinations including a destroy and repair operator to minimize the number of routes. Best test results could be achieved with the combination of soft TW and best improvement strategy, where the initial solution is generated with the TO-NNB heuristic. Compared to the best known solutions on the VRPTW, a 5.4% difference is achieved regarding the CNV. The tests on TS are more extensive, including tests on TT, intensification, diversification, minimizing the number of vehicles, initial solution and time windows. The first tests on TS are performed without any route minimization priority with the purpose to realize near optima solutions. A comparison to the optimal solution shows 6.1% difference regarding CTC. By testing the destroy and repair operator on the TS algorithm with regard to minimize the number of routes, CNV savings in the amount of 23.6% (100 vehicles) could be reached. Furthermore, the TS algorithm could outperform three TS-algorithms from literature regarding CNV and CTC. Tests are not only performed to optimize the TS algorithm, but also to analyze different types of VRPSTW. The tests involved the performance measurement of the TS algorithm on three different types of soft TW and hard TW. The computational results show for the TW test on Type a that on the complete set of 56 instances, the TS heuristic could outperform 4 cases compared to the literature and equal solution costs are achieved in 12 cases. Furthermore, in most cases tardiness can be completely avoided. The soft TW test on Type b could not improve any solution, but tie 5 of 21 instances, taking much less computational time than literature. For the tests on Type c three scenarios are considered with different penalty and waiting time allowance. Not all instances of the first test scenario, where no tardiness is allowed and waiting time is limited, could be solved. In the other two test scenarios, several solutions could be outperformed by generating lower NV and higher non-violated

51 Conclusion

TW. The test on hard time windows show a difference of 5.7% in CNV from the best known solutions on VRPTW. According to Bräysyand Gendreau [6] good heuristics are not only measured against solution quality and speed, but also simplicity, flexibility and robustness. The TS algorithm of this work could show strengths regarding flexibility, efficiency, speed and robustness. However, even though the VRPSTW has a wide application in the real world, this work could not be implemented on real-life instances. Therefore, this attributes could not be tested on real-life applications.

52 Appendices

A. Appendix A

A.1. VRPTW

A.1.1. Problem Deﬁnition

X X k min xijcij (A.1) k∈K (i,j)∈A

X X k s. t. xij = 1 ∀i ∈ N (A.2) k∈K j∈δ+(i) X k x0j = 1 ∀k ∈ K (A.3) j∈δ+(0) X k X k xij − xji = 0 ∀j ∈ N, k ∈ K (A.4) i∈δ−(j) i∈δ+(j) X k xi,n+1 = 1 ∀k ∈ K (A.5) i∈δ−(n+1) X X k di xij ≤ Q ∀k ∈ K (A.6) i∈N j∈δ+(i) k k k xij(wi + si + tij − wj ) ≤ 0 ∀ (i, j) ∈ A, k ∈ K (A.7) k ai ≤ wi ≤ bi ∀i ∈ V, k ∈ K (A.8) k xij ∈ {0, 1} ∀ (i, j) ∈ A, k ∈ K (A.9)

55 Appendix A

A.1.2. An Example

Figure A1.: The left ﬁgure illustrates a complete undirected graph, where the vertex positions are derived from the table bellow. The indegree and outdegree of the vertices are denoted in braces. By solving the VRPTW the undirected graph converts in a directed one due to time window restrictions.

Given the notation on VRP in Chapter 1, the VRPTW in Figure A1 is defined on a complete undirected graph G(V,A), where the depot is represented by the vertex 0 and n + 1 (here 4). Let V (G) = {0, 1, 2, 3, 4} be the set of vertices and A(G) = {{0, 1} , {0, 2} , {0, 3} , {1, 2} , {1, 3} , {1, 4} , {2, 1} , {2, 3} , {2, 4} , {3, 1} , {3, 2} , {3, 4}} the arc set. All feasible routes correspond to paths in G, starting from vertex 0 (source) and ending (sink) at vertex 4, given in the second graph of Figure A1, where the direction is given by the time windows. A route is a sequence r1 = (0, 1, 2, 4) in which the set S = {1, 2} ⊆ N, where N = V \{0, 4}, is visited. The first table in Figure A1 gives information on the vertices (0, 1, 2, 3, 4), with their positions, time windows, service times and demands. Further it gives information on the amount of vehicles and their capacity. The second table in Figure A1 illustrates the adjacency matrix A, which indicates whether pairs of customers are adjacent or not. If there is an edge from i to j then Aij=1, else Aij=0. If we consider the problem definition of the VRPTW in the Subsection A.1.1 before and adapt it on the simple example in Figure A1, then the first equation (A.1) states that the objective function is to minimize the costs over all edges. The constraints of the problem definition are presented in the equations (A.2) to (A.9) and the routes are feasible if all these constraints hold. A solution to a VRPTW is given if |K| feasible routes exist, one for each vehicle.

56 A.2. VRPSTW

A.2. VRPSTW

A.2.1. Experiment on Minimizing the Number of Vehicles During the tests on minimizing the NV an experiment was performed on diﬀerent toleranceV alues. The basic idea of toleranceV alue is described in Algorithm 7. After a route (size ≤ 20) is destroyed and inserted in random routes and on random positions, local search is performed, where improved solutions are always accepted. However, if the solution is smaller than toleranceV alue∗bestEval, then it is accepted too. This means that with higher toleranceV alues, poorer solutions with lower NV are more likely to be accepted. The experiments were performed on the problem sets R1 and RC1 of Solomon’s [72] benchmark instances, as these two sets show the biggest diﬀerences in the average NV compared to the best known solutions (see Table B12). Further, only toleranceV alues from 1.1 - 1.5 were tested. The experimental results are presented in Table A1.

Table A1.: Average Test Results of toleranceV alue Average Solutions Problem set toleranceV alue CNV CTC Vio. TW R1 & RC1 1.1 264.5 27,076.20 1.43 R1 & RC1 1.2 261.3 27,546.54 6.24 R1 & RC1 1.3 260.7 28,157.89 12.26 R1 & RC1 1.4 260.4 28,486.52 15.29 R1 & RC1 1.5 257.8 29,271.27 23.65

As illustrated in Table A1 the higher the toleranceV alue, the higher (lower) the CTC (CNV) and TW violation of the average solutions. Therefore, a correlation between toleranceV alue, NV and cost can be assumed. The purpose of this experiment is to ﬁnd a toleranceV alue, which is in balance with NV and cost (TW violation). Considering the average solutions of toleranceV alue = 1.1 as basis, then increasing the value to toleranceV alue = 1.2 leads to a decrease of 1.2% in the avg. CNV and an increase of 1.7% in the avg. CTC. Increasing the toleranceV alue = 1.1 to toleranceV alue = 1.3, leads to an avg. CNV decrease of 1.4% and an avg. CTC increase of 4%. Changing the toleranceV alue to 1.5, leads to a decrease of 2.5% in the avg. CNV but an increase of 8.1% in the avg. CTC. Considering the decrease and increase ratio of NV and cost, toleranceV alue = 1.2 is found to be in a better balance.

B. Appendix B

B.1. Computational Experiments

Table B1.: Test on Acceptance Strategy with HTW and TO-NNB Heuristic

Best Solutions ILS-FF Best Solutions ILS-BF Best Known Sol. Best Gap Best Gap

Problem NV Cost Time NV Cost Time NV Cost ILS-FF ILS-BF

C1-Avg. 10.22 848.56 0.78 10.11 847.51 1.00 10.00 826.70 2.65% 2.52% R1-Avg. 14.58 1265.13 0.00 14.75 1263.53 0.00 13.25 1173.61 8.35% 8.12% RC1-Avg. 14.25 1441.45 0.13 14.13 1450.23 0.88 12.63 1334.49 8.13% 8.93%

C2-Avg. 3.50 613.63 6.00 3.25 610.81 10.25 3.00 587.38 4.47% 3.99% R2-Avg. 4.91 958.57 5.18 4.64 956.00 9.73 5.27 872.53 9.92% 9.59% RC2-Avg. 5.88 1094.57 3.14 5.50 1098.64 7.25 6.25 1000.73 9.83% 9.62%

Table B2.: Test on Acceptance Strategy with HTW and RIS

Best Solutions ILS-FF Best Solutions ILS-BF Best Known Sol. Best Gap Best Gap

Problem NV Cost Time NV Cost Time NV Cost ILS-FF ILS-BF

C1-Avg. 10.56 873.82 0.78 10.56 865.03 0.33 10.00 826.70 5.70% 4.64% R1-Avg. 14.67 1256.38 0.33 14.50 1267.76 0.58 13.25 1173.61 7.38% 8.49% RC1-Avg. 14.75 1459.44 0.00 15.00 1459.63 0.25 12.63 1334.49 9.54% 9.63%

C2-Avg. 3.75 614.95 5.13 3.63 610.93 4.50 3.00 587.38 4.69% 4.01% R2-Avg. 6.27 942.13 2.00 5.91 943.29 4.27 5.27 872.53 8.10% 8.17% RC2-Avg. 7.13 1073.64 0.75 7.38 1075.86 1.13 6.25 1000.73 7.53% 7.52%

Table B3.: Test on Acceptance Strategy with STW and TO-NNB Heuristic

Best Solutions ILS-FF Best Solutions ILS-BF Best Known Sol. Best Gap Best Gap

Problem NV Cost Time NV Cost Time NV Cost ILS-FF ILS-BF

C1-Avg. 10.67 877.96 0.22 10.44 863.35 0.00 10.00 828.38 6.21% 4.44% R1-Avg. 14.50 1263.01 0.00 14.58 1266.97 0.08 11.92 1210.34 8.07% 8.44% RC1-Avg. 14.38 1446.22 0.00 14.13 1444.87 0.13 11.50 1384.16 8.69% 8.46%

C2-Avg. 3.63 615.07 3.88 3.50 606.36 9.75 3.00 589.86 4.71% 3.23% R2-Avg. 4.82 958.95 3.55 4.73 954.82 6.64 2.73 951.03 10.05% 9.49% RC2-Avg. 6.00 1087.22 3.50 6.00 1096.75 5.88 3.25 1119.24 8.99% 9.73%

Table B4.: Test on Acceptance Strategy with STW and RIS

Best Solutions ILS-FF Best Solutions ILS-BF Best Known Sol. Best Gap Best Gap

Problem NV Cost Time NV Cost Time NV Cost ILS-FF ILS-BF

C1-Avg. 10.89 885.56 0.00 10.67 878.15 0.00 10.00 828.38 7.12% 6.22% R1-Avg. 14.33 1248.63 0.08 14.75 1262.31 0.00 11.92 1210.34 6.84% 7.99% RC1-Avg. 14.25 1448.97 0.00 14.63 1466.60 0.25 11.50 1384.16 8.92% 10.07%

C2-Avg. 3.88 628.71 3.13 3.13 605.83 6.50 3.00 589.86 7.03% 3.14% R2-Avg. 6.18 936.24 1.36 6.27 945.99 1.55 2.73 951.03 7.49% 8.50% RC2-Avg. 7.13 1088.44 1.13 7.38 1083.50 1.75 3.25 1119.24 8.83% 8.52%

59 Appendix B

Table B5.: Overview Tests on ILS Time Win. Initial Sol. Accep. Str. CNV CTC Hard TO-NNB First Fit 510.00 58,560.11 Hard TO-NNB Best Fit 502.00 58,583.26 Hard RIS First Fit 545.00 58,488.63 Hard RIS Best Fit 542.00 58,545.92 Soft TO-NNB First Fit 515.00 58,794.22 Soft TO-NNB Best Fit 510.00 58,660.66 Soft RIS First Fit 540.00 58,581.21 Soft RIS Best Fit 543.00 58,704.18 Optimal Solution 482.00 54,502.10

60 B.1. Computational Experiments

Table B6.: Detailed Results HL-experiment for the VRPSTW

Best Solution HL Avg Solution HL Optimal Solution Best Gap

Problem NV Cost Time NV Cost Time NV Cost

C101 10.00 828.94 33.32 10.10 853.21 42.55 10.00 827.3 0.20% C102 11.00 862.74 20.24 11.20 906.30 23.40 10.00 827.3 4.28% C103 11.00 878.08 20.74 10.60 926.47 37.54 10.00 826.3 6.27% C104 10.00 901.33 20.46 10.00 946.11 25.17 10.00 822.9 9.53% C105 10.00 852.95 20.40 10.60 886.29 25.07 10.00 827.3 3.10% C106 11.00 863.66 25.73 11.30 910.44 26.21 10.00 827.3 4.40% C107 10.00 853.39 20.57 10.80 899.11 22.28 10.00 827.3 3.15% C108 11.00 871.13 20.59 10.90 908.46 21.91 10.00 827.3 5.30% C109 10.00 918.18 19.63 10.10 943.74 21.32 10.00 827.3 10.99%

C1-Avg. 10.44 870.04 22.41 10.62 908.90 27.27 10.00 826.70 5.24%

R101 21.00 1698.78 37.98 21.80 1760.09 39.07 20.00 1637.7 3.73% R102 18.00 1497.68 23.93 18.50 1517.93 26.34 18.00 1466.6 2.12% R103 15.00 1247.11 24.54 15.10 1262.78 25.27 14.00 1208.7 3.18% R104 12.00 1034.19 21.83 11.90 1070.82 23.39 11.00 971.5 6.45% R105 16.00 1409.75 35.48 16.20 1445.64 41.14 15.00 1355.3 4.02% R106 14.00 1294.75 21.65 14.30 1318.69 22.23 13.00 1234.6 4.87% R107 12.00 1125.32 21.47 12.50 1142.92 30.09 11.00 1064.6 5.70% R108 11.00 1002.82 30.70 11.20 1023.71 31.33 10.00 932.1 7.59% R109 14.00 1197.68 32.34 14.10 1237.87 33.00 13.00 1146.9 4.43% R110 12.00 1124.79 31.98 12.80 1148.98 32.37 12.00 1068.0 5.32% R111 12.00 1102.98 31.75 13.00 1132.63 32.37 12.00 1048.7 5.18% R112 12.00 1019.62 31.20 11.20 1053.96 31.58 10.00 948.6 7.49%

R1-Avg. 14.08 1229.62 28.74 14.38 1259.67 30.68 13.25 1173.61 4.77%

RC101 17.00 1735.04 34.17 17.60 1759.39 36.83 15.00 1619.8 7.11% RC102 15.00 1524.44 21.60 15.50 1563.02 23.36 14.00 1457.4 4.60% RC103 12.00 1344.00 20.36 13.00 1376.03 21.15 11.00 1258.0 6.84% RC104 11.00 1212.82 20.08 11.60 1241.15 22.21 10.00 1132.3 7.11% RC105 16.00 1619.66 22.60 16.10 1636.73 47.84 15.00 1513.7 7.00% RC106 14.00 1466.91 21.91 14.20 1490.50 22.29 13.00 1372.7 6.86% RC107 13.00 1310.74 21.32 13.20 1372.27 22.23 12.00 1207.8 8.52% RC108 12.00 1205.53 21.70 12.00 1242.71 22.82 11.00 1114.2 8.20%

RC1-Avg. 13.75 1427.39 22.97 14.15 1460.22 27.34 12.63 1334.49 6.96%

C201 3.00 591.56 30.34 3.50 602.95 33.49 3.00 589.1 0.42% C202 4.00 612.90 18.83 4.00 627.76 20.62 3.00 589.1 4.04% C203 3.00 600.92 18.45 3.80 630.46 20.01 3.00 588.7 2.08% C204 3.00 615.53 18.46 3.90 650.70 20.32 3.00 588.1 4.66% C205 3.00 588.88 18.40 3.70 607.43 21.85 3.00 586.4 0.42% C206 4.00 589.72 20.92 3.80 611.95 22.79 3.00 586.0 0.64% C207 3.00 588.29 19.45 3.40 603.17 24.20 3.00 585.8 0.42% C208 3.00 588.32 22.35 3.40 601.87 24.44 3.00 585.8 0.43%

C2-Avg. 3.25 597.02 20.90 3.69 617.04 23.46 3.00 587.38 1.64%

R201 8.00 1200.05 20.27 6.70 1230.67 25.05 8.00 1143.2 4.97% R202 6.00 1083.32 18.68 5.80 1111.02 19.00 8.00 1029.6 5.22% R203 5.00 910.40 18.76 5.00 938.85 24.09 6.00 870.8 4.55% R204 4.00 753.13 9.50 4.00 803.42 23.71 5.00 731.3 2.98% R205 5.00 1024.94 20.48 4.80 1053.54 25.61 5.00 949.8 7.91% R206 5.00 905.50 19.32 4.50 946.99 23.83 5.00 875.9 3.38% R207 4.00 857.43 3.05 3.50 904.11 25.43 3.00 794.0 7.99% R208* 3.00 730.42 4.31 3.60 754.90 24.76 3.00 701.2 4.17% R209 5.00 926.59 21.45 4.60 947.20 21.87 5.00 854.8 8.40% R210 5.00 957.74 17.86 4.70 980.79 20.03 6.00 900.5 6.36% R211 4.00 796.59 2.51 3.60 847.01 19.97 4.00 746.7 6.68%

R2-Avg. 4.91 922.37 14.20 4.62 956.23 23.03 5.27 872.53 5.71%

RC201 8.00 1324.07 34.54 7.90 1356.44 36.22 9.00 1261.8 4.93% RC202 5.00 1171.44 21.28 6.40 1186.47 21.68 8.00 1092.3 7.25% RC203 5.00 973.55 21.37 4.60 1019.14 21.75 5.00 923.7 5.40% RC204 4.00 831.72 12.47 3.90 852.93 20.71 4.00 783.5 6.15% RC205 7.00 1179.83 20.74 6.60 1262.65 21.98 7.00 1154.0 2.24% RC206 5.00 1119.68 21.24 5.20 1142.65 21.69 7.00 1051.1 6.52% RC207 6.00 1011.33 18.60 5.30 1056.30 21.20 6.00 962.9 5.03% RC208 5.00 839.48 18.74 4.10 896.20 21.05 4.00 776.5 8.11%

RC2-Avg. 5.63 1056.39 21.12 5.50 1096.60 23.28 6.25 1000.73 5.56%

61 Appendix B

Table B7.: Detailed Test Result ILS with TO-NNB Heuristic and FF for the VRPTW

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 8.00 0.00 0.00 0.00 10.00 828.94 6.80 0.00 0.00 0.00 10.00 828.94 0.00% C102 10.00 834.64 4.00 0.00 0.00 0.00 10.00 939.38 5.30 0.00 0.00 0.00 10.00 828.94 0.69% C103 10.00 1039.77 3.00 0.00 0.00 0.00 10.00 1128.75 7.70 0.00 0.00 0.00 10.00 828.06 25.57% C104 10.00 925.70 8.00 0.00 0.00 0.00 10.00 1032.34 5.10 0.00 0.00 0.00 10.00 824.78 12.24% C105 10.00 828.94 3.00 0.00 0.00 0.00 10.30 858.07 4.70 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 4.00 0.00 0.00 0.00 10.20 857.08 6.10 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 4.00 0.00 0.00 0.00 10.00 876.27 5.50 0.00 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 3.00 0.00 0.00 0.00 10.40 885.05 4.20 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 828.94 6.00 0.00 0.00 0.00 10.00 867.58 5.50 0.00 0.00 0.00 10.00 828.94 0.00%

C1-Avg. 10.00 863.75 4.78 0.00 0.00 0.00 10.10 919.27 5.66 0.00 0.00 0.00 10.00 828.38 4.28%

R101 20.00 1657.48 1.00 0.00 0.00 0.00 21.10 1683.44 1.00 0.00 0.00 0.00 19.00 1650.80 0.40% R102 18.00 1524.02 5.00 0.00 0.00 0.00 19.00 1524.04 2.90 0.00 0.00 0.00 17.00 1486.12 2.55% R103 14.00 1244.32 3.00 0.00 0.00 0.00 15.00 1288.91 2.40 0.00 0.00 0.00 13.00 1292.68 -3.74% R104 10.00 1059.63 11.00 0.00 0.00 0.00 10.90 1067.84 6.20 0.00 0.00 0.00 9.00 1007.31 5.19% R105 14.00 1515.53 4.00 0.00 0.00 0.00 15.20 1463.18 2.60 0.00 0.00 0.00 14.00 1377.11 10.05% R106 13.00 1263.97 7.00 0.00 0.00 0.00 13.20 1300.75 4.50 0.00 0.00 0.00 12.00 1252.03 0.95% R107 11.00 1147.65 5.00 0.00 0.00 0.00 11.40 1193.97 6.30 0.00 0.00 0.00 10.00 1104.66 3.89% R108 10.00 1003.27 7.00 0.00 0.00 0.00 10.00 1033.55 6.00 0.00 0.00 0.00 9.00 960.88 4.41% R109 12.00 1275.67 5.00 0.00 0.00 0.00 12.70 1292.36 4.70 0.00 0.00 0.00 11.00 1194.73 6.77% R110 11.00 1201.17 10.00 0.00 0.00 0.00 11.70 1208.56 6.30 0.00 0.00 0.00 10.00 1118.80 7.36% R111 11.00 1129.66 6.00 0.00 0.00 0.00 11.60 1173.87 5.20 0.00 0.00 0.00 10.00 1096.72 3.00% R112 10.00 1036.39 9.00 0.00 0.00 0.00 10.60 1060.01 5.40 0.00 0.00 0.00 9.00 982.14 5.52%

R1-Avg. 12.83 1254.90 6.08 0.00 0.00 0.00 13.53 1274.21 4.46 0.00 0.00 0.00 11.92 1210.34 3.86%

RC101 15.00 1693.77 2.00 0.00 0.00 0.00 16.40 1733.18 1.20 0.00 0.00 0.00 14.00 1696.94 -0.19% RC102 14.00 1546.04 4.00 0.00 0.00 0.00 14.50 1580.79 3.60 0.00 0.00 0.00 12.00 1554.75 -0.56% RC103 12.00 1325.07 3.00 0.00 0.00 0.00 12.40 1395.08 2.90 0.00 0.00 0.00 11.00 1261.70 5.03% RC104 11.00 1186.68 2.00 0.00 0.00 0.00 11.10 1235.24 2.60 0.00 0.00 0.00 10.00 1135.48 4.51% RC105 15.00 1581.01 2.00 0.00 0.00 0.00 16.00 1633.42 1.30 0.00 0.00 0.00 13.00 1629.44 -2.97% RC106 13.00 1450.70 1.00 0.00 0.00 0.00 13.30 1485.16 1.60 0.00 0.00 0.00 11.00 1424.73 1.82% RC107 12.00 1317.19 2.00 0.00 0.00 0.00 12.30 1357.58 2.10 0.00 0.00 0.00 11.00 1230.48 7.05% RC108 11.00 1201.11 3.00 0.00 0.00 0.00 11.50 1260.57 2.60 0.00 0.00 0.00 10.00 1139.82 5.38%

RC1-Avg. 12.88 1412.70 2.38 0.00 0.00 0.00 13.44 1460.13 2.24 0.00 0.00 0.00 11.50 1384.16 2.51%

C201 3.00 591.56 54.00 0.00 0.00 0.00 3.00 597.55 55.80 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 69.00 0.00 0.00 0.00 3.10 628.59 87.70 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 603.70 127.00 0.00 0.00 0.00 3.20 642.48 102.30 0.00 0.00 0.00 3.00 591.17 2.12% C204 3.00 614.76 43.00 0.00 0.00 0.00 3.20 673.67 81.60 0.00 0.00 0.00 3.00 590.60 4.09% C205 3.00 609.36 48.00 0.00 0.00 0.00 3.00 609.36 64.80 0.00 0.00 0.00 3.00 588.88 3.48% C206 3.00 588.49 94.00 0.00 0.00 0.00 3.00 597.35 78.50 0.00 0.00 0.00 3.00 588.50 0.00% C207 3.00 588.29 128.00 0.00 0.00 0.00 3.00 599.30 121.40 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 68.00 0.00 0.00 0.00 3.00 588.32 60.80 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 597.00 78.88 0.00 0.00 0.00 3.06 617.08 81.61 0.00 0.00 0.00 3.00 589.86 1.21%

R201 4.00 1327.70 46.00 0.00 0.00 0.00 4.00 1363.87 46.40 0.00 0.00 0.00 4.00 1252.37 6.01% R202 4.00 1143.82 27.00 0.00 0.00 0.00 4.00 1188.71 48.50 0.00 0.00 0.00 3.00 1191.70 -4.02% R203 3.00 1016.24 43.00 0.00 0.00 0.00 3.40 1056.78 36.10 0.00 0.00 0.00 3.00 939.50 8.17% R204 3.00 794.88 45.00 0.00 0.00 0.00 3.00 851.59 40.10 0.00 0.00 0.00 2.00 825.52 -3.71% R205 3.00 1127.43 58.00 0.00 0.00 0.00 3.90 1114.12 25.30 0.00 0.00 0.00 3.00 994.42 13.38% R206 3.00 976.98 39.00 0.00 0.00 0.00 3.30 1015.36 38.60 0.00 0.00 0.00 3.00 906.14 7.82% R207 3.00 871.83 68.00 0.00 0.00 0.00 3.00 936.74 47.40 0.00 0.00 0.00 2.00 890.60 -2.11% R208 2.00 783.88 97.00 0.00 0.00 0.00 2.70 799.90 61.00 0.00 0.00 0.00 2.00 726.82 7.85% R209 3.00 999.92 48.00 0.00 0.00 0.00 3.70 992.35 31.10 0.00 0.00 0.00 3.00 909.16 9.98% R210 3.00 1060.47 46.00 0.00 0.00 0.00 3.40 1069.35 42.00 0.00 0.00 0.00 3.00 939.37 12.89% R211 3.00 860.81 50.00 0.00 0.00 0.00 3.60 877.32 31.40 0.00 0.00 0.00 2.00 885.71 -2.81%

R2-Avg. 3.09 996.72 51.55 0.00 0.00 0.00 3.45 1024.19 40.72 0.00 0.00 0.00 2.73 951.03 4.86%

RC201 4.00 1497.63 42.00 0.00 0.00 0.00 4.10 1584.88 32.20 0.00 0.00 0.00 4.00 1406.94 6.45% RC202 4.00 1239.19 42.00 0.00 0.00 0.00 4.00 1313.67 44.00 0.00 0.00 0.00 3.00 1365.65 -9.26% RC203 3.00 1105.28 45.00 0.00 0.00 0.00 3.30 1205.16 47.30 0.00 0.00 0.00 3.00 1049.62 5.30% RC204 3.00 856.32 44.00 0.00 0.00 0.00 3.00 923.21 47.00 0.00 0.00 0.00 3.00 798.46 7.25% RC205 4.00 1383.20 35.00 0.00 0.00 0.00 4.00 1461.87 45.50 0.00 0.00 0.00 4.00 1297.70 6.59% RC206 3.00 1302.94 69.00 0.00 0.00 0.00 3.50 1296.26 49.80 0.00 0.00 0.00 3.00 1146.32 13.66% RC207 3.00 1232.46 46.00 0.00 0.00 0.00 3.60 1212.70 40.40 0.00 0.00 0.00 3.00 1061.14 16.14% RC208 3.00 935.92 52.00 0.00 0.00 0.00 3.80 926.21 27.60 0.00 0.00 0.00 3.00 828.14 13.01%

RC2-Avg. 3.38 1194.12 46.88 0.00 0.00 0.00 3.66 1240.49 41.73 0.00 0.00 0.00 3.25 1119.24 7.39%

62 B.1. Computational Experiments

Table B8.: Detailed Test Result ILS with TO-NNB Heuristic and BF for the VRPTW

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 6.00 0.00 0.00 0.00 10.00 828.94 4.90 0.00 0.00 0.00 10.00 828.94 0.00% C102 10.00 854.07 7.00 0.00 0.00 0.00 10.00 942.88 3.40 0.00 0.00 0.00 10.00 828.94 3.03% C103 10.00 974.08 6.00 0.00 0.00 0.00 10.00 1078.07 3.60 0.00 0.00 0.00 10.00 828.06 17.63% C104 10.00 866.50 3.00 0.00 0.00 0.00 10.00 990.47 3.20 0.00 0.00 0.00 10.00 824.78 5.06% C105 10.00 828.94 6.00 0.00 0.00 0.00 10.40 864.85 3.90 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 3.00 0.00 0.00 0.00 10.00 839.28 3.00 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 5.00 0.00 0.00 0.00 10.00 880.39 6.60 0.00 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 4.00 0.00 0.00 0.00 10.20 879.78 3.00 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 829.70 7.00 0.00 0.00 0.00 10.00 886.93 4.10 0.00 0.00 0.00 10.00 828.94 0.09%

C1-Avg. 10.00 852.11 5.22 0.00 0.00 0.00 10.07 910.18 3.97 0.00 0.00 0.00 10.00 828.38 2.87%

R101 20.00 1675.95 1.00 0.00 0.00 0.00 21.40 1690.83 0.30 0.00 0.00 0.00 19.00 1650.80 1.52% R102 18.00 1502.81 2.00 0.00 0.00 0.00 19.00 1510.80 1.50 0.00 0.00 0.00 17.00 1486.12 1.12% R103 15.00 1246.93 1.00 0.00 0.00 0.00 15.40 1291.76 1.00 0.00 0.00 0.00 13.00 1292.68 -3.54% R104 10.00 1067.85 6.00 0.00 0.00 0.00 11.00 1089.05 3.70 0.00 0.00 0.00 9.00 1007.31 6.01% R105 15.00 1420.20 3.00 0.00 0.00 0.00 15.40 1465.16 1.30 0.00 0.00 0.00 14.00 1377.11 3.13% R106 12.00 1301.67 2.00 0.00 0.00 0.00 13.40 1308.72 1.60 0.00 0.00 0.00 12.00 1252.03 3.96% R107 11.00 1147.39 6.00 0.00 0.00 0.00 11.60 1204.81 5.50 0.00 0.00 0.00 10.00 1104.66 3.87% R108 10.00 1005.93 4.00 0.00 0.00 0.00 10.00 1044.87 8.70 0.00 0.00 0.00 9.00 960.88 4.69% R109 12.00 1321.57 4.00 0.00 0.00 0.00 12.90 1287.14 4.00 0.00 0.00 0.00 11.00 1194.73 10.62% R110 12.00 1147.78 7.00 0.00 0.00 0.00 12.10 1196.17 5.60 0.00 0.00 0.00 10.00 1118.80 2.59% R111 11.00 1123.57 6.00 0.00 0.00 0.00 11.60 1159.80 5.70 0.00 0.00 0.00 10.00 1096.72 2.45% R112 10.00 1007.95 4.00 0.00 0.00 0.00 10.60 1042.01 5.50 0.00 0.00 0.00 9.00 982.14 2.63%

R1-Avg. 13.00 1247.47 3.83 0.00 0.00 0.00 13.70 1274.26 3.70 0.00 0.00 0.00 11.92 1210.34 3.25%

RC101 15.00 1763.97 1.00 0.00 0.00 0.00 16.40 1748.40 2.00 0.00 0.00 0.00 14.00 1696.94 3.95% RC102 14.00 1564.33 1.00 0.00 0.00 0.00 14.90 1579.26 1.10 0.00 0.00 0.00 12.00 1554.75 0.62% RC103 12.00 1352.99 3.00 0.00 0.00 0.00 12.30 1384.40 3.30 0.00 0.00 0.00 11.00 1261.70 7.24% RC104 11.00 1195.72 2.00 0.00 0.00 0.00 11.00 1225.32 2.50 0.00 0.00 0.00 10.00 1135.48 5.31% RC105 15.00 1603.52 5.00 0.00 0.00 0.00 16.50 1658.13 1.80 0.00 0.00 0.00 13.00 1629.44 -1.59% RC106 13.00 1467.68 2.00 0.00 0.00 0.00 13.60 1503.28 1.60 0.00 0.00 0.00 11.00 1424.73 3.01% RC107 12.00 1308.46 4.00 0.00 0.00 0.00 12.20 1362.97 3.40 0.00 0.00 0.00 11.00 1230.48 6.34% RC108 11.00 1182.38 3.00 0.00 0.00 0.00 11.50 1253.94 3.80 0.00 0.00 0.00 10.00 1139.82 3.73%

RC1-Avg. 12.88 1429.88 2.63 0.00 0.00 0.00 13.55 1464.46 2.44 0.00 0.00 0.00 11.50 1384.16 3.58%

C201 3.00 591.56 44.00 0.00 0.00 0.00 3.00 594.55 51.10 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 54.00 0.00 0.00 0.00 3.00 632.56 50.20 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 591.17 51.00 0.00 0.00 0.00 3.40 658.22 55.60 0.00 0.00 0.00 3.00 591.17 0.00% C204 3.00 594.64 37.00 0.00 0.00 0.00 3.10 667.75 59.40 0.00 0.00 0.00 3.00 590.60 0.68% C205 3.00 609.36 40.00 0.00 0.00 0.00 3.00 609.36 43.20 0.00 0.00 0.00 3.00 588.88 3.48% C206 3.00 588.49 47.00 0.00 0.00 0.00 3.00 593.91 45.10 0.00 0.00 0.00 3.00 588.50 0.00% C207 3.00 588.29 52.00 0.00 0.00 0.00 3.00 588.29 50.20 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 47.00 0.00 0.00 0.00 3.00 588.32 47.50 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 592.92 46.50 0.00 0.00 0.00 3.06 616.62 50.29 0.00 0.00 0.00 3.00 589.86 0.52%

R201 4.00 1315.78 28.00 0.00 0.00 0.00 4.00 1358.04 39.30 0.00 0.00 0.00 4.00 1252.37 5.06% R202 4.00 1140.55 43.00 0.00 0.00 0.00 4.00 1187.88 45.30 0.00 0.00 0.00 3.00 1191.70 -4.29% R203 3.00 963.05 84.00 0.00 0.00 0.00 3.20 1032.73 61.50 0.00 0.00 0.00 3.00 939.50 2.51% R204 2.00 961.51 242.00 0.00 0.00 0.00 2.90 845.18 97.40 0.00 0.00 0.00 2.00 825.52 16.47% R205 3.00 1102.64 96.00 0.00 0.00 0.00 3.40 1130.60 72.70 0.00 0.00 0.00 3.00 994.42 10.88% R206 3.00 999.47 97.00 0.00 0.00 0.00 3.40 1014.71 76.60 0.00 0.00 0.00 3.00 906.14 10.30% R207 3.00 897.84 99.00 0.00 0.00 0.00 3.00 955.71 130.80 0.00 0.00 0.00 2.00 890.60 0.81% R208 2.00 794.29 289.00 0.00 0.00 0.00 2.90 778.22 107.20 0.00 0.00 0.00 2.00 726.82 9.28% R209 3.00 1023.41 103.00 0.00 0.00 0.00 3.60 1031.29 62.00 0.00 0.00 0.00 3.00 909.16 12.57% R210 3.00 1048.11 101.00 0.00 0.00 0.00 3.30 1067.55 60.20 0.00 0.00 0.00 3.00 939.37 11.58% R211 3.00 871.24 40.00 0.00 0.00 0.00 3.40 881.54 39.60 0.00 0.00 0.00 2.00 885.71 -1.63%

R2-Avg. 3.00 1010.72 111.09 0.00 0.00 0.00 3.37 1025.77 72.05 0.00 0.00 0.00 2.73 951.03 6.69%

RC201 4.00 1536.70 103.00 0.00 0.00 0.00 4.40 1529.55 47.90 0.00 0.00 0.00 4.00 1406.94 9.22% RC202 4.00 1283.20 29.00 0.00 0.00 0.00 4.00 1354.42 36.20 0.00 0.00 0.00 3.00 1365.65 -6.04% RC203 3.00 1133.52 49.00 0.00 0.00 0.00 3.40 1195.18 40.40 0.00 0.00 0.00 3.00 1049.62 7.99% RC204 3.00 858.60 49.00 0.00 0.00 0.00 3.00 947.25 45.80 0.00 0.00 0.00 3.00 798.46 7.53% RC205 4.00 1415.49 24.00 0.00 0.00 0.00 4.00 1490.89 33.20 0.00 0.00 0.00 4.00 1297.70 9.08% RC206 3.00 1284.71 78.00 0.00 0.00 0.00 3.60 1279.07 48.00 0.00 0.00 0.00 3.00 1146.32 12.07% RC207 3.00 1138.10 64.00 0.00 0.00 0.00 3.60 1166.50 62.30 0.00 0.00 0.00 3.00 1061.14 7.25% RC208 3.00 946.09 73.00 0.00 0.00 0.00 3.40 978.99 50.40 0.00 0.00 0.00 3.00 828.14 14.24%

RC2-Avg. 3.38 1199.55 58.63 0.00 0.00 0.00 3.68 1242.73 45.53 0.00 0.00 0.00 3.25 1119.24 7.67%

63 Appendix B

Table B9.: Detailed Test Result ILS with RIS and FF for the VRPTW

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 5.00 0.00 0.00 0.00 10.00 836.63 5.70 0.00 0.00 0.00 10.00 828.94 0.00% C102 10.00 831.53 4.00 0.00 0.00 0.00 10.00 2594260.00 4.20 2.59 0.00 0.00 10.00 828.94 0.31% C103 10.00 884.26 6.00 0.00 0.00 0.00 10.00 1036.11 4.00 0.00 0.00 0.00 10.00 828.06 6.79% C104 10.00 868.47 3.00 0.00 0.00 0.00 10.00 988.60 4.60 0.00 0.00 0.00 10.00 824.78 5.30% C105 10.00 828.94 4.00 0.00 0.00 0.00 10.10 841.83 4.20 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 3.00 0.00 0.00 0.00 10.20 867.03 4.70 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 7.00 0.00 0.00 0.00 10.00 8689830.00 5.60 8.69 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 3.00 0.00 0.00 0.00 10.20 882.91 3.70 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 856.84 7.00 0.00 0.00 0.00 10.00 919.88 4.60 0.00 0.00 0.00 10.00 828.94 3.37%

C1-Avg. 10.00 842.86 4.67 0.00 0.00 0.00 10.06 1254495.89 4.59 1.25 0.00 0.00 10.00 828.38 1.75%

R101 19.00 1699.03 5.00 0.00 0.00 0.00 20.80 1703.15 2.50 0.00 0.00 0.00 19.00 1650.80 2.92% R102 18.00 1481.26 4.00 0.00 0.00 0.00 18.60 12026.20 3.50 0.01 0.00 0.00 17.00 1486.12 -0.33% R103 14.00 1241.80 6.00 0.00 0.00 0.00 14.70 1282.04 4.20 0.00 0.00 0.00 13.00 1292.68 -3.94% R104 10.00 1036.21 5.00 0.00 0.00 0.00 10.50 1067.28 9.00 0.00 0.00 0.00 9.00 1007.31 2.87% R105 15.00 1416.57 5.00 0.00 0.00 0.00 15.40 1452.46 5.20 0.00 0.00 0.00 14.00 1377.11 2.87% R106 13.00 1294.79 6.00 0.00 0.00 0.00 13.50 1343.61 4.00 0.00 0.00 0.00 12.00 1252.03 3.42% R107 11.00 1132.22 9.00 0.00 0.00 0.00 11.50 1184.74 7.60 0.00 0.00 0.00 10.00 1104.66 2.49% R108 10.00 1010.67 12.00 0.00 0.00 0.00 10.20 1034.18 9.10 0.00 0.00 0.00 9.00 960.88 5.18% R109 12.00 1235.29 8.00 0.00 0.00 0.00 12.80 1276.52 6.20 0.00 0.00 0.00 11.00 1194.73 3.39% R110 11.00 1143.51 13.00 0.00 0.00 0.00 11.30 1199.50 10.50 0.00 0.00 0.00 10.00 1118.8 2.20% R111 11.00 1157.71 10.00 0.00 0.00 0.00 11.70 1190.06 7.60 0.00 0.00 0.00 10.00 1096.72 5.56% R112 10.00 1019.07 13.00 0.00 0.00 0.00 10.50 1055.22 10.70 0.00 0.00 0.00 9.00 982.14 3.76%

R1-Avg. 12.83 1239.01 8.00 0.00 0.00 0.00 13.46 2151.25 6.68 0.00 0.00 0.00 11.92 1210.34 2.53%

RC101 16.00 1699.38 5.00 0.00 0.00 0.00 16.40 1742.17 4.30 0.00 0.00 0.00 14.00 1696.94 0.14% RC102 14.00 1520.54 5.00 0.00 0.00 0.00 14.90 1590.75 4.70 0.00 0.00 0.00 12.00 1554.75 -2.20% RC103 12.00 1358.40 5.00 0.00 0.00 0.00 12.30 1402.67 5.70 0.00 0.00 0.00 11.00 1261.7 7.67% RC104 11.00 1201.87 8.00 0.00 0.00 0.00 11.00 1258.11 7.20 0.00 0.00 0.00 10.00 1135.48 5.85% RC105 15.00 1649.90 7.00 0.00 0.00 0.00 16.10 1656.13 5.40 0.00 0.00 0.00 13.00 1629.44 1.26% RC106 13.00 1437.46 3.00 0.00 0.00 0.00 13.30 1490.11 5.50 0.00 0.00 0.00 11.00 1424.73 0.89% RC107 12.00 1331.07 9.00 0.00 0.00 0.00 12.20 1365.74 7.00 0.00 0.00 0.00 11.00 1230.48 8.17% RC108 11.00 1193.62 7.00 0.00 0.00 0.00 11.10 1242.74 9.10 0.00 0.00 0.00 10.00 1139.82 4.72%

RC1-Avg. 13.00 1424.03 6.13 0.00 0.00 0.00 13.41 1468.55 6.11 0.00 0.00 0.00 11.50 1384.16 3.31%

C201 3.00 591.56 47.00 0.00 0.00 0.00 3.00 32762300.00 50.50 32.76 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 53.00 0.00 0.00 0.00 3.00 615.22 56.20 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 617.57 59.00 0.00 0.00 0.00 3.40 644.98 50.40 0.00 0.00 0.00 3.00 591.17 4.47% C204 3.00 617.23 46.00 0.00 0.00 0.00 3.50 669.90 34.00 0.00 0.00 0.00 3.00 590.6 4.51% C205 3.00 588.88 63.00 0.00 0.00 0.00 3.00 613.72 51.60 0.00 0.00 0.00 3.00 588.88 0.00% C206 3.00 588.49 47.00 0.00 0.00 0.00 3.00 588.49 48.50 0.00 0.00 0.00 3.00 588.5 0.00% C207 3.00 588.29 56.00 0.00 0.00 0.00 3.00 588.98 72.80 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 83.00 0.00 0.00 0.00 3.00 642.36 86.10 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 596.49 56.75 0.00 0.00 0.00 3.11 4095832.96 56.26 4.10 0.00 0.00 3.00 589.86 1.12%

R201 4.00 1318.86 152.00 0.00 0.00 0.00 4.10 1343.63 72.00 0.00 0.00 0.00 4.00 1252.37 5.31% R202 4.00 1151.55 149.00 0.00 0.00 0.00 4.00 1197.09 84.60 0.00 0.00 0.00 3.00 1191.7 -3.37% R203 3.00 1031.24 113.00 0.00 0.00 0.00 3.40 1033.19 72.60 0.00 0.00 0.00 3.00 939.5 9.76% R204 3.00 803.23 97.00 0.00 0.00 0.00 3.00 856.92 94.10 0.00 0.00 0.00 2.00 825.52 -2.70% R205 3.00 1096.60 95.00 0.00 0.00 0.00 3.30 1123.79 79.30 0.00 0.00 0.00 3.00 994.42 10.28% R206 3.00 986.07 108.00 0.00 0.00 0.00 3.50 1011.40 72.60 0.00 0.00 0.00 3.00 906.14 8.82% R207 3.00 876.05 31.00 0.00 0.00 0.00 3.00 951.39 122.60 0.00 0.00 0.00 2.00 890.6 -1.63% R208 2.00 786.94 220.00 0.00 0.00 0.00 2.70 785.66 118.20 0.00 0.00 0.00 2.00 726.82 8.27% R209 3.00 1095.86 141.00 0.00 0.00 0.00 3.80 1007.17 62.60 0.00 0.00 0.00 3.00 909.16 20.54% R210 3.00 1027.94 107.00 0.00 0.00 0.00 3.80 1018.28 57.50 0.00 0.00 0.00 3.00 939.37 9.43% R211 3.00 872.78 120.00 0.00 0.00 0.00 3.60 863.99 60.80 0.00 0.00 0.00 2.00 885.71 -1.46%

R2-Avg. 3.09 1004.28 121.18 0.00 0.00 0.00 3.47 1017.50 81.54 0.00 0.00 0.00 2.73 951.03 5.75%

RC201 4.00 1532.55 70.00 0.00 0.00 0.00 4.10 1567.52 72.00 0.00 0.00 0.00 4.00 1406.94 8.93% RC202 4.00 1279.83 29.00 0.00 0.00 0.00 4.00 1362.48 54.70 0.00 0.00 0.00 3.00 1365.65 -6.28% RC203 3.00 1167.56 96.00 0.00 0.00 0.00 3.30 1190.55 75.00 0.00 0.00 0.00 3.00 1049.62 11.24% RC204 3.00 842.68 90.00 0.00 0.00 0.00 3.00 932.27 82.60 0.00 0.00 0.00 3.00 798.46 5.54% RC205 4.00 1394.79 104.00 0.00 0.00 0.00 4.00 1466.12 73.60 0.00 0.00 0.00 4.00 1297.7 7.49% RC206 3.00 1277.36 88.00 0.00 0.00 0.00 3.60 1271.60 62.80 0.00 0.00 0.00 3.00 1146.32 11.43% RC207 3.00 1173.90 62.00 0.00 0.00 0.00 3.50 1188.61 78.90 0.00 0.00 0.00 3.00 1061.14 10.63% RC208 3.00 948.88 80.00 0.00 0.00 0.00 3.50 953.06 60.40 0.00 0.00 0.00 3.00 828.14 14.58%

RC2-Avg. 3.38 1202.19 77.38 0.00 0.00 0.00 3.63 1241.53 70.00 0.00 0.00 0.00 3.25 1119.24 7.94%

64 B.1. Computational Experiments

Table B10.: Detailed Test Result ILS with RIS and BF for the VRPTW

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 13.00 0.00 0.00 0.00 10.00 836.63 11.30 0.00 0.00 0.00 10.00 828.94 0.00% C102 10.00 828.94 5.00 0.00 0.00 0.00 10.00 979.22 5.10 0.00 0.00 0.00 10.00 828.94 0.00% C103 10.00 956.24 3.00 0.00 0.00 0.00 10.00 1104.55 4.70 0.00 0.00 0.00 10.00 828.06 15.48% C104 10.00 906.98 3.00 0.00 0.00 0.00 10.00 1014.69 5.00 0.00 0.00 0.00 10.00 824.78 9.97% C105 10.00 828.94 3.00 0.00 0.00 0.00 10.00 834.35 5.10 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 9.00 0.00 0.00 0.00 10.10 855.38 7.10 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 4.00 0.00 0.00 0.00 10.00 6609850.00 6.80 6.61 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 3.00 0.00 0.00 0.00 10.10 857.06 7.10 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 863.33 10.00 0.00 0.00 0.00 10.00 999.11 6.00 0.00 0.00 0.00 10.00 828.94 4.15%

C1-Avg. 10.00 855.57 5.89 0.00 0.00 0.00 10.02 735259.00 6.47 0.73 0.00 0.00 10.00 828.38 3.29%

R101 20.00 1669.94 2.00 0.00 0.00 0.00 20.90 1693.64 1.90 0.00 0.00 0.00 19.00 1650.80 1.16% R102 18.00 1497.06 2.00 0.00 0.00 0.00 18.60 1524.82 2.50 0.00 0.00 0.00 17.00 1486.12 0.74% R103 14.00 1234.38 6.00 0.00 0.00 0.00 14.80 425559.00 3.50 0.42 0.00 0.00 13.00 1292.68 -4.51% R104 10.00 1051.02 7.00 0.00 0.00 0.00 10.90 1071.35 5.20 0.00 0.00 0.00 9.00 1007.31 4.34% R105 14.00 1467.05 2.00 0.00 0.00 0.00 15.30 1447.18 2.60 0.00 0.00 0.00 14.00 1377.11 6.53% R106 13.00 1290.46 2.00 0.00 0.00 0.00 13.90 1330.86 2.50 0.00 0.00 0.00 12.00 1252.03 3.07% R107 11.00 1108.31 6.00 0.00 0.00 0.00 11.10 1171.10 5.60 0.00 0.00 0.00 10.00 1104.66 0.33% R108 10.00 994.82 5.00 0.00 0.00 0.00 10.20 1029.37 4.50 0.00 0.00 0.00 9.00 960.88 3.53% R109 12.00 1209.14 8.00 0.00 0.00 0.00 13.10 1273.43 2.70 0.00 0.00 0.00 11.00 1194.73 1.21% R110 11.00 1193.15 8.00 0.00 0.00 0.00 11.70 1196.98 6.40 0.00 0.00 0.00 10.00 1118.80 6.64% R111 11.00 1133.70 3.00 0.00 0.00 0.00 11.60 1167.16 6.00 0.00 0.00 0.00 10.00 1096.72 3.37% R112 10.00 1006.71 6.00 0.00 0.00 0.00 10.30 1049.76 6.70 0.00 0.00 0.00 9.00 982.14 2.50%

R1-Avg. 12.83 1237.98 4.75 0.00 0.00 0.00 13.53 36626.22 4.18 0.04 0.00 0.00 11.92 1210.34 2.41%

RC101 16.00 1722.30 5.00 0.00 0.00 0.00 16.60 1774.26 2.80 0.00 0.00 0.00 14.00 1696.94 1.49% RC102 14.00 1511.98 5.00 0.00 0.00 0.00 14.50 278612.00 4.80 0.28 0.00 0.00 12.00 1554.75 -2.75% RC103 12.00 1321.61 7.00 0.00 0.00 0.00 12.10 1382.37 5.50 0.00 0.00 0.00 11.00 1261.70 4.75% RC104 10.00 1255.62 9.00 0.00 0.00 0.00 10.90 1240.42 7.10 0.00 0.00 0.00 10.00 1135.48 10.58% RC105 15.00 1626.15 4.00 0.00 0.00 0.00 16.10 1663.13 4.50 0.00 0.00 0.00 13.00 1629.44 -0.20% RC106 13.00 1427.79 4.00 0.00 0.00 0.00 13.60 1209050.00 3.60 1.21 0.00 0.00 11.00 1424.73 0.21% RC107 11.00 1317.06 16.00 0.00 0.00 0.00 12.00 1347.25 7.10 0.00 0.00 0.00 11.00 1230.48 7.04% RC108 11.00 1182.20 3.00 0.00 0.00 0.00 11.30 1252.64 4.00 0.00 0.00 0.00 10.00 1139.82 3.72%

RC1-Avg. 12.75 1420.59 6.63 0.00 0.00 0.00 13.39 187040.26 4.93 0.19 0.00 0.00 11.50 1384.16 3.11%

C201 3.00 591.56 52.00 0.00 0.00 0.00 3.00 597.55 69.60 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 82.00 0.00 0.00 0.00 3.10 634.97 65.20 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 607.55 59.00 0.00 0.00 0.00 3.30 650.58 61.90 0.00 0.00 0.00 3.00 591.17 2.77% C204 3.00 614.88 95.00 0.00 0.00 0.00 3.50 663.24 66.70 0.00 0.00 0.00 3.00 590.60 4.11% C205 3.00 588.88 87.00 0.00 0.00 0.00 3.00 617.61 86.80 0.00 0.00 0.00 3.00 588.88 0.00% C206 3.00 588.49 45.00 0.00 0.00 0.00 3.10 595.43 51.70 0.00 0.00 0.00 3.00 588.50 0.00% C207 3.00 588.29 53.00 0.00 0.00 0.00 3.00 604.49 55.20 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 48.00 0.00 0.00 0.00 3.00 644.77 64.70 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 594.94 65.13 0.00 0.00 0.00 3.13 626.08 65.23 0.00 0.00 0.00 3.00 589.86 0.86%

R201 4.00 1322.27 59.00 0.00 0.00 0.00 4.00 1352.69 50.30 0.00 0.00 0.00 4.00 1252.37 5.58% R202 3.00 1249.06 111.00 0.00 0.00 0.00 3.80 1213.50 67.50 0.00 0.00 0.00 3.00 1191.70 4.81% R203 3.00 987.16 110.00 0.00 0.00 0.00 3.20 1042.43 72.60 0.00 0.00 0.00 3.00 939.50 5.07% R204 2.00 886.99 332.00 0.00 0.00 0.00 2.90 884.78 97.40 0.00 0.00 0.00 2.00 825.52 7.45% R205 3.00 1089.62 91.00 0.00 0.00 0.00 3.60 1133.35 46.00 0.00 0.00 0.00 3.00 994.42 9.57% R206 3.00 987.27 68.00 0.00 0.00 0.00 3.70 1017.14 38.30 0.00 0.00 0.00 3.00 906.14 8.95% R207 3.00 894.23 82.00 0.00 0.00 0.00 3.00 965.60 93.70 0.00 0.00 0.00 2.00 890.60 0.41% R208 3.00 743.27 48.00 0.00 0.00 0.00 3.00 785.73 59.30 0.00 0.00 0.00 2.00 726.82 2.26% R209 3.00 1011.61 92.00 0.00 0.00 0.00 3.40 1033.37 63.10 0.00 0.00 0.00 3.00 909.16 11.27% R210 3.00 1068.54 78.00 0.00 0.00 0.00 3.70 1035.88 43.90 0.00 0.00 0.00 3.00 939.37 13.75% R211 3.00 867.13 58.00 0.00 0.00 0.00 3.40 888.76 44.30 0.00 0.00 0.00 2.00 885.71 -2.10%

R2-Avg. 3.00 1009.74 102.64 0.00 0.00 0.00 3.43 1032.11 61.49 0.00 0.00 0.00 2.73 951.03 6.09%

RC201 4.00 1502.45 52.00 0.00 0.00 0.00 4.10 1565.18 38.80 0.00 0.00 0.00 4.00 1406.94 6.79% RC202 4.00 1283.82 33.00 0.00 0.00 0.00 4.00 1333.37 42.30 0.00 0.00 0.00 3.00 1365.65 -5.99% RC203 3.00 1183.50 102.00 0.00 0.00 0.00 3.50 1183.38 56.50 0.00 0.00 0.00 3.00 1049.62 12.76% RC204 3.00 867.63 63.00 0.00 0.00 0.00 3.00 960.70 82.30 0.00 0.00 0.00 3.00 798.46 8.66% RC205 4.00 1420.67 38.00 0.00 0.00 0.00 4.00 1497.88 48.60 0.00 0.00 0.00 4.00 1297.70 9.48% RC206 3.00 1312.97 80.00 0.00 0.00 0.00 3.80 1302.17 50.50 0.00 0.00 0.00 3.00 1146.32 14.54% RC207 3.00 1192.46 160.00 0.00 0.00 0.00 3.70 1149.65 61.30 0.00 0.00 0.00 3.00 1061.14 12.38% RC208 3.00 933.98 71.00 0.00 0.00 0.00 3.60 957.80 44.10 0.00 0.00 0.00 3.00 828.14 12.78%

RC2-Avg. 3.38 1212.18 74.88 0.00 0.00 0.00 3.71 1243.77 53.05 0.00 0.00 0.00 3.25 1119.24 8.92%

65 Appendix B

Table B11.: Detailed Test Result ILS with TO-NNB Heuristic and FF for the VRPSTW

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 11.00 0.00 0.00 0.00 10.00 828.94 7.40 0.00 0.00 0.00 10.00 828.94 0.00% C102 10.00 832.46 10.00 0.00 0.00 0.00 10.00 972.88 7.80 0.00 0.00 0.00 10.00 828.94 0.42% C103 10.00 881.69 3.00 0.00 0.00 0.00 10.00 1071.03 4.60 0.00 0.00 0.00 10.00 828.06 6.48% C104 10.00 861.94 3.00 0.00 0.00 0.00 10.00 1008.38 3.40 0.00 0.00 0.00 10.00 824.78 4.51% C105 10.00 828.94 3.00 0.00 0.00 0.00 10.70 909.23 3.80 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 3.00 0.00 0.00 0.00 10.50 897.01 4.10 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 4.00 0.00 0.00 0.00 10.00 892.72 7.30 0.00 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 15.00 0.00 0.00 0.00 10.40 879.37 5.00 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 828.94 3.00 0.00 0.00 0.00 10.00 892.92 6.20 0.00 0.00 0.00 10.00 828.94 0.00%

C1-Avg. 10.00 838.86 6.11 0.00 0.00 0.00 10.18 928.05 5.51 0.00 0.00 0.00 10.00 828.38 1.27%

R101 19.00 1664.82 1.00 0.30 0.00 0.00 19.60 1737.60 1.20 0.70 0.00 0.00 19.00 1650.80 0.85% R102 17.00 1527.87 1.00 0.42 0.00 0.00 18.10 1552.44 1.60 0.59 0.00 0.00 17.00 1486.12 2.81% R103 14.00 1302.77 3.00 0.00 0.00 0.00 15.00 1293.86 2.00 0.00 0.00 0.00 13.00 1292.68 0.78% R104 11.00 1047.02 7.00 0.00 0.00 0.00 11.10 1070.88 4.60 0.00 0.00 0.00 9.00 1007.31 3.94% R105 15.00 1434.99 3.00 0.00 0.00 0.00 15.30 1481.67 1.80 0.02 0.00 0.00 14.00 1377.11 4.20% R106 13.00 1293.82 5.00 0.00 0.00 0.00 13.20 1298.53 2.50 0.00 0.00 0.00 12.00 1252.03 3.34% R107 11.00 1131.27 3.00 0.00 0.00 0.00 11.50 1190.25 3.00 0.16 0.00 0.00 10.00 1104.66 2.41% R108 10.00 1015.40 3.00 0.00 0.00 0.00 10.30 1047.85 3.60 0.00 0.00 0.00 9.00 960.88 5.67% R109 12.00 1245.57 8.00 0.00 0.00 0.00 12.80 1285.69 5.30 0.00 0.00 0.00 11.00 1194.73 4.26% R110 12.00 1158.89 2.00 0.00 0.00 0.00 12.10 1198.19 2.60 0.00 0.00 0.00 10.00 1118.80 3.58% R111 11.00 1131.59 3.00 0.00 0.00 0.00 11.90 1154.94 4.10 0.00 0.00 0.00 10.00 1096.72 3.18% R112 10.00 1047.62 4.00 0.00 0.00 0.00 10.90 1049.91 3.10 0.00 0.00 0.00 9.00 982.14 6.67%

R1-Avg. 12.92 1250.14 3.58 0.06 0.00 0.00 13.48 1280.15 2.95 0.12 0.00 0.00 11.92 1210.34 3.47%

RC101 15.00 1703.12 1.00 0.00 0.00 0.00 16.00 1763.33 1.60 0.20 0.00 0.00 14.00 1696.94 0.36% RC102 14.00 1557.18 4.00 0.00 0.00 0.00 14.30 1591.43 2.90 0.14 0.00 0.00 12.00 1554.75 0.16% RC103 12.00 1344.17 3.00 0.00 0.00 0.00 12.60 1419.18 3.00 0.09 0.00 0.00 11.00 1261.70 6.54% RC104 11.00 1170.37 4.00 0.00 0.00 0.00 11.00 1245.65 4.80 0.08 0.00 0.00 10.00 1135.48 3.07% RC105 15.00 1645.40 9.00 0.00 0.00 0.00 15.50 1747.05 5.60 1.17 0.00 0.00 13.00 1629.44 0.98% RC106 13.00 1442.49 5.00 0.00 0.00 0.00 13.20 1493.62 4.60 0.16 0.00 0.00 11.00 1424.73 1.25% RC107 11.00 1414.65 5.00 0.26 0.00 0.00 12.30 1373.86 2.40 0.10 0.00 0.00 11.00 1230.48 14.97% RC108 11.00 1209.08 10.00 0.02 0.00 0.00 11.10 1239.64 7.20 0.00 0.00 0.00 10.00 1139.82 6.08%

RC1-Avg. 12.75 1435.81 5.13 0.03 0.00 0.00 13.25 1484.22 4.01 0.24 0.00 0.00 11.50 1384.16 4.18%

C201 3.00 591.56 75.00 0.00 0.00 0.00 3.00 594.55 53.20 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 67.00 0.00 0.00 0.00 3.00 626.54 69.00 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 600.21 95.00 0.00 0.00 0.00 3.10 628.58 55.70 0.00 0.00 0.00 3.00 591.17 1.53% C204 3.00 613.87 90.00 0.00 0.00 0.00 3.40 679.99 48.90 0.00 0.00 0.00 3.00 590.60 3.94% C205 3.00 609.36 76.00 0.00 0.00 0.00 3.00 609.36 51.00 0.00 0.00 0.00 3.00 588.88 3.48% C206 3.00 588.49 77.00 0.00 0.00 0.00 3.00 599.86 57.80 0.00 0.00 0.00 3.00 588.50 0.00% C207 3.00 588.29 52.00 0.00 0.00 0.00 3.00 599.93 56.00 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 46.00 0.00 0.00 0.00 3.00 588.32 50.60 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 596.46 72.25 0.00 0.00 0.00 3.06 615.89 55.28 0.00 0.00 0.00 3.00 589.86 1.12%

R201 4.00 1334.80 24.00 0.00 0.00 0.00 4.00 1391.03 38.30 0.00 0.00 0.00 4.00 1252.37 6.58% R202 3.00 1246.43 71.00 0.00 0.00 0.00 3.80 1215.52 54.80 0.00 0.00 0.00 3.00 1191.70 4.59% R203 3.00 971.48 45.00 0.00 0.00 0.00 3.20 1045.55 47.30 0.00 0.00 0.00 3.00 939.50 3.40% R204 3.00 800.21 38.00 0.00 0.00 0.00 3.00 846.46 40.60 0.00 0.00 0.00 2.00 825.52 -3.07% R205 3.00 1112.66 80.00 0.00 0.00 0.00 3.70 1107.11 37.00 0.00 0.00 0.00 3.00 994.42 11.89% R206 3.00 994.68 51.00 0.00 0.00 0.00 3.30 1035.17 52.30 0.00 0.00 0.00 3.00 906.14 9.77% R207 3.00 887.10 52.00 0.00 0.00 0.00 3.00 935.13 67.80 0.00 0.00 0.00 2.00 890.60 -0.39% R208 2.00 796.99 290.00 0.00 0.00 0.00 2.60 794.77 115.10 0.00 0.00 0.00 2.00 726.82 9.65% R209 3.00 1002.53 71.00 0.00 0.00 0.00 3.70 1016.11 45.40 0.01 0.00 0.00 3.00 909.16 10.27% R210 3.00 1037.73 58.00 0.00 0.00 0.00 3.60 1040.89 50.90 0.00 0.00 0.00 3.00 939.37 10.47% R211 3.00 817.47 75.00 0.00 0.00 0.00 3.40 864.52 60.10 0.00 0.00 0.00 2.00 885.71 -7.70%

R2-Avg. 3.00 1000.19 77.73 0.00 0.00 0.00 3.39 1026.57 55.42 0.00 0.00 0.00 2.73 951.03 5.04%

RC201 4.00 1493.53 98.00 0.00 0.00 0.00 4.30 1525.12 69.00 0.00 0.00 0.00 4.00 1406.94 6.15% RC202 4.00 1249.66 68.00 0.00 0.00 0.00 4.00 1320.65 45.00 0.00 0.00 0.00 3.00 1365.65 -8.49% RC203 3.00 1201.18 100.00 0.00 0.00 0.00 3.50 1193.93 70.10 0.00 0.00 0.00 3.00 1049.62 14.44% RC204 3.00 851.64 39.00 0.00 0.00 0.00 3.00 908.96 46.50 0.00 0.00 0.00 3.00 798.46 6.66% RC205 4.00 1389.70 27.00 0.00 0.00 0.00 4.00 1492.35 53.00 0.01 0.00 0.00 4.00 1297.70 7.09% RC206 3.00 1296.52 87.00 0.00 0.00 0.00 3.60 1291.26 67.40 0.00 0.00 0.00 3.00 1146.32 13.10% RC207 3.00 1270.85 108.00 0.00 0.00 0.00 3.90 1159.03 47.10 0.00 0.00 0.00 3.00 1061.14 19.76% RC208 3.00 987.97 46.00 0.00 0.00 0.00 3.80 941.35 38.10 0.00 0.00 0.00 3.00 828.14 19.30%

RC2-Avg. 3.38 1217.63 71.63 0.00 0.00 0.00 3.76 1229.08 54.53 0.00 0.00 0.00 3.25 1119.24 9.75%

66 B.1. Computational Experiments

Table B12.: Detailed Test Result ILS with TO-NNB Heuristic and BF for the VRPSTW

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 10.00 0.00 0.00 0.00 10.00 828.94 5.50 0.00 0.00 0.00 10.00 828.94 0.00% C102 10.00 834.64 3.00 0.00 0.00 0.00 10.00 964.54 4.50 0.00 0.00 0.00 10.00 828.94 0.69% C103 10.00 838.77 3.00 0.00 0.00 0.00 10.00 1056.93 4.10 0.00 0.00 0.00 10.00 828.06 1.29% C104 10.00 938.68 3.00 0.00 0.00 0.00 10.00 1041.38 4.10 0.00 0.00 0.00 10.00 824.78 13.81% C105 10.00 828.94 7.00 0.00 0.00 0.00 10.30 863.49 4.10 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 7.00 0.00 0.00 0.00 10.30 860.23 4.40 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 3.00 0.00 0.00 0.00 10.00 840.58 3.80 0.00 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 7.00 0.00 0.00 0.00 10.30 902.33 4.70 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 828.94 5.00 0.00 0.00 0.00 10.00 873.61 4.70 0.00 0.00 0.00 10.00 828.94 0.00%

C1-Avg. 10.00 842.86 5.33 0.00 0.00 0.00 10.10 914.67 4.43 0.00 0.00 0.00 10.00 828.38 1.75%

R101 18.00 1679.00 3.00 0.30 0.00 0.00 19.20 1733.63 2.80 0.69 0.00 0.00 19.00 1650.80 1.71% R102 17.00 1509.34 6.00 0.42 0.00 0.00 17.70 1565.41 2.80 0.76 0.00 0.00 17.00 1486.12 1.56% R103 14.00 1266.91 7.00 0.00 0.00 0.00 14.90 1290.65 1.90 0.00 0.00 0.00 13.00 1292.68 -1.99% R104 10.00 1064.86 7.00 0.00 0.00 0.00 10.70 1075.27 5.20 0.00 0.00 0.00 9.00 1007.31 5.71% R105 15.00 1415.99 4.00 0.00 0.00 0.00 15.20 1452.49 2.80 0.00 0.00 0.00 14.00 1377.11 2.82% R106 13.00 1284.10 5.00 0.00 0.00 0.00 13.00 1309.14 4.20 0.00 0.00 0.00 12.00 1252.03 2.56% R107 11.00 1131.41 3.00 0.00 0.00 0.00 11.40 1170.20 4.40 0.00 0.00 0.00 10.00 1104.66 2.42% R108 10.00 1016.23 10.00 0.00 0.00 0.00 10.20 1044.95 5.70 0.00 0.00 0.00 9.00 960.88 5.76% R109 12.00 1274.08 6.00 0.00 0.00 0.00 13.00 1295.77 3.70 0.00 0.00 0.00 11.00 1194.73 6.64% R110 11.00 1233.50 4.00 0.00 0.00 0.00 12.20 1188.06 2.80 0.00 0.00 0.00 10.00 1118.80 10.25% R111 11.00 1281.05 4.00 1.22 0.00 0.00 12.10 1170.41 2.80 0.12 0.00 0.00 10.00 1096.72 16.81% R112 10.00 1034.56 10.00 0.01 0.00 0.00 10.60 1044.32 6.60 0.00 0.00 0.00 9.00 982.14 5.34%

R1-Avg. 12.67 1265.92 5.75 0.16 0.00 0.00 13.35 1278.36 3.81 0.13 0.00 0.00 11.92 1210.34 4.97%

RC101 15.00 1714.05 2.00 0.00 0.00 0.00 16.30 1762.12 2.80 0.01 0.00 0.00 14.00 1696.94 1.01% RC102 14.00 1570.00 5.00 0.29 0.00 0.00 14.70 1593.20 2.30 0.25 0.00 0.00 12.00 1554.75 0.98% RC103 12.00 1321.08 3.00 0.00 0.00 0.00 12.70 1395.27 3.90 0.00 0.00 0.00 11.00 1261.70 4.71% RC104 10.00 1245.21 5.00 0.00 0.00 0.00 11.00 1226.99 2.80 0.00 0.00 0.00 10.00 1135.48 9.66% RC105 15.00 1635.52 4.00 0.00 0.00 0.00 16.20 1682.92 2.10 0.28 0.00 0.00 13.00 1629.44 0.37% RC106 12.00 1784.52 4.00 3.11 0.00 0.00 13.00 1531.67 3.70 0.47 0.00 0.00 11.00 1424.73 25.25% RC107 12.00 1325.86 6.00 0.00 0.00 0.00 12.20 1369.51 3.60 0.06 0.00 0.00 11.00 1230.48 7.75% RC108 11.00 1250.59 3.00 0.00 0.00 0.00 11.60 1265.03 3.30 0.00 0.00 0.00 10.00 1139.82 9.72%

RC1-Avg. 12.63 1480.85 4.00 0.42 0.00 0.00 13.46 1478.34 3.06 0.13 0.00 0.00 11.50 1384.16 7.43%

C201 3.00 591.56 60.00 0.00 0.00 0.00 3.00 597.55 51.80 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 48.00 0.00 0.00 0.00 3.10 620.86 54.60 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 600.21 52.00 0.00 0.00 0.00 3.20 644.40 53.00 0.00 0.00 0.00 3.00 591.17 1.53% C204 3.00 619.91 50.00 0.00 0.00 0.00 3.40 659.49 49.10 0.00 0.00 0.00 3.00 590.60 4.96% C205 3.00 609.36 45.00 0.00 0.00 0.00 3.00 609.36 44.30 0.00 0.00 0.00 3.00 588.88 3.48% C206 3.00 588.49 37.00 0.00 0.00 0.00 3.00 588.49 46.40 0.00 0.00 0.00 3.00 588.50 0.00% C207 3.00 588.29 61.00 0.00 0.00 0.00 3.00 588.63 50.50 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 41.00 0.00 0.00 0.00 3.00 588.32 47.10 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 597.21 49.25 0.00 0.00 0.00 3.09 612.14 49.60 0.00 0.00 0.00 3.00 589.86 1.25%

R201 4.00 1331.61 34.00 0.00 0.00 0.00 4.10 1376.29 32.30 0.00 0.00 0.00 4.00 1252.37 6.33% R202 3.00 1281.82 134.00 0.00 0.00 0.00 3.80 1198.43 54.50 0.00 0.00 0.00 3.00 1191.70 7.56% R203 3.00 1028.03 75.00 0.00 0.00 0.00 3.40 1031.20 49.70 0.00 0.00 0.00 3.00 939.50 9.42% R204 3.00 810.40 55.00 0.00 0.00 0.00 3.00 835.90 74.10 0.00 0.00 0.00 2.00 825.52 -1.83% R205 3.00 1094.21 56.00 0.00 0.00 0.00 3.40 1124.11 45.60 0.00 0.00 0.00 3.00 994.42 10.03% R206 3.00 998.72 58.00 0.00 0.00 0.00 3.40 1025.36 43.40 0.00 0.00 0.00 3.00 906.14 10.22% R207 3.00 899.60 39.00 0.00 0.00 0.00 3.00 947.99 49.00 0.00 0.00 0.00 2.00 890.60 1.01% R208 2.00 758.44 145.00 0.00 0.00 0.00 2.70 774.04 80.10 0.00 0.00 0.00 2.00 726.82 4.35% R209 3.00 999.77 65.00 0.00 0.00 0.00 3.70 1015.82 38.00 0.00 0.00 0.00 3.00 909.16 9.97% R210 3.00 1064.21 50.00 0.00 0.00 0.00 3.50 1062.91 42.10 0.00 0.00 0.00 3.00 939.37 13.29% R211 3.00 871.71 45.00 0.00 0.00 0.00 3.70 872.17 35.40 0.00 0.00 0.00 2.00 885.71 -1.58%

R2-Avg. 3.00 1012.59 68.73 0.00 0.00 0.00 3.43 1024.02 49.47 0.00 0.00 0.00 2.73 951.03 6.25%

RC201 4.00 1527.33 61.00 0.00 0.00 0.00 4.00 1566.53 46.50 0.00 0.00 0.00 4.00 1406.94 8.56% RC202 4.00 1242.33 35.00 0.00 0.00 0.00 4.00 1335.59 58.20 0.00 0.00 0.00 3.00 1365.65 -9.03% RC203 3.00 1173.15 50.00 0.00 0.00 0.00 3.40 1221.26 46.50 0.00 0.00 0.00 3.00 1049.62 11.77% RC204 3.00 871.58 42.00 0.00 0.00 0.00 3.00 949.19 45.50 0.00 0.00 0.00 3.00 798.46 9.16% RC205 4.00 1422.84 28.00 0.00 0.00 0.00 4.00 1485.78 46.60 0.00 0.00 0.00 4.00 1297.70 9.65% RC206 3.00 1291.04 55.00 0.00 0.00 0.00 3.90 1273.89 37.30 0.00 0.00 0.00 3.00 1146.32 12.62% RC207 3.00 1147.33 83.00 0.00 0.00 0.00 3.60 1179.94 51.50 0.00 0.00 0.00 3.00 1061.14 8.12% RC208 3.00 927.44 73.00 0.00 0.00 0.00 3.60 961.70 45.10 0.00 0.00 0.00 3.00 828.14 11.99%

RC2-Avg. 3.38 1200.38 53.38 0.00 0.00 0.00 3.69 1246.73 47.15 0.00 0.00 0.00 3.25 1119.24 7.85%

67 Appendix B

Table B13.: Detailed Test Result ILS with RIS and FF for the VRPSTW

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 8.00 0.00 0.00 0.00 10.00 38491.90 6.50 374.60 0.00 0.00 10.00 828.94 0.00% C102 10.00 859.00 8.00 0.00 0.00 0.00 10.00 1428.99 6.80 3.71 0.00 0.00 10.00 828.94 3.63% C103 10.00 972.06 12.00 0.00 0.00 0.00 10.00 1059.64 4.90 0.00 0.00 0.00 10.00 828.06 17.39% C104 10.00 878.69 9.00 0.00 0.00 0.00 10.00 996.74 6.80 0.00 0.00 0.00 10.00 824.78 6.54% C105 10.00 828.94 4.00 0.00 0.00 0.00 10.20 865.00 9.90 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 10.00 0.00 0.00 0.00 10.30 883.03 7.50 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 4.00 0.00 0.00 0.00 10.00 2481.68 6.20 14.57 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 8.00 0.00 0.00 0.00 10.10 875.22 8.10 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 829.39 8.00 0.00 0.00 0.00 10.00 978.60 6.60 0.00 0.00 0.00 10.00 828.94 0.05%

C1-Avg. 10.00 853.76 7.89 0.00 0.00 0.00 10.07 5340.09 7.03 43.65 0.00 0.00 10.00 828.38 3.07%

R101 19.00 1674.87 2.00 0.00 0.00 0.00 19.70 1696.44 3.40 0.13 0.00 0.00 19.00 1650.80 1.46% R102 17.00 1547.03 5.00 0.42 0.00 0.00 17.60 1613.71 5.50 0.98 0.00 0.00 17.00 1486.12 4.10% R103 14.00 1243.12 2.00 0.00 0.00 0.00 14.90 1302.84 3.10 0.00 0.00 0.00 13.00 1292.68 -3.83% R104 10.00 1071.59 10.00 0.00 0.00 0.00 10.80 1088.00 9.10 0.00 0.00 0.00 9.00 1007.31 6.38% R105 15.00 1416.99 3.00 0.00 0.00 0.00 15.50 1450.35 1.50 0.00 0.00 0.00 14.00 1377.11 2.90% R106 12.00 1385.45 3.00 0.39 0.00 0.00 13.40 1351.27 2.50 0.04 0.00 0.00 12.00 1252.03 10.66% R107 11.00 1130.33 3.00 0.00 0.00 0.00 11.80 1171.68 2.90 0.01 0.00 0.00 10.00 1104.66 2.32% R108 10.00 991.60 3.00 0.00 0.00 0.00 10.30 1030.52 3.80 0.00 0.00 0.00 9.00 960.88 3.20% R109 12.00 1269.23 4.00 0.00 0.00 0.00 12.90 1273.01 2.30 0.02 0.00 0.00 11.00 1194.73 6.24% R110 11.00 1176.75 7.00 0.00 0.00 0.00 11.90 1193.54 5.70 0.00 0.00 0.00 10.00 1118.80 5.18% R111 11.00 1168.27 7.00 0.00 0.00 0.00 11.90 1173.06 5.70 0.01 0.00 0.00 10.00 1096.72 6.52% R112 10.00 1026.10 5.00 0.00 0.00 0.00 10.60 1063.58 9.00 0.00 0.00 0.00 9.00 982.14 4.48%

R1-Avg. 12.67 1258.44 4.50 0.07 0.00 0.00 13.44 1284.00 4.54 0.10 0.00 0.00 11.92 1210.34 4.13%

RC101 15.00 1748.43 7.00 0.00 0.00 0.00 16.00 1795.24 4.20 0.42 0.00 0.00 14.00 1696.94 3.03% RC102 13.00 1628.43 10.00 0.86 0.00 0.00 14.20 1591.23 6.10 0.20 0.00 0.00 12.00 1554.75 4.74% RC103 12.00 1344.68 12.00 0.00 0.00 0.00 12.40 1422.64 7.20 0.26 0.00 0.00 11.00 1261.70 6.58% RC104 10.00 1238.45 15.00 0.00 0.00 0.00 11.00 1251.56 8.60 0.00 0.00 0.00 10.00 1135.48 9.07% RC105 14.00 1590.53 6.00 0.00 0.00 0.00 15.60 1695.37 4.60 0.67 0.00 0.00 13.00 1629.44 -2.39% RC106 13.00 1479.64 9.00 0.00 0.00 0.00 13.60 1520.86 5.50 0.00 0.00 0.00 11.00 1424.73 3.85% RC107 12.00 1300.21 6.00 0.00 0.00 0.00 12.20 1366.14 7.30 0.09 0.00 0.00 11.00 1230.48 5.67% RC108 11.00 1191.72 6.00 0.00 0.00 0.00 11.40 1230.76 7.40 0.00 0.00 0.00 10.00 1139.82 4.55%

RC1-Avg. 12.50 1440.26 8.88 0.11 0.00 0.00 13.30 1484.23 6.36 0.21 0.00 0.00 11.50 1384.16 4.39%

C201 3.00 591.56 95.00 0.00 0.00 0.00 3.00 597.55 66.00 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 75.00 0.00 0.00 0.00 3.00 619.37 119.50 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 600.54 47.00 0.00 0.00 0.00 3.00 626.47 69.40 0.00 0.00 0.00 3.00 591.17 1.59% C204 3.00 618.90 69.00 0.00 0.00 0.00 3.20 651.60 46.70 0.00 0.00 0.00 3.00 590.60 4.79% C205 3.00 588.88 48.00 0.00 0.00 0.00 3.00 604.72 45.90 0.00 0.00 0.00 3.00 588.88 0.00% C206 3.00 588.49 62.00 0.00 0.00 0.00 3.00 598.09 68.00 0.00 0.00 0.00 3.00 588.50 0.00% C207 3.00 588.29 75.00 0.00 0.00 0.00 3.00 588.29 68.20 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 44.00 0.00 0.00 0.00 3.00 624.66 55.30 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 594.57 64.38 0.00 0.00 0.00 3.03 613.84 67.38 0.00 0.00 0.00 3.00 589.86 0.80%

R201 4.00 1328.58 23.00 0.00 0.00 0.00 4.00 1386.63 37.90 0.00 0.00 0.00 4.00 1252.37 6.09% R202 4.00 1136.32 186.00 0.00 0.00 0.00 4.00 1170.63 73.30 0.00 0.00 0.00 3.00 1191.70 -4.65% R203 3.00 1039.19 94.00 0.00 0.00 0.00 3.50 1051.40 63.30 0.00 0.00 0.00 3.00 939.50 10.61% R204 3.00 814.41 60.00 0.00 0.00 0.00 3.00 866.46 140.60 0.00 0.00 0.00 2.00 825.52 -1.35% R205 3.00 1062.63 46.00 0.00 0.00 0.00 3.70 1094.92 35.50 0.00 0.00 0.00 3.00 994.42 6.86% R206 3.00 1010.16 46.00 0.00 0.00 0.00 3.50 1045.55 33.40 0.00 0.00 0.00 3.00 906.14 11.48% R207 3.00 872.98 68.00 0.00 0.00 0.00 3.00 948.28 49.80 0.00 0.00 0.00 2.00 890.60 -1.98% R208 3.00 760.94 80.00 0.00 0.00 0.00 3.00 787.92 53.60 0.00 0.00 0.00 2.00 726.82 4.69% R209 3.00 943.64 50.00 0.00 0.00 0.00 3.50 1008.64 56.70 0.00 0.00 0.00 3.00 909.16 3.79% R210 3.00 986.49 87.00 0.00 0.00 0.00 3.90 1034.59 37.10 0.00 0.00 0.00 3.00 939.37 5.02% R211 3.00 873.29 48.00 0.00 0.00 0.00 3.50 869.18 41.00 0.00 0.00 0.00 2.00 885.71 -1.40%

R2-Avg. 3.18 984.42 71.64 0.00 0.00 0.00 3.51 1024.02 56.56 0.00 0.00 0.00 2.73 951.03 3.56%

RC201 4.00 1485.91 31.00 0.00 0.00 0.00 4.10 1565.72 65.60 0.00 0.00 0.00 4.00 1406.94 5.61% RC202 4.00 1275.96 25.00 0.00 0.00 0.00 4.00 1347.81 36.20 0.00 0.00 0.00 3.00 1365.65 -6.57% RC203 3.00 1161.21 102.00 0.00 0.00 0.00 3.40 1171.64 59.50 0.00 0.00 0.00 3.00 1049.62 10.63% RC204 3.00 854.28 62.00 0.00 0.00 0.00 3.00 906.07 55.50 0.00 0.00 0.00 3.00 798.46 6.99% RC205 4.00 1376.46 45.00 0.00 0.00 0.00 4.00 1473.50 50.00 0.00 0.00 0.00 4.00 1297.70 6.07% RC206 4.00 1175.52 35.00 0.00 0.00 0.00 4.00 1248.75 53.60 0.00 0.00 0.00 3.00 1146.32 2.55% RC207 3.00 1218.44 128.00 0.00 0.00 0.00 3.70 1144.82 59.00 0.00 0.00 0.00 3.00 1061.14 14.82% RC208 3.00 998.08 92.00 0.00 0.00 0.00 3.60 944.97 54.60 0.01 0.00 0.00 3.00 828.14 20.52%

RC2-Avg. 3.50 1193.23 65.00 0.00 0.00 0.00 3.73 1225.41 54.25 0.00 0.00 0.00 3.25 1119.24 7.58%

68 B.1. Computational Experiments

Table B14.: Detailed Test Result ILS with RIS and BF for the VRPSTW

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 12.00 0.00 0.00 0.00 10.00 29966.50 13.30 289.82 0.00 0.00 10.00 828.94 0.00% C102 10.00 828.94 10.00 0.00 0.00 0.00 10.00 980.83 7.50 0.00 0.00 0.00 10.00 828.94 0.00% C103 10.00 951.53 9.00 0.00 0.00 0.00 10.00 1080.72 7.90 0.00 0.00 0.00 10.00 828.06 14.91% C104 10.00 920.93 10.00 0.00 0.00 0.00 10.00 976.05 7.50 0.00 0.00 0.00 10.00 824.78 11.66% C105 10.00 828.94 9.00 0.00 0.00 0.00 10.10 842.85 7.00 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 5.00 0.00 0.00 0.00 10.30 853.59 8.10 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 11.00 0.00 0.00 0.00 10.00 2766.55 10.30 16.37 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 3.00 0.00 0.00 0.00 10.20 889.42 7.80 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 828.94 7.00 0.00 0.00 0.00 10.00 960.47 5.50 0.00 0.00 0.00 10.00 828.94 0.00%

C1-Avg. 10.00 852.78 8.44 0.00 0.00 0.00 10.07 4368.55 8.32 34.02 0.00 0.00 10.00 828.38 2.95%

R101 19.00 1672.24 3.00 0.42 0.00 0.00 20.30 1868.93 2.10 1.77 0.00 0.00 19.00 1650.80 1.30% R102 18.00 1523.62 3.00 0.00 0.00 0.00 18.30 1574.41 2.30 0.53 0.00 0.00 17.00 1486.12 2.52% R103 14.00 1291.39 3.00 0.00 0.00 0.00 15.00 1294.53 4.10 0.00 0.00 0.00 13.00 1292.68 -0.10% R104 10.00 1035.62 7.00 0.00 0.00 0.00 11.10 1079.83 4.50 0.13 0.00 0.00 9.00 1007.31 2.81% R105 15.00 1407.67 5.00 0.00 0.00 0.00 15.50 1445.26 2.80 0.00 0.00 0.00 14.00 1377.11 2.22% R106 13.00 1287.92 6.00 0.00 0.00 0.00 13.10 1316.59 5.20 0.01 0.00 0.00 12.00 1252.03 2.87% R107 11.00 1135.30 6.00 0.00 0.00 0.00 11.30 1181.35 8.30 0.00 0.00 0.00 10.00 1104.66 2.77% R108 10.00 985.10 4.00 0.00 0.00 0.00 10.20 1046.68 5.90 0.00 0.00 0.00 9.00 960.88 2.52% R109 12.00 1236.26 11.00 0.00 0.00 0.00 12.90 1280.97 4.90 0.00 0.00 0.00 11.00 1194.73 3.48% R110 12.00 1143.55 8.00 0.00 0.00 0.00 12.00 1189.28 6.90 0.00 0.00 0.00 10.00 1118.80 2.21% R111 11.00 1105.38 4.00 0.00 0.00 0.00 11.80 1177.77 2.80 0.00 0.00 0.00 10.00 1096.72 0.79% R112 10.00 1004.97 4.00 0.00 0.00 0.00 10.40 1049.61 6.40 0.00 0.00 0.00 9.00 982.14 2.32%

R1-Avg. 12.92 1235.75 5.33 0.04 0.00 0.00 13.49 1292.10 4.68 0.20 0.00 0.00 11.92 1210.34 2.14%

RC101 15.00 1735.49 2.00 0.00 0.00 0.00 16.50 1774.00 1.50 0.05 0.00 0.00 14.00 1696.94 2.27% RC102 14.00 1572.51 1.00 0.00 0.00 0.00 15.10 1680.20 1.10 0.64 0.00 0.00 12.00 1554.75 1.14% RC103 12.00 1327.30 2.00 0.00 0.00 0.00 12.80 1406.28 2.50 0.00 0.00 0.00 11.00 1261.70 5.20% RC104 10.00 1216.75 11.00 0.00 0.00 0.00 11.00 1240.07 5.10 0.00 0.00 0.00 10.00 1135.48 7.16% RC105 15.00 1587.60 7.00 0.00 0.00 0.00 16.20 1640.74 2.60 0.02 0.00 0.00 13.00 1629.44 -2.57% RC106 13.00 1447.53 2.00 0.00 0.00 0.00 13.40 1494.62 2.10 0.00 0.00 0.00 11.00 1424.73 1.60% RC107 12.00 1279.43 2.00 0.00 0.00 0.00 12.40 1355.13 2.90 0.00 0.00 0.00 11.00 1230.48 3.98% RC108 11.00 1185.83 4.00 0.00 0.00 0.00 11.40 1234.05 3.00 0.00 0.00 0.00 10.00 1139.82 4.04%

RC1-Avg. 12.75 1419.06 3.88 0.00 0.00 0.00 13.60 1478.14 2.60 0.09 0.00 0.00 11.50 1384.16 2.85%

C201 3.00 591.56 80.00 0.00 0.00 0.00 3.00 99607.60 80.10 792.40 0.00 0.20 3.00 591.56 0.00% C202 3.00 591.56 87.00 0.00 0.00 0.00 3.00 630.46 74.90 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 600.21 139.00 0.00 0.00 0.00 3.20 626.77 80.90 0.00 0.00 0.00 3.00 591.17 1.53% C204 3.00 617.04 166.00 0.00 0.00 0.00 3.30 683.03 102.20 0.00 0.00 0.00 3.00 590.60 4.48% C205 3.00 588.88 128.00 0.00 0.00 0.00 3.00 610.53 161.20 0.00 0.00 0.00 3.00 588.88 0.00% C206 3.00 588.49 100.00 0.00 0.00 0.00 3.00 596.27 117.40 0.00 0.00 0.00 3.00 588.50 0.00% C207 3.00 588.29 94.00 0.00 0.00 0.00 3.00 589.32 73.90 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 52.00 0.00 0.00 0.00 3.00 612.56 62.40 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 594.29 105.75 0.00 0.00 0.00 3.06 12994.57 94.13 99.05 0.00 0.02 3.00 589.86 0.75%

R201 4.00 1291.29 28.00 0.00 0.00 0.00 4.00 1392.45 39.10 0.00 0.00 0.00 4.00 1252.37 3.11% R202 3.00 1275.46 148.00 0.00 0.00 0.00 3.90 1196.79 61.90 0.03 0.00 0.00 3.00 1191.70 7.03% R203 3.00 1019.00 113.00 0.00 0.00 0.00 3.40 1037.90 78.40 0.00 0.00 0.00 3.00 939.50 8.46% R204 3.00 779.67 53.00 0.00 0.00 0.00 3.00 854.95 74.60 0.00 0.00 0.00 2.00 825.52 -5.55% R205 3.00 1104.37 69.00 0.00 0.00 0.00 3.40 1171.42 51.80 0.00 0.00 0.00 3.00 994.42 11.06% R206 3.00 1000.54 45.00 0.00 0.00 0.00 3.20 1037.10 42.80 0.00 0.00 0.00 3.00 906.14 10.42% R207 3.00 858.63 61.00 0.00 0.00 0.00 3.00 921.95 51.50 0.00 0.00 0.00 2.00 890.60 -3.59% R208 2.00 782.52 104.00 0.00 0.00 0.00 2.90 788.94 79.10 0.00 0.00 0.00 2.00 726.82 7.66% R209 3.00 1049.96 113.00 0.00 0.00 0.00 3.80 1015.97 67.20 0.00 0.00 0.00 3.00 909.16 15.49% R210 3.00 1014.08 76.00 0.00 0.00 0.00 3.60 1059.72 58.80 0.00 0.00 0.00 3.00 939.37 7.95% R211 3.00 821.66 78.00 0.00 0.00 0.00 3.70 887.69 48.70 0.00 0.00 0.00 2.00 885.71 -7.23%

R2-Avg. 3.00 999.74 80.73 0.00 0.00 0.00 3.45 1033.17 59.45 0.00 0.00 0.00 2.73 951.03 4.98%

RC201 4.00 1472.90 42.00 0.00 0.00 0.00 4.30 1532.25 33.20 0.00 0.00 0.00 4.00 1406.94 4.69% RC202 4.00 1274.38 36.00 0.00 0.00 0.00 4.00 1344.07 55.60 0.00 0.00 0.00 3.00 1365.65 -6.68% RC203 3.00 1165.12 44.00 0.00 0.00 0.00 3.20 1188.83 69.70 0.00 0.00 0.00 3.00 1049.62 11.00% RC204 3.00 854.81 64.00 0.00 0.00 0.00 3.00 922.42 72.10 0.00 0.00 0.00 3.00 798.46 7.06% RC205 4.00 1402.28 37.00 0.00 0.00 0.00 4.00 1468.11 41.90 0.00 0.00 0.00 4.00 1297.70 8.06% RC206 3.00 1361.77 92.00 0.00 0.00 0.00 3.90 1247.88 62.50 0.00 0.00 0.00 3.00 1146.32 18.79% RC207 3.00 1227.32 112.00 0.00 0.00 0.00 3.80 1136.98 65.60 0.00 0.00 0.00 3.00 1061.14 15.66% RC208 3.00 910.34 56.00 0.00 0.00 0.00 3.40 961.70 54.80 0.00 0.00 0.00 3.00 828.14 9.93%

RC2-Avg. 3.38 1208.61 60.38 0.00 0.00 0.00 3.70 1225.28 56.93 0.00 0.00 0.00 3.25 1119.24 8.56%

69 Appendix B

Table B15.: Overview Tests on TT

Best Solutions Best Solutions Optimal Solution Best Gap Best Gap

Problem NV Cost Time NV Cost Time NV Cost TT=1 TT=2

C1-Avg. 10.44 861.90 1.22 10.44 863.38 2.11 10.00 826.70 4.26% 4.45% R1-Avg. 14.67 1254.40 0.67 14.83 1257.43 0.50 13.25 1173.61 7.37% 7.58% RC1-Avg. 14.13 1448.60 2.13 14.25 1441.86 1.13 12.63 1334.49 8.75% 8.19%

C2-Avg. TT=1 3.25 607.54 36.13 TT=2 3.13 601.76 27.00 3.00 587.38 3.43% 2.45% R2-Avg. 4.91 949.69 23.73 5.00 945.87 16.64 5.27 872.53 8.79% 8.53% RC2-Avg. 6.00 1089.61 18.25 6.38 1093.04 8.75 6.25 1000.73 8.90% 9.37%

Problem NV Cost Time NV Cost Time NV Cost TT=3 TT=4

C1-Avg. 10.22 857.02 2.78 10.22 852.72 2.89 10.00 826.70 3.67% 3.15% R1-Avg. 14.83 1253.89 1.58 14.42 1260.01 2.17 13.25 1173.61 7.31% 7.84% RC1-Avg. 14.50 1430.29 0.88 14.00 1433.34 1.13 12.63 1334.49 7.41% 7.63%

C2-Avg. TT=3 3.63 613.11 28.13 TT=4 3.50 609.48 39.13 3.00 587.38 4.38% 3.76% R2-Avg. 5.00 946.21 20.18 4.91 939.56 18.18 5.27 872.53 8.63% 7.64% RC2-Avg. 6.13 1085.89 12.63 5.88 1088.26 19.50 6.25 1000.73 8.51% 8.96%

Problem NV Cost Time NV Cost Time NV Cost TT=5 TT=6

C1-Avg. 10.11 847.68 2.78 10.00 837.95 1.89 10.00 826.70 2.54% 1.36% R1-Avg. 14.75 1257.83 1.83 14.67 1262.46 1.75 13.25 1173.61 7.53% 8.02% RC1-Avg. 14.13 1437.71 1.00 14.38 1441.84 1.75 12.63 1334.49 7.90% 8.22%

C2-Avg. TT=5 3.38 606.05 49.63 TT=6 3.25 604.42 37.00 3.00 587.38 3.18% 2.90% R2-Avg. 5.18 955.34 32.55 5.00 953.36 22.27 5.27 872.53 9.63% 9.45% RC2-Avg. 6.25 1085.98 13.25 6.13 1093.60 17.88 6.25 1000.73 8.67% 9.50%

Problem NV Cost Time NV Cost Time NV Cost TT=7 TT=8

C1-Avg. 10.44 854.14 1.78 10.33 850.77 3.00 10.00 826.70 3.32% 2.92% R1-Avg. 14.67 1259.84 1.00 14.67 1252.56 1.00 13.25 1173.61 7.73% 7.10% RC1-Avg. 14.25 1444.45 0.75 14.13 1443.76 2.25 12.63 1334.49 8.37% 8.35%

C2-Avg. TT=7 3.25 609.48 27.25 TT=8 3.50 606.55 30.50 3.00 587.38 3.76% 3.26% R2-Avg. 5.27 942.64 14.64 5.36 940.73 28.36 5.27 872.53 8.22% 7.99% RC2-Avg. 6.25 1081.49 10.88 6.25 1076.57 21.38 6.25 1000.73 8.42% 7.92%

Problem NV Cost Time NV Cost Time NV Cost TT=9 TT=10

C1-Avg. 10.33 850.55 2.44 10.22 853.29 1.89 10.00 826.70 2.89% 3.22% R1-Avg. 14.58 1252.72 1.17 14.58 1252.04 1.92 13.25 1173.61 7.15% 7.09% RC1-Avg. 10.00 1357.40 5.00 14.25 1438.92 1.75 12.63 1334.49 8.16% 7.91%

C2-Avg. TT=9 3.25 605.29 34.88 TT=10 3.13 598.95 37.88 3.00 587.38 3.05% 1.97% R2-Avg. 5.45 935.12 29.82 5.45 942.79 20.64 5.27 872.53 7.17% 8.15% RC2-Avg. 6.38 1090.14 13.75 6.13 1080.80 10.88 6.25 1000.73 9.33% 8.06%

Problem NV Cost Time NV Cost Time NV Cost TT=11 TT=12

C1-Avg. 10.11 841.03 1.78 10.22 851.48 2.78 10.00 826.70 1.74% 3.00% R1-Avg. 14.33 1258.22 1.50 14.83 1265.47 1.75 13.25 1173.61 7.57% 8.37% RC1-Avg. 14.25 1446.55 1.88 14.38 1437.87 1.50 12.63 1334.49 8.54% 7.90%

C2-Avg. TT=11 3.13 602.14 30.75 TT=12 3.13 606.19 54.88 3.00 587.38 2.51% 3.20% R2-Avg. 5.55 937.33 36.27 5.36 932.51 29.55 5.27 872.53 7.48% 6.89% RC2-Avg. 6.50 1075.66 18.00 6.38 1085.40 18.00 6.25 1000.73 7.64% 8.87%

Problem NV Cost Time NV Cost Time NV Cost TT=[1,10] TT=[11,20]

C1-Avg. 10.11 851.42 2.44 10.44 851.21 2.89 10.00 826.70 2.99% 2.97% R1-Avg. 14.75 1257.87 1.25 14.67 1257.94 1.67 13.25 1173.61 7.68% 7.70% RC1-Avg. 14.25 1442.44 1.38 14.38 1436.38 2.13 12.63 1334.49 8.21% 7.75% C2-Avg. 3.38 613.53 39.88 3.38 612.10 43.75 3.00 587.38 4.45% 4.21% R2-Avg. 5.09 949.57 58.55 5.55 945.90 15.55 5.27 872.53 8.99% 8.52%

RC2-Avg. TT=[1,10] 6.13 1082.86 13.75 TT=[11,20] 6.38 1080.52 11.25 6.25 1000.73 8.39% 8.03%

70 B.1. Computational Experiments

Table B16.: Detailed Test Result TS with Tabu Tenure =1

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 3.00 0.00 0.00 0.00 10.00 828.94 2.70 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 854.07 1.00 0.00 0.00 0.00 10.20 958.80 1.00 0.00 0.00 0.00 10.00 827.3 3.24% C103 10.00 893.04 1.00 0.00 0.00 0.00 10.80 980.18 1.00 0.00 0.00 0.00 10.00 826.3 8.08% C104 11.00 905.94 1.00 0.00 0.00 0.00 10.40 1027.46 2.20 0.00 0.00 0.00 10.00 822.9 10.09% C105 11.00 860.35 1.00 0.00 0.00 0.00 11.40 921.68 1.00 0.00 0.00 0.00 10.00 827.3 3.99% C106 11.00 864.93 1.00 0.00 0.00 0.00 11.20 905.14 1.00 0.00 0.00 0.00 10.00 827.3 4.55% C107 10.00 828.94 1.00 0.00 0.00 0.00 10.00 860.16 1.00 0.00 0.00 0.00 10.00 827.3 0.20% C108 11.00 890.01 1.00 0.00 0.00 0.00 11.40 941.91 1.00 0.00 0.00 0.00 10.00 827.3 7.58% C109 10.00 830.90 1.00 0.00 0.00 0.00 10.40 877.62 1.00 0.00 0.00 0.00 10.00 827.3 0.44%

C1-Avg. 10.44 861.90 1.22 0.00 0.00 0.00 10.64 922.43 1.32 0.00 0.00 0.00 10.00 826.70 4.26%

R101 20.00 1664.47 0.00 0.00 0.00 0.00 21.10 1689.66 0.00 0.00 0.00 0.00 20.00 1637.7 1.63% R102 18.00 1484.26 0.00 0.00 0.00 0.00 19.20 1519.16 0.00 0.01 0.00 0.00 18.00 1466.6 1.20% R103 16.00 1280.68 0.00 0.00 0.00 0.00 16.60 1328.02 0.10 0.00 0.00 0.00 14.00 1208.7 5.96% R104 13.00 1062.79 1.00 0.00 0.00 0.00 12.90 1092.17 2.00 0.00 0.00 0.00 11.00 971.5 9.40% R105 17.00 1446.09 1.00 0.00 0.00 0.00 16.90 1470.07 0.50 0.00 0.00 0.00 15.00 1355.3 6.70% R106 14.00 1299.95 0.00 0.00 0.00 0.00 14.60 1323.05 0.20 0.00 0.00 0.00 13.00 1234.6 5.29% R107 13.00 1185.41 1.00 0.00 0.00 0.00 13.40 1223.63 1.70 0.00 0.00 0.00 11.00 1064.6 11.35% R108 12.00 1018.75 1.00 0.00 0.00 0.00 11.80 1062.05 0.90 0.00 0.00 0.00 10.00 932.1 9.30% R109 15.00 1273.39 0.00 0.00 0.00 0.00 14.60 1313.03 0.00 0.00 0.00 0.00 13.00 1146.9 11.03% R110 14.00 1173.45 2.00 0.00 0.00 0.00 13.30 1225.23 1.60 0.00 0.00 0.00 12.00 1068.0 9.87% R111 12.00 1124.40 1.00 0.00 0.00 0.00 13.00 1189.17 1.00 0.00 0.00 0.00 12.00 1048.7 7.22% R112 12.00 1039.15 1.00 0.00 0.00 0.00 11.80 1076.28 2.00 0.00 0.00 0.00 10.00 948.6 9.55%

R1-Avg. 14.67 1254.40 0.67 0.00 0.00 0.00 14.93 1292.63 0.83 0.00 0.00 0.00 13.25 1173.61 7.37%

RC101 17.00 1715.69 2.00 0.00 0.00 0.00 17.20 1751.68 1.80 0.01 0.00 0.00 15.00 1619.8 5.92% RC102 15.00 1543.21 2.00 0.00 0.00 0.00 15.70 1631.24 1.70 0.01 0.00 0.00 14.00 1457.4 5.89% RC103 13.00 1384.30 3.00 0.00 0.00 0.00 14.10 1424.31 2.00 0.00 0.00 0.00 11.00 1258.0 10.04% RC104 12.00 1221.42 3.00 0.00 0.00 0.00 11.80 1267.97 3.10 0.00 0.00 0.00 10.00 1132.3 7.87% RC105 17.00 1654.34 1.00 0.02 0.00 0.00 17.70 1683.91 1.20 0.00 0.00 0.00 15.00 1513.7 9.29% RC106 14.00 1469.42 1.00 0.00 0.00 0.00 13.80 1497.88 1.90 0.00 0.00 0.00 13.00 1372.7 7.05% RC107 13.00 1355.19 3.00 0.00 0.00 0.00 13.60 1407.44 2.30 0.00 0.00 0.00 12.00 1207.8 12.20% RC108 12.00 1245.20 2.00 0.00 0.00 0.00 13.00 1299.10 2.80 0.00 0.00 0.00 11.00 1114.2 11.76%

RC1-Avg. 14.13 1448.60 2.13 0.00 0.00 0.00 14.61 1495.44 2.10 0.00 0.00 0.00 12.63 1334.49 8.75%

C201 3.00 591.56 26.00 0.00 0.00 0.00 3.00 591.56 25.60 0.00 0.00 0.00 3.00 589.1 0.42% C202 4.00 620.39 28.00 0.00 0.00 0.00 4.30 662.12 21.50 0.00 0.00 0.00 3.00 589.1 5.31% C203 4.00 620.30 8.00 0.00 0.00 0.00 4.20 679.65 15.20 0.00 0.00 0.00 3.00 588.7 5.37% C204 3.00 628.92 22.00 0.00 0.00 0.00 4.00 699.31 19.80 0.00 0.00 0.00 3.00 588.1 6.94% C205 3.00 609.36 49.00 0.00 0.00 0.00 3.70 626.32 25.00 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 28.00 0.00 0.00 0.00 4.20 629.69 22.80 0.00 0.00 0.00 3.00 586.0 0.43% C207 3.00 612.97 26.00 0.00 0.00 0.00 4.10 633.56 19.00 0.00 0.00 0.00 3.00 585.8 4.64% C208 3.00 588.32 102.00 0.00 0.00 0.00 3.00 588.32 40.80 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.25 607.54 36.13 0.00 0.00 0.00 3.81 638.82 23.71 0.00 0.00 0.00 3.00 587.38 3.43%

R201 7.00 1234.53 8.00 0.00 0.00 0.00 5.90 1288.78 12.70 0.00 0.00 0.00 8.00 1143.2 7.99% R202 7.00 1111.01 6.00 0.00 0.00 0.00 6.60 1165.80 9.90 0.00 0.00 0.00 8.00 1029.6 7.91% R203 5.00 951.42 27.00 0.00 0.00 0.00 4.80 989.79 19.10 0.00 0.00 0.00 6.00 870.8 9.26% R204 4.00 781.46 52.00 0.00 0.00 0.00 4.00 850.46 45.90 0.00 0.00 0.00 5.00 731.3 6.86% R205 5.00 1057.53 8.00 0.00 0.00 0.00 4.80 1090.81 27.60 0.00 0.00 0.00 5.00 949.8 11.34% R206 4.00 963.17 31.00 0.00 0.00 0.00 4.20 999.34 32.20 0.00 0.00 0.00 5.00 875.9 9.96% R207 4.00 897.13 29.00 0.00 0.00 0.00 3.40 939.94 41.00 0.00 0.00 0.00 3.00 794.0 12.99% R208 4.00 732.11 37.00 0.00 0.00 0.00 3.70 754.67 33.20 0.00 0.00 0.00 3.00 701.2 4.41% R209 4.00 951.26 21.00 0.00 0.00 0.00 4.50 999.55 20.10 0.00 0.00 0.00 5.00 854.8 11.28% R210 5.00 958.49 21.00 0.00 0.00 0.00 5.10 1007.80 19.00 0.00 0.00 0.00 6.00 900.5 6.44% R211 5.00 808.51 21.00 0.00 0.00 0.00 4.40 855.00 22.30 0.00 0.00 0.00 4.00 746.7 8.28%

R2-Avg. 4.91 949.69 23.73 0.00 0.00 0.00 4.67 994.72 25.73 0.00 0.00 0.00 5.27 872.53 8.79%

RC201 8.00 1356.83 12.00 0.00 0.00 0.00 8.00 1436.23 8.10 0.00 0.00 0.00 9.00 1261.8 7.53% RC202 8.00 1173.35 19.00 0.00 0.00 0.00 6.80 1250.55 8.10 0.00 0.00 0.00 8.00 1092.3 7.42% RC203 5.00 1041.13 15.00 0.00 0.00 0.00 4.40 1129.57 17.90 0.00 0.00 0.00 5.00 923.7 12.71% RC204 4.00 835.51 37.00 0.00 0.00 0.00 3.50 921.53 41.70 0.00 0.00 0.00 4.00 783.5 6.64% RC205 7.00 1274.31 5.00 0.00 0.00 0.00 7.10 1336.20 7.50 0.00 0.00 0.00 7.00 1154.0 10.43% RC206 5.00 1132.03 13.00 0.00 0.00 0.00 5.60 1202.51 14.90 0.00 0.00 0.00 7.00 1051.1 7.70% RC207 7.00 1060.18 22.00 0.00 0.00 0.00 5.80 1115.43 24.80 0.00 0.00 0.00 6.00 962.9 10.10% RC208 4.00 843.58 23.00 0.00 0.00 0.00 4.30 947.50 29.30 0.00 0.00 0.00 4.00 776.5 8.64%

RC2-Avg. 6.00 1089.61 18.25 0.00 0.00 0.00 5.69 1167.44 19.04 0.00 0.00 0.00 6.25 1000.73 8.90%

71 Appendix B

Table B17.: Detailed Test Result TS with Tabu Tenure =2

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 4.00 0.00 0.00 0.00 10.00 828.94 4.00 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 828.94 4.00 0.00 0.00 0.00 10.20 930.58 2.90 0.00 0.00 0.00 10.00 827.3 0.20% C103 11.00 859.33 1.00 0.00 0.00 0.00 10.90 973.55 1.00 0.00 0.00 0.00 10.00 826.3 4.00% C104 11.00 976.27 1.00 0.00 0.00 0.00 10.20 1066.39 1.10 0.00 0.00 0.00 10.00 822.9 18.64% C105 11.00 898.10 1.00 0.00 0.00 0.00 11.70 960.94 1.10 0.00 0.00 0.00 10.00 827.3 8.56% C106 10.00 828.94 4.00 0.00 0.00 0.00 10.80 883.44 2.40 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 1.00 0.00 0.00 0.00 10.30 871.79 1.00 0.00 0.00 0.00 10.00 827.3 0.20% C108 11.00 892.06 2.00 0.00 0.00 0.00 11.70 968.41 1.50 0.00 0.00 0.00 10.00 827.3 7.83% C109 10.00 828.94 1.00 0.00 0.00 0.00 10.00 885.39 1.00 0.00 0.00 0.00 10.00 827.3 0.20%

C1-Avg. 10.44 863.38 2.11 0.00 0.00 0.00 10.64 929.94 1.78 0.00 0.00 0.00 10.00 826.70 4.45%

R101 21.00 1658.04 0.00 0.00 0.00 0.00 21.10 1685.76 0.00 0.00 0.00 0.00 20.00 1637.7 1.24% R102 19.00 1502.58 1.00 0.12 0.00 0.00 19.40 1529.80 0.50 0.04 0.00 0.00 18.00 1466.6 2.45% R103 16.00 1275.55 0.00 0.00 0.00 0.00 16.60 1332.54 0.00 0.00 0.00 0.00 14.00 1208.7 5.53% R104 13.00 1065.76 1.00 0.00 0.00 0.00 13.30 1099.26 0.60 0.00 0.00 0.00 11.00 971.5 9.70% R105 17.00 1463.77 0.00 0.00 0.00 0.00 17.30 1507.71 0.00 0.00 0.00 0.00 15.00 1355.3 8.00% R106 15.00 1321.76 0.00 0.00 0.00 0.00 15.30 1352.98 0.00 0.00 0.00 0.00 13.00 1234.6 7.06% R107 13.00 1169.09 1.00 0.00 0.00 0.00 13.20 1208.21 0.60 0.00 0.00 0.00 11.00 1064.6 9.81% R108 11.00 1026.72 1.00 0.00 0.00 0.00 11.70 1059.23 1.70 0.00 0.00 0.00 10.00 932.1 10.15% R109 14.00 1270.06 0.00 0.00 0.00 0.00 14.20 1308.92 0.10 0.00 0.00 0.00 13.00 1146.9 10.74% R110 14.00 1187.98 0.00 0.00 0.00 0.00 13.60 1254.74 0.20 0.00 0.00 0.00 12.00 1068.0 11.23% R111 13.00 1137.79 1.00 0.00 0.00 0.00 13.30 1169.95 1.10 0.00 0.00 0.00 12.00 1048.7 8.50% R112 12.00 1010.04 1.00 0.00 0.00 0.00 12.10 1082.56 0.90 0.00 0.00 0.00 10.00 948.6 6.48%

R1-Avg. 14.83 1257.43 0.50 0.01 0.00 0.00 15.09 1299.31 0.48 0.00 0.00 0.00 13.25 1173.61 7.58%

RC101 17.00 1708.67 0.00 0.00 0.00 0.00 17.40 1739.63 0.30 0.00 0.00 0.00 15.00 1619.8 5.49% RC102 16.00 1586.73 0.00 0.00 0.00 0.00 16.20 1611.28 0.50 0.00 0.00 0.00 14.00 1457.4 8.87% RC103 14.00 1418.50 2.00 0.00 0.00 0.00 14.40 1448.54 1.20 0.00 0.00 0.00 11.00 1258.0 12.76% RC104 11.00 1193.56 1.00 0.00 0.00 0.00 11.80 1260.61 3.50 0.00 0.00 0.00 10.00 1132.3 5.41% RC105 17.00 1618.81 1.00 0.00 0.00 0.00 17.70 1691.01 1.10 0.00 0.00 0.00 15.00 1513.7 6.94% RC106 14.00 1447.35 2.00 0.00 0.00 0.00 14.00 1498.37 1.00 0.00 0.00 0.00 13.00 1372.7 5.44% RC107 13.00 1335.84 2.00 0.00 0.00 0.00 13.60 1393.86 1.10 0.00 0.00 0.00 12.00 1207.8 10.60% RC108 12.00 1225.45 1.00 0.00 0.00 0.00 12.60 1276.60 1.00 0.00 0.00 0.00 11.00 1114.2 9.98%

RC1-Avg. 14.25 1441.86 1.13 0.00 0.00 0.00 14.71 1489.99 1.21 0.00 0.00 0.00 12.63 1334.49 8.19%

C201 3.00 591.56 27.00 0.00 0.00 0.00 3.00 600.27 23.70 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 591.56 21.00 0.00 0.00 0.00 4.30 662.50 20.00 0.00 0.00 0.00 3.00 589.1 0.42% C203 4.00 626.39 19.00 0.00 0.00 0.00 4.10 660.91 15.10 0.00 0.00 0.00 3.00 588.7 6.40% C204 3.00 630.09 17.00 0.00 0.00 0.00 4.10 665.42 17.40 0.00 0.00 0.00 3.00 588.1 7.14% C205 3.00 609.36 45.00 0.00 0.00 0.00 3.70 624.14 33.60 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 26.00 0.00 0.00 0.00 4.30 638.02 18.60 0.00 0.00 0.00 3.00 586.0 0.43% C207 3.00 588.29 24.00 0.00 0.00 0.00 4.00 625.90 19.00 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 37.00 0.00 0.00 0.00 3.20 592.80 29.70 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.13 601.76 27.00 0.00 0.00 0.00 3.84 633.75 22.14 0.00 0.00 0.00 3.00 587.38 2.45%

R201 7.00 1208.00 6.00 0.00 0.00 0.00 6.90 1265.53 7.40 0.00 0.00 0.00 8.00 1143.2 5.67% R202 7.00 1100.46 8.00 0.00 0.00 0.00 6.50 1155.07 8.20 0.00 0.00 0.00 8.00 1029.6 6.88% R203 5.00 966.74 15.00 0.00 0.00 0.00 5.10 1000.40 15.30 0.00 0.00 0.00 6.00 870.8 11.02% R204 5.00 813.91 26.00 0.00 0.00 0.00 4.00 837.08 26.40 0.00 0.00 0.00 5.00 731.3 11.30% R205 6.00 1020.12 18.00 0.00 0.00 0.00 5.20 1082.29 12.90 0.00 0.00 0.00 5.00 949.8 7.40% R206 5.00 956.03 8.00 0.00 0.00 0.00 4.40 992.66 16.90 0.00 0.00 0.00 5.00 875.9 9.15% R207 3.00 891.77 31.00 0.00 0.00 0.00 3.30 928.07 37.10 0.00 0.00 0.00 3.00 794.0 12.31% R208 3.00 740.76 30.00 0.00 0.00 0.00 3.50 793.69 32.20 0.00 0.00 0.00 3.00 701.2 5.64% R209 4.00 941.52 14.00 0.00 0.00 0.00 4.20 988.18 16.90 0.00 0.00 0.00 5.00 854.8 10.14% R210 6.00 967.57 16.00 0.00 0.00 0.00 5.30 1049.59 13.70 0.00 0.00 0.00 6.00 900.5 7.45% R211 4.00 797.66 11.00 0.00 0.00 0.00 4.40 849.30 16.90 0.00 0.00 0.00 4.00 746.7 6.83%

R2-Avg. 5.00 945.87 16.64 0.00 0.00 0.00 4.80 994.71 18.54 0.00 0.00 0.00 5.27 872.53 8.53%

RC201 8.00 1340.23 6.00 0.00 0.00 0.00 8.30 1430.12 6.30 0.01 0.00 0.00 9.00 1261.8 6.22% RC202 7.00 1179.98 12.00 0.00 0.00 0.00 7.10 1258.09 10.20 0.00 0.00 0.00 8.00 1092.3 8.03% RC203 6.00 986.66 9.00 0.00 0.00 0.00 5.00 1122.82 18.50 0.00 0.00 0.00 5.00 923.7 6.82% RC204 4.00 847.73 11.00 0.00 0.00 0.00 3.80 900.25 23.90 0.00 0.00 0.00 4.00 783.5 8.20% RC205 8.00 1291.34 5.00 0.00 0.00 0.00 6.80 1340.88 7.10 0.00 0.00 0.00 7.00 1154.0 11.90% RC206 6.00 1148.96 8.00 0.00 0.00 0.00 5.60 1184.44 10.30 0.00 0.00 0.00 7.00 1051.1 9.31% RC207 6.00 1065.23 8.00 0.00 0.00 0.00 5.80 1118.74 8.70 0.00 0.00 0.00 6.00 962.9 10.63% RC208 6.00 884.20 11.00 0.00 0.00 0.00 4.50 942.91 14.80 0.00 0.00 0.00 4.00 776.5 13.87%

RC2-Avg. 6.38 1093.04 8.75 0.00 0.00 0.00 5.86 1162.28 12.48 0.00 0.00 0.00 6.25 1000.73 9.37%

72 B.1. Computational Experiments

Table B18.: Detailed Test Result TS with Tabu Tenure =3

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 4.00 0.00 0.00 0.00 10.00 828.94 2.70 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 834.64 5.00 0.00 0.00 0.00 10.60 953.59 3.90 0.00 0.00 0.00 10.00 827.3 0.89% C103 10.00 886.42 4.00 0.00 0.00 0.00 10.80 957.81 3.00 0.00 0.00 0.00 10.00 826.3 7.28% C104 10.00 918.30 4.00 0.00 0.00 0.00 10.20 1024.74 3.80 0.00 0.00 0.00 10.00 822.9 11.59% C105 11.00 865.82 1.00 0.00 0.00 0.00 11.50 936.13 1.20 0.00 0.00 0.00 10.00 827.3 4.66% C106 10.00 828.94 1.00 0.00 0.00 0.00 11.10 910.51 1.00 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 1.00 0.00 0.00 0.00 10.20 875.31 1.00 0.00 0.00 0.00 10.00 827.3 0.20% C108 11.00 892.25 1.00 0.00 0.00 0.00 11.20 941.66 2.60 0.00 0.00 0.00 10.00 827.3 7.85% C109 10.00 828.94 4.00 0.00 0.00 0.00 10.40 886.09 3.70 0.00 0.00 0.00 10.00 827.3 0.20%

C1-Avg. 10.22 857.02 2.78 0.00 0.00 0.00 10.67 923.86 2.54 0.00 0.00 0.00 10.00 826.70 3.67%

R101 21.00 1677.53 1.00 0.00 0.00 0.00 21.40 1696.61 0.40 0.00 0.00 0.00 20.00 1637.7 2.43% R102 19.00 1494.03 1.00 0.00 0.00 0.00 19.20 1526.61 1.00 0.01 0.00 0.00 18.00 1466.6 1.87% R103 17.00 1289.09 1.00 0.00 0.00 0.00 16.60 1328.85 0.50 0.00 0.00 0.00 14.00 1208.7 6.65% R104 13.00 1064.25 2.00 0.00 0.00 0.00 13.50 1107.52 1.90 0.00 0.00 0.00 11.00 971.5 9.55% R105 17.00 1418.23 1.00 0.00 0.00 0.00 17.10 1484.12 1.10 0.00 0.00 0.00 15.00 1355.3 4.64% R106 15.00 1321.01 0.00 0.00 0.00 0.00 15.50 1354.90 0.90 0.00 0.00 0.00 13.00 1234.6 7.00% R107 13.00 1154.09 3.00 0.00 0.00 0.00 13.60 1210.01 1.70 0.00 0.00 0.00 11.00 1064.6 8.41% R108 11.00 1023.89 1.00 0.00 0.00 0.00 11.80 1058.58 1.20 0.00 0.00 0.00 10.00 932.1 9.85% R109 14.00 1248.98 1.00 0.00 0.00 0.00 14.20 1314.37 0.30 0.01 0.00 0.00 13.00 1146.9 8.90% R110 14.00 1187.05 2.00 0.00 0.00 0.00 13.40 1230.79 2.30 0.00 0.00 0.00 12.00 1068.0 11.15% R111 12.00 1127.52 3.00 0.00 0.00 0.00 12.90 1177.92 1.70 0.00 0.00 0.00 12.00 1048.7 7.52% R112 12.00 1041.01 3.00 0.00 0.00 0.00 12.00 1076.00 2.70 0.00 0.00 0.00 10.00 948.6 9.74%

R1-Avg. 14.83 1253.89 1.58 0.00 0.00 0.00 15.10 1297.19 1.31 0.00 0.00 0.00 13.25 1173.61 7.31%

RC101 17.00 1695.43 2.00 0.00 0.00 0.00 17.50 1746.83 0.90 0.00 0.00 0.00 15.00 1619.8 4.67% RC102 16.00 1539.35 0.00 0.00 0.00 0.00 15.60 1619.70 0.40 0.00 0.00 0.00 14.00 1457.4 5.62% RC103 14.00 1415.24 0.00 0.00 0.00 0.00 14.20 1438.65 0.10 0.00 0.00 0.00 11.00 1258.0 12.50% RC104 12.00 1212.99 1.00 0.00 0.00 0.00 12.10 1287.59 1.00 0.00 0.00 0.00 10.00 1132.3 7.13% RC105 17.00 1611.09 0.00 0.00 0.00 0.00 17.60 1671.82 0.00 0.00 0.00 0.00 15.00 1513.7 6.43% RC106 14.00 1428.20 0.00 0.00 0.00 0.00 14.10 1495.08 0.10 0.00 0.00 0.00 13.00 1372.7 4.04% RC107 13.00 1301.55 1.00 0.00 0.00 0.00 13.50 1384.22 0.90 0.00 0.00 0.00 12.00 1207.8 7.76% RC108 13.00 1238.46 3.00 0.00 0.00 0.00 12.80 1296.77 2.00 0.00 0.00 0.00 11.00 1114.2 11.15%

RC1-Avg. 14.50 1430.29 0.88 0.00 0.00 0.00 14.68 1492.58 0.68 0.00 0.00 0.00 12.63 1334.49 7.41%

C201 3.00 591.56 29.00 0.00 0.00 0.00 3.00 591.56 33.50 0.00 0.00 0.00 3.00 589.1 0.42% C202 4.00 621.64 25.00 0.00 0.00 0.00 4.30 673.10 22.10 0.00 0.00 0.00 3.00 589.1 5.52% C203 4.00 618.08 16.00 0.00 0.00 0.00 4.10 669.97 14.80 0.00 0.00 0.00 3.00 588.7 4.99% C204 4.00 652.35 17.00 0.00 0.00 0.00 4.20 699.24 20.80 0.00 0.00 0.00 3.00 588.1 10.92% C205 4.00 611.84 45.00 0.00 0.00 0.00 4.00 625.98 34.60 0.00 0.00 0.00 3.00 586.4 4.34% C206 4.00 632.82 28.00 0.00 0.00 0.00 4.50 657.49 26.90 0.00 0.00 0.00 3.00 586.0 7.99% C207 3.00 588.29 26.00 0.00 0.00 0.00 4.10 626.86 26.10 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 39.00 0.00 0.00 0.00 3.30 596.06 37.60 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.63 613.11 28.13 0.00 0.00 0.00 3.94 642.53 27.05 0.00 0.00 0.00 3.00 587.38 4.38%

R201 7.00 1222.41 7.00 0.00 0.00 0.00 7.20 1274.56 10.40 0.00 0.00 0.00 8.00 1143.2 6.93% R202 7.00 1088.18 3.00 0.00 0.00 0.00 6.90 1130.57 9.20 0.00 0.00 0.00 8.00 1029.6 5.69% R203 6.00 933.29 7.00 0.00 0.00 0.00 5.10 981.23 18.10 0.00 0.00 0.00 6.00 870.8 7.18% R204 5.00 793.89 43.00 0.00 0.00 0.00 4.30 839.16 33.60 0.00 0.00 0.00 5.00 731.3 8.56% R205 5.00 1004.98 15.00 0.00 0.00 0.00 5.30 1081.77 12.40 0.00 0.00 0.00 5.00 949.8 5.81% R206 4.00 959.14 18.00 0.00 0.00 0.00 4.70 984.02 18.90 0.00 0.00 0.00 5.00 875.9 9.50% R207 4.00 870.57 43.00 0.00 0.00 0.00 3.60 907.78 36.40 0.00 0.00 0.00 3.00 794.0 9.64% R208 3.00 778.13 30.00 0.00 0.00 0.00 3.40 799.62 42.00 0.00 0.00 0.00 3.00 701.2 10.97% R209 5.00 934.28 15.00 0.00 0.00 0.00 4.80 997.10 17.40 0.00 0.00 0.00 5.00 854.8 9.30% R210 5.00 997.66 14.00 0.00 0.00 0.00 5.30 1036.04 16.60 0.00 0.00 0.00 6.00 900.5 10.79% R211 4.00 825.81 27.00 0.00 0.00 0.00 4.10 875.70 34.60 0.00 0.00 0.00 4.00 746.7 10.59%

R2-Avg. 5.00 946.21 20.18 0.00 0.00 0.00 4.97 991.60 22.69 0.00 0.00 0.00 5.27 872.53 8.63%

RC201 7.00 1367.77 5.00 0.00 0.00 0.00 8.00 1406.05 7.10 0.01 0.00 0.00 9.00 1261.8 8.40% RC202 8.00 1138.73 5.00 0.00 0.00 0.00 7.20 1203.15 6.50 0.00 0.00 0.00 8.00 1092.3 4.25% RC203 6.00 1004.41 10.00 0.00 0.00 0.00 5.20 1103.44 12.10 0.00 0.00 0.00 5.00 923.7 8.74% RC204 4.00 856.99 36.00 0.00 0.00 0.00 3.70 916.71 26.70 0.00 0.00 0.00 4.00 783.5 9.38% RC205 8.00 1238.75 4.00 0.00 0.00 0.00 7.30 1340.14 6.40 0.00 0.00 0.00 7.00 1154.0 7.34% RC206 5.00 1181.41 13.00 0.00 0.00 0.00 5.60 1220.31 10.40 0.00 0.00 0.00 7.00 1051.1 12.40% RC207 6.00 1082.39 13.00 0.00 0.00 0.00 5.20 1136.31 11.50 0.00 0.00 0.00 6.00 962.9 12.41% RC208 5.00 816.68 15.00 0.00 0.00 0.00 4.20 948.19 17.90 0.00 0.00 0.00 4.00 776.5 5.18%

RC2-Avg. 6.13 1085.89 12.63 0.00 0.00 0.00 5.80 1159.29 12.33 0.00 0.00 0.00 6.25 1000.73 8.51%

73 Appendix B

Table B19.: Detailed Test Result TS with Tabu Tenure =4

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 5.00 0.00 0.00 0.00 10.00 828.94 3.90 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 835.56 1.00 0.00 0.00 0.00 10.60 950.61 2.60 0.00 0.00 0.00 10.00 827.3 1.00% C103 10.00 846.15 1.00 0.00 0.00 0.00 11.10 981.15 1.00 0.00 0.00 0.00 10.00 826.3 2.40% C104 11.00 932.59 4.00 0.00 0.00 0.00 10.20 1074.05 3.90 0.00 0.00 0.00 10.00 822.9 13.33% C105 10.00 895.50 4.00 0.00 0.00 0.00 11.30 932.85 3.20 0.00 0.00 0.00 10.00 827.3 8.24% C106 10.00 828.94 4.00 0.00 0.00 0.00 11.30 907.01 2.90 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 4.00 0.00 0.00 0.00 10.20 879.66 3.30 0.00 0.00 0.00 10.00 827.3 0.20% C108 11.00 848.94 1.00 0.00 0.00 0.00 11.40 941.06 1.10 0.00 0.00 0.00 10.00 827.3 2.62% C109 10.00 828.94 2.00 0.00 0.00 0.00 10.10 866.58 3.10 0.00 0.00 0.00 10.00 827.3 0.20%

C1-Avg. 10.22 852.72 2.89 0.00 0.00 0.00 10.69 929.10 2.78 0.00 0.00 0.00 10.00 826.70 3.15%

R101 20.00 1659.33 1.00 0.00 0.00 0.00 21.10 1689.00 1.00 0.00 0.00 0.00 20.00 1637.7 1.32% R102 19.00 1495.38 2.00 0.00 0.00 0.00 19.20 1524.16 1.10 0.00 0.00 0.00 18.00 1466.6 1.96% R103 17.00 1314.04 2.00 0.00 0.00 0.00 16.70 1332.16 1.70 0.00 0.00 0.00 14.00 1208.7 8.72% R104 13.00 1067.47 3.00 0.00 0.00 0.00 13.70 1113.84 2.40 0.00 0.00 0.00 11.00 971.5 9.88% R105 16.00 1440.79 2.00 0.00 0.00 0.00 16.60 1466.88 1.40 0.00 0.00 0.00 15.00 1355.3 6.31% R106 14.00 1310.37 2.00 0.00 0.00 0.00 15.40 1345.21 0.90 0.00 0.00 0.00 13.00 1234.6 6.14% R107 13.00 1202.62 2.00 0.00 0.00 0.00 13.50 1235.01 1.20 0.00 0.00 0.00 11.00 1064.6 12.96% R108 11.00 1003.08 3.00 0.00 0.00 0.00 11.40 1048.02 2.70 0.00 0.00 0.00 10.00 932.1 7.62% R109 14.00 1276.30 1.00 0.00 0.00 0.00 14.80 1318.93 1.20 0.00 0.00 0.00 13.00 1146.9 11.28% R110 13.00 1177.50 3.00 0.00 0.00 0.00 13.40 1224.17 1.70 0.00 0.00 0.00 12.00 1068.0 10.25% R111 12.00 1134.26 2.00 0.00 0.00 0.00 12.60 1189.79 2.20 0.00 0.00 0.00 12.00 1048.7 8.16% R112 11.00 1038.98 3.00 0.00 0.00 0.00 11.80 1076.41 2.90 0.00 0.00 0.00 10.00 948.6 9.53%

R1-Avg. 14.42 1260.01 2.17 0.00 0.00 0.00 15.02 1296.97 1.70 0.00 0.00 0.00 13.25 1173.61 7.84%

RC101 17.00 1697.08 1.00 0.00 0.00 0.00 17.00 1739.11 1.00 0.00 0.00 0.00 15.00 1619.8 4.77% RC102 15.00 1572.57 2.00 0.00 0.00 0.00 15.70 1629.17 1.70 0.00 0.00 0.00 14.00 1457.4 7.90% RC103 13.00 1385.04 2.00 0.00 0.00 0.00 14.00 1429.13 1.80 0.00 0.00 0.00 11.00 1258.0 10.10% RC104 12.00 1205.46 1.00 0.00 0.00 0.00 12.00 1255.83 1.70 0.00 0.00 0.00 10.00 1132.3 6.46% RC105 17.00 1605.09 0.00 0.00 0.00 0.00 17.50 1678.64 0.00 0.00 0.00 0.00 15.00 1513.7 6.04% RC106 13.00 1425.73 1.00 0.00 0.00 0.00 13.80 1487.56 0.50 0.00 0.00 0.00 13.00 1372.7 3.86% RC107 13.00 1332.32 1.00 0.00 0.00 0.00 13.80 1389.54 1.30 0.00 0.00 0.00 12.00 1207.8 10.31% RC108 12.00 1243.45 1.00 0.00 0.00 0.00 12.70 1294.94 0.90 0.00 0.00 0.00 11.00 1114.2 11.60%

RC1-Avg. 14.00 1433.34 1.13 0.00 0.00 0.00 14.56 1487.99 1.11 0.00 0.00 0.00 12.63 1334.49 7.63%

C201 3.00 591.56 36.00 0.00 0.00 0.00 3.00 591.56 33.50 0.00 0.00 0.00 3.00 589.1 0.42% C202 4.00 626.97 40.00 0.00 0.00 0.00 4.40 666.25 27.00 0.00 0.00 0.00 3.00 589.1 6.43% C203 4.00 630.29 25.00 0.00 0.00 0.00 4.30 664.17 21.50 0.00 0.00 0.00 3.00 588.7 7.07% C204 4.00 636.22 29.00 0.00 0.00 0.00 4.50 719.01 16.30 0.00 0.00 0.00 3.00 588.1 8.18% C205 3.00 609.36 27.00 0.00 0.00 0.00 3.80 627.69 27.10 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 66.00 0.00 0.00 0.00 4.20 633.23 36.40 0.00 0.00 0.00 3.00 586.0 0.43% C207 4.00 604.67 63.00 0.00 0.00 0.00 4.60 644.32 24.60 0.00 0.00 0.00 3.00 585.8 3.22% C208 3.00 588.32 27.00 0.00 0.00 0.00 3.10 590.51 32.50 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.50 609.48 39.13 0.00 0.00 0.00 3.99 642.09 27.36 0.00 0.00 0.00 3.00 587.38 3.76%

R201 8.00 1228.88 11.00 0.00 0.00 0.00 7.10 1266.71 8.10 0.00 0.00 0.00 8.00 1143.2 7.49% R202 6.00 1109.81 6.00 0.00 0.00 0.00 6.70 1136.99 8.80 0.00 0.00 0.00 8.00 1029.6 7.79% R203 5.00 940.14 11.00 0.00 0.00 0.00 5.10 989.12 18.30 0.00 0.00 0.00 6.00 870.8 7.96% R204 4.00 765.25 14.00 0.00 0.00 0.00 4.20 830.11 33.20 0.00 0.00 0.00 5.00 731.3 4.64% R205 6.00 1015.98 13.00 0.00 0.00 0.00 5.20 1060.88 15.20 0.00 0.00 0.00 5.00 949.8 6.97% R206 4.00 957.85 31.00 0.00 0.00 0.00 4.30 982.89 28.50 0.00 0.00 0.00 5.00 875.9 9.36% R207 4.00 836.56 43.00 0.00 0.00 0.00 3.90 907.67 48.10 0.00 0.00 0.00 3.00 794.0 5.36% R208 4.00 740.21 14.00 0.00 0.00 0.00 3.30 780.36 51.90 0.00 0.00 0.00 3.00 701.2 5.56% R209 4.00 953.28 23.00 0.00 0.00 0.00 4.20 998.96 25.30 0.00 0.00 0.00 5.00 854.8 11.52% R210 5.00 957.93 18.00 0.04 0.00 0.00 4.80 1008.56 18.50 0.00 0.00 0.00 6.00 900.5 6.38% R211 4.00 829.24 16.00 0.00 0.00 0.00 4.40 868.15 19.50 0.00 0.00 0.00 4.00 746.7 11.05%

R2-Avg. 4.91 939.56 18.18 0.00 0.00 0.00 4.84 984.58 25.04 0.00 0.00 0.00 5.27 872.53 7.64%

RC201 8.00 1344.66 4.00 0.00 0.00 0.00 8.60 1402.70 7.00 0.01 0.00 0.00 9.00 1261.8 6.57% RC202 8.00 1156.01 14.00 0.00 0.00 0.00 7.30 1228.67 8.30 0.00 0.00 0.00 8.00 1092.3 5.83% RC203 5.00 998.82 8.00 0.00 0.00 0.00 5.40 1057.15 14.00 0.00 0.00 0.00 5.00 923.7 8.13% RC204 4.00 844.67 55.00 0.00 0.00 0.00 4.00 884.78 34.00 0.00 0.00 0.00 4.00 783.5 7.81% RC205 7.00 1257.61 27.00 0.00 0.00 0.00 7.30 1317.39 13.00 0.00 0.00 0.00 7.00 1154.0 8.98% RC206 5.00 1165.33 12.00 0.00 0.00 0.00 5.80 1203.77 11.20 0.00 0.00 0.00 7.00 1051.1 10.87% RC207 6.00 1052.50 9.00 0.00 0.00 0.00 5.80 1098.88 14.00 0.00 0.00 0.00 6.00 962.9 9.31% RC208 4.00 886.51 27.00 0.00 0.00 0.00 4.40 914.55 18.80 0.00 0.00 0.00 4.00 776.5 14.17%

RC2-Avg. 5.88 1088.26 19.50 0.00 0.00 0.00 6.08 1138.49 15.04 0.00 0.00 0.00 6.25 1000.73 8.96%

74 B.1. Computational Experiments

Table B20.: Detailed Test Result TS with Tabu Tenure =5

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 4.00 0.00 0.00 0.00 10.00 828.94 4.30 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 850.52 2.00 0.00 0.00 0.00 10.60 934.17 2.60 0.00 0.00 0.00 10.00 827.3 2.81% C103 11.00 879.77 4.00 0.00 0.00 0.00 10.80 954.07 2.80 0.00 0.00 0.00 10.00 826.3 6.47% C104 10.00 899.82 3.00 0.00 0.00 0.00 10.40 1014.46 3.90 0.00 0.00 0.00 10.00 822.9 9.35% C105 10.00 828.94 2.00 0.00 0.00 0.00 11.10 920.71 2.90 0.00 0.00 0.00 10.00 827.3 0.20% C106 10.00 828.94 2.00 0.00 0.00 0.00 11.10 906.14 3.00 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 2.00 0.00 0.00 0.00 10.20 878.82 3.20 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 828.94 3.00 0.00 0.00 0.00 11.00 900.42 3.00 0.00 0.00 0.00 10.00 827.3 0.20% C109 10.00 854.31 3.00 0.00 0.00 0.00 10.20 920.14 3.50 0.00 0.00 0.00 10.00 827.3 3.27%

C1-Avg. 10.11 847.68 2.78 0.00 0.00 0.00 10.60 917.54 3.24 0.00 0.00 0.00 10.00 826.70 2.54%

R101 21.00 1681.58 1.00 0.00 0.00 0.00 21.40 1691.74 0.70 0.00 0.00 0.00 20.00 1637.7 2.68% R102 19.00 1500.23 1.00 0.00 0.00 0.00 19.50 1538.61 1.00 0.00 0.00 0.00 18.00 1466.6 2.29% R103 17.00 1318.14 1.00 0.00 0.00 0.00 16.70 1336.84 1.70 0.00 0.00 0.00 14.00 1208.7 9.05% R104 12.00 1042.73 2.00 0.00 0.00 0.00 13.20 1102.40 2.00 0.00 0.00 0.00 11.00 971.5 7.33% R105 17.00 1456.11 1.00 0.00 0.00 0.00 17.00 1479.93 1.20 0.00 0.00 0.00 15.00 1355.3 7.44% R106 15.00 1310.71 1.00 0.00 0.00 0.00 15.10 1343.45 1.40 0.00 0.00 0.00 13.00 1234.6 6.16% R107 13.00 1149.54 3.00 0.00 0.00 0.00 13.10 1193.63 2.40 0.00 0.00 0.00 11.00 1064.6 7.98% R108 12.00 1006.23 3.00 0.00 0.00 0.00 11.80 1049.35 2.90 0.00 0.00 0.00 10.00 932.1 7.95% R109 14.00 1268.51 2.00 0.00 0.00 0.00 14.40 1325.22 1.90 0.00 0.00 0.00 13.00 1146.9 10.60% R110 13.00 1190.50 1.00 0.00 0.00 0.00 13.60 1227.74 1.40 0.00 0.00 0.00 12.00 1068.0 11.47% R111 12.00 1121.51 3.00 0.00 0.00 0.00 13.10 1173.17 2.70 0.00 0.00 0.00 12.00 1048.7 6.94% R112 12.00 1048.13 3.00 0.00 0.00 0.00 12.00 1077.92 2.70 0.00 0.00 0.00 10.00 948.6 10.49%

R1-Avg. 14.75 1257.83 1.83 0.00 0.00 0.00 15.08 1295.00 1.83 0.00 0.00 0.00 13.25 1173.61 7.53%

RC101 17.00 1698.34 1.00 0.00 0.00 0.00 17.20 1746.47 0.70 0.00 0.00 0.00 15.00 1619.8 4.85% RC102 15.00 1578.15 2.00 0.00 0.00 0.00 16.00 1621.68 1.00 0.00 0.00 0.00 14.00 1457.4 8.29% RC103 13.00 1383.05 1.00 0.00 0.00 0.00 14.10 1438.03 0.50 0.00 0.00 0.00 11.00 1258.0 9.94% RC104 12.00 1223.70 1.00 0.00 0.00 0.00 11.70 1267.39 1.80 0.00 0.00 0.00 10.00 1132.3 8.07% RC105 17.00 1636.62 1.00 0.00 0.00 0.00 17.60 1671.56 0.80 0.01 0.00 0.00 15.00 1513.7 8.12% RC106 14.00 1427.12 0.00 0.00 0.00 0.00 13.90 1500.45 0.60 0.00 0.00 0.00 13.00 1372.7 3.96% RC107 13.00 1336.27 1.00 0.00 0.00 0.00 13.60 1383.83 1.40 0.00 0.00 0.00 12.00 1207.8 10.64% RC108 12.00 1218.43 1.00 0.00 0.00 0.00 12.70 1278.33 1.10 0.00 0.00 0.00 11.00 1114.2 9.35%

RC1-Avg. 14.13 1437.71 1.00 0.00 0.00 0.00 14.60 1488.47 0.99 0.00 0.00 0.00 12.63 1334.49 7.90%

C201 3.00 591.56 52.00 0.00 0.00 0.00 3.00 591.56 56.30 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 591.56 47.00 0.00 0.00 0.00 4.30 644.88 39.40 0.00 0.00 0.00 3.00 589.1 0.42% C203 4.00 637.82 28.00 0.00 0.00 0.00 4.40 690.68 30.60 0.00 0.00 0.00 3.00 588.7 8.34% C204 4.00 636.61 28.00 0.00 0.00 0.00 4.20 676.68 33.60 0.00 0.00 0.00 3.00 588.1 8.25% C205 3.00 609.36 75.00 0.00 0.00 0.00 3.60 617.14 56.70 0.00 0.00 0.00 3.00 586.4 3.92% C206 4.00 604.87 39.00 0.00 0.00 0.00 4.40 643.95 44.70 0.00 0.00 0.00 3.00 586.0 3.22% C207 3.00 588.29 56.00 0.00 0.00 0.00 4.00 626.24 43.90 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 72.00 0.00 0.00 0.00 3.20 591.60 69.00 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.38 606.05 49.63 0.00 0.00 0.00 3.89 635.34 46.78 0.00 0.00 0.00 3.00 587.38 3.18%

R201 7.00 1211.93 19.00 0.00 0.00 0.00 7.20 1252.27 18.20 0.00 0.00 0.00 8.00 1143.2 6.01% R202 8.00 1118.87 17.00 0.00 0.00 0.00 7.30 1159.09 16.70 0.00 0.00 0.00 8.00 1029.6 8.67% R203 6.00 941.18 36.00 0.00 0.00 0.00 5.30 994.59 40.10 0.00 0.00 0.00 6.00 870.8 8.08% R204 5.00 816.18 38.00 0.00 0.00 0.00 4.20 860.97 65.80 0.00 0.00 0.00 5.00 731.3 11.61% R205 6.00 1054.91 37.00 0.00 0.00 0.00 4.90 1104.35 38.10 0.00 0.00 0.00 5.00 949.8 11.07% R206 5.00 973.21 39.00 0.00 0.00 0.00 4.80 992.67 34.80 0.00 0.00 0.00 5.00 875.9 11.11% R207 3.00 900.29 76.00 0.00 0.00 0.00 3.50 935.91 71.70 0.00 0.00 0.00 3.00 794.0 13.39% R208 3.00 760.49 55.00 0.00 0.00 0.00 3.20 793.74 69.70 0.00 0.00 0.00 3.00 701.2 8.45% R209 5.00 961.97 13.00 0.00 0.00 0.00 5.00 994.70 19.50 0.00 0.00 0.00 5.00 854.8 12.54% R210 5.00 960.70 13.00 0.00 0.00 0.00 5.00 1050.06 26.70 0.00 0.00 0.00 6.00 900.5 6.68% R211 4.00 809.05 15.00 0.00 0.00 0.00 4.30 890.12 18.80 0.00 0.00 0.00 4.00 746.7 8.35%

R2-Avg. 5.18 955.34 32.55 0.00 0.00 0.00 4.97 1002.59 38.19 0.00 0.00 0.00 5.27 872.53 9.63%

RC201 9.00 1326.21 4.00 0.00 0.00 0.00 8.40 1434.81 5.40 0.01 0.00 0.00 9.00 1261.8 5.10% RC202 7.00 1190.95 7.00 0.00 0.00 0.00 6.60 1259.20 7.60 0.00 0.00 0.00 8.00 1092.3 9.03% RC203 5.00 1017.12 14.00 0.00 0.00 0.00 4.90 1110.85 13.10 0.00 0.00 0.00 5.00 923.7 10.11% RC204 4.00 838.11 11.00 0.00 0.00 0.00 3.80 874.35 32.50 0.00 0.00 0.00 4.00 783.5 6.97% RC205 9.00 1264.63 3.00 0.00 0.00 0.00 7.20 1335.23 11.60 0.00 0.00 0.00 7.00 1154.0 9.59% RC206 7.00 1131.60 21.00 0.00 0.00 0.00 5.80 1223.13 16.50 0.00 0.00 0.00 7.00 1051.1 7.66% RC207 5.00 1052.86 19.00 0.00 0.00 0.00 5.70 1088.83 16.90 0.00 0.00 0.00 6.00 962.9 9.34% RC208 4.00 866.39 27.00 0.00 0.00 0.00 4.40 929.24 26.50 0.00 0.00 0.00 4.00 776.5 11.58%

RC2-Avg. 6.25 1085.98 13.25 0.00 0.00 0.00 5.85 1156.95 16.26 0.00 0.00 0.00 6.25 1000.73 8.67%

75 Appendix B

Table B21.: Detailed Test Result TS with Tabu Tenure =6

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 4.00 0.00 0.00 0.00 10.00 828.94 2.70 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 831.53 1.00 0.00 0.00 0.00 10.60 918.72 1.60 0.00 0.00 0.00 10.00 827.3 0.51% C103 10.00 839.29 1.00 0.00 0.00 0.00 10.80 971.03 1.30 0.00 0.00 0.00 10.00 826.3 1.57% C104 10.00 868.42 1.00 0.00 0.00 0.00 10.00 993.60 1.10 0.00 0.00 0.00 10.00 822.9 5.53% C105 10.00 854.31 3.00 0.00 0.00 0.00 11.20 934.88 1.90 0.00 0.00 0.00 10.00 827.3 3.27% C106 10.00 828.94 1.00 0.00 0.00 0.00 11.20 894.61 2.90 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 2.00 0.00 0.00 0.00 10.20 873.39 3.20 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 832.25 2.00 0.00 0.00 0.00 11.30 931.88 1.90 0.00 0.00 0.00 10.00 827.3 0.60% C109 10.00 828.94 2.00 0.00 0.00 0.00 10.10 895.91 2.50 0.00 0.00 0.00 10.00 827.3 0.20%

C1-Avg. 10.00 837.95 1.89 0.00 0.00 0.00 10.60 915.88 2.12 0.00 0.00 0.00 10.00 826.70 1.36%

R101 21.00 1679.13 0.00 0.00 0.00 0.00 21.50 1695.53 0.40 0.00 0.00 0.00 20.00 1637.7 2.53% R102 19.00 1513.80 1.00 0.00 0.00 0.00 19.20 1530.89 0.30 0.02 0.00 0.00 18.00 1466.6 3.22% R103 17.00 1320.19 2.00 0.00 0.00 0.00 17.00 1348.19 1.50 0.00 0.00 0.00 14.00 1208.7 9.22% R104 13.00 1068.43 1.00 0.00 0.00 0.00 13.20 1089.86 2.00 0.00 0.00 0.00 11.00 971.5 9.98% R105 16.00 1442.26 2.00 0.00 0.00 0.00 17.30 1490.54 1.00 0.00 0.00 0.00 15.00 1355.3 6.42% R106 14.00 1288.97 0.00 0.00 0.00 0.00 15.00 1335.75 0.20 0.00 0.00 0.00 13.00 1234.6 4.40% R107 13.00 1183.41 3.00 0.00 0.00 0.00 13.70 1219.30 2.30 0.00 0.00 0.00 11.00 1064.6 11.16% R108 12.00 1013.16 3.00 0.00 0.00 0.00 11.80 1048.56 3.10 0.00 0.00 0.00 10.00 932.1 8.70% R109 14.00 1265.74 2.00 0.00 0.00 0.00 14.40 1299.01 2.10 0.00 0.00 0.00 13.00 1146.9 10.36% R110 13.00 1174.44 1.00 0.03 0.00 0.00 13.60 1232.78 1.70 0.00 0.00 0.00 12.00 1068.0 9.97% R111 13.00 1157.18 3.00 0.00 0.00 0.00 13.00 1192.50 2.60 0.00 0.00 0.00 12.00 1048.7 10.34% R112 11.00 1042.79 3.00 0.00 0.00 0.00 12.20 1089.43 2.40 0.00 0.00 0.00 10.00 948.6 9.93%

R1-Avg. 14.67 1262.46 1.75 0.00 0.00 0.00 15.16 1297.70 1.63 0.00 0.00 0.00 13.25 1173.61 8.02%

RC101 17.00 1719.98 1.00 0.00 0.00 0.00 17.50 1748.10 1.00 0.00 0.00 0.00 15.00 1619.8 6.18% RC102 15.00 1535.63 3.00 0.00 0.00 0.00 15.90 1622.12 2.00 0.00 0.00 0.00 14.00 1457.4 5.37% RC103 14.00 1396.79 2.00 0.00 0.00 0.00 14.20 1445.92 1.90 0.00 0.00 0.00 11.00 1258.0 11.03% RC104 12.00 1211.72 3.00 0.00 0.00 0.00 12.00 1263.23 2.60 0.00 0.00 0.00 10.00 1132.3 7.01% RC105 17.00 1627.16 1.00 0.00 0.00 0.00 17.30 1667.63 1.10 0.01 0.00 0.00 15.00 1513.7 7.50% RC106 14.00 1456.02 1.00 0.00 0.00 0.00 14.10 1492.50 1.50 0.00 0.00 0.00 13.00 1372.7 6.07% RC107 13.00 1380.16 2.00 0.00 0.00 0.00 13.70 1404.17 2.00 0.00 0.00 0.00 12.00 1207.8 14.27% RC108 13.00 1207.26 1.00 0.00 0.00 0.00 12.70 1279.44 1.60 0.00 0.00 0.00 11.00 1114.2 8.35%

RC1-Avg. 14.38 1441.84 1.75 0.00 0.00 0.00 14.68 1490.39 1.71 0.00 0.00 0.00 12.63 1334.49 8.22%

C201 3.00 591.56 36.00 0.00 0.00 0.00 3.00 591.56 35.50 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 591.56 46.00 0.00 0.00 0.00 3.90 639.49 31.90 0.00 0.00 0.00 3.00 589.1 0.42% C203 4.00 630.87 21.00 0.00 0.00 0.00 4.50 681.26 17.40 0.00 0.00 0.00 3.00 588.7 7.16% C204 4.00 646.89 37.00 0.00 0.00 0.00 4.10 682.45 21.70 0.00 0.00 0.00 3.00 588.1 10.00% C205 3.00 609.36 59.00 0.00 0.00 0.00 3.60 619.56 36.10 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 24.00 0.00 0.00 0.00 4.60 650.22 27.80 0.00 0.00 0.00 3.00 586.0 0.43% C207 3.00 588.29 30.00 0.00 0.00 0.00 4.10 638.35 27.80 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 43.00 0.00 0.00 0.00 3.20 593.40 40.60 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.25 604.42 37.00 0.00 0.00 0.00 3.88 637.04 29.85 0.00 0.00 0.00 3.00 587.38 2.90%

R201 7.00 1202.87 8.00 0.00 0.00 0.00 6.80 1253.10 12.10 0.00 0.00 0.00 8.00 1143.2 5.22% R202 6.00 1105.58 7.00 0.00 0.00 0.00 7.00 1134.27 11.90 0.00 0.00 0.00 8.00 1029.6 7.38% R203 5.00 942.97 36.00 0.00 0.00 0.00 4.90 977.41 24.20 0.00 0.00 0.00 6.00 870.8 8.29% R204 4.00 802.47 29.00 0.00 0.00 0.00 4.10 831.37 32.90 0.00 0.00 0.00 5.00 731.3 9.73% R205 6.00 1063.34 11.00 0.00 0.00 0.00 5.30 1093.84 24.30 0.00 0.00 0.00 5.00 949.8 11.95% R206 5.00 958.74 26.00 0.00 0.00 0.00 4.90 987.33 23.00 0.00 0.00 0.00 5.00 875.9 9.46% R207 4.00 904.12 27.00 0.00 0.00 0.00 3.80 925.21 36.20 0.00 0.00 0.00 3.00 794.0 13.87% R208 4.00 747.70 21.00 0.00 0.00 0.00 3.60 781.48 43.50 0.00 0.00 0.00 3.00 701.2 6.63% R209 5.00 928.64 15.00 0.00 0.00 0.00 5.10 954.10 19.40 0.00 0.00 0.00 5.00 854.8 8.64% R210 5.00 978.65 37.00 0.00 0.00 0.00 5.30 1027.02 28.10 0.00 0.00 0.00 6.00 900.5 8.68% R211 4.00 851.85 28.00 0.00 0.00 0.00 4.30 887.38 26.80 0.00 0.00 0.00 4.00 746.7 14.08%

R2-Avg. 5.00 953.36 22.27 0.00 0.00 0.00 5.01 986.59 25.67 0.00 0.00 0.00 5.27 872.53 9.45%

RC201 9.00 1373.11 10.00 0.00 0.00 0.00 8.20 1424.90 10.30 0.01 0.00 0.00 9.00 1261.8 8.82% RC202 9.00 1153.69 13.00 0.00 0.00 0.00 7.50 1233.60 12.40 0.00 0.00 0.00 8.00 1092.3 5.62% RC203 5.00 1000.07 19.00 0.00 0.00 0.00 5.50 1087.22 25.00 0.00 0.00 0.00 5.00 923.7 8.27% RC204 3.00 863.60 55.00 0.00 0.00 0.00 4.00 882.38 34.40 0.00 0.00 0.00 4.00 783.5 10.22% RC205 8.00 1267.44 9.00 0.00 0.00 0.00 7.40 1327.65 9.60 0.00 0.00 0.00 7.00 1154.0 9.83% RC206 6.00 1139.58 9.00 0.00 0.00 0.00 5.80 1190.55 16.00 0.00 0.00 0.00 7.00 1051.1 8.42% RC207 5.00 1063.02 10.00 0.00 0.00 0.00 5.50 1112.65 17.00 0.00 0.00 0.00 6.00 962.9 10.40% RC208 4.00 888.26 18.00 0.00 0.00 0.00 4.50 957.05 22.30 0.00 0.00 0.00 4.00 776.5 14.39%

RC2-Avg. 6.13 1093.60 17.88 0.00 0.00 0.00 6.05 1152.00 18.38 0.00 0.00 0.00 6.25 1000.73 9.50%

76 B.1. Computational Experiments

Table B22.: Detailed Test Result TS with Tabu Tenure =7

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 3.00 0.00 0.00 0.00 10.00 828.94 1.80 0.00 0.00 0.00 10.00 827.3 0.20% C102 11.00 853.87 1.00 0.00 0.00 0.00 10.90 912.23 1.70 0.00 0.00 0.00 10.00 827.3 3.21% C103 11.00 912.32 1.00 0.00 0.00 0.00 11.20 984.41 1.10 0.00 0.00 0.00 10.00 826.3 10.41% C104 10.00 876.67 5.00 0.00 0.00 0.00 10.60 974.53 3.20 0.00 0.00 0.00 10.00 822.9 6.53% C105 11.00 852.95 1.00 0.00 0.00 0.00 11.40 944.78 1.90 0.00 0.00 0.00 10.00 827.3 3.10% C106 10.00 832.27 2.00 0.00 0.00 0.00 11.10 909.94 2.70 0.00 0.00 0.00 10.00 827.3 0.60% C107 10.00 828.94 1.00 0.00 0.00 0.00 10.30 874.68 3.50 0.00 0.00 0.00 10.00 827.3 0.20% C108 11.00 872.36 1.00 0.00 0.00 0.00 11.30 942.97 2.40 0.00 0.00 0.00 10.00 827.3 5.45% C109 10.00 828.94 1.00 0.00 0.00 0.00 10.10 874.81 3.40 0.00 0.00 0.00 10.00 827.3 0.20%

C1-Avg. 10.44 854.14 1.78 0.00 0.00 0.00 10.77 916.37 2.41 0.00 0.00 0.00 10.00 826.70 3.32%

R101 21.00 1677.65 0.00 0.00 0.00 0.00 21.30 1695.74 0.00 0.00 0.00 0.00 20.00 1637.7 2.44% R102 19.00 1511.89 0.00 0.00 0.00 0.00 19.30 1527.25 0.00 0.01 0.00 0.00 18.00 1466.6 3.09% R103 16.00 1295.46 0.00 0.00 0.00 0.00 16.60 1332.75 0.00 0.00 0.00 0.00 14.00 1208.7 7.18% R104 13.00 1050.73 2.00 0.00 0.00 0.00 13.40 1095.68 2.20 0.00 0.00 0.00 11.00 971.5 8.16% R105 18.00 1461.90 1.00 0.00 0.00 0.00 17.20 1499.73 1.40 0.01 0.00 0.00 15.00 1355.3 7.87% R106 15.00 1309.96 2.00 0.00 0.00 0.00 15.10 1349.20 1.80 0.00 0.00 0.00 13.00 1234.6 6.10% R107 12.00 1157.22 2.00 0.00 0.00 0.00 13.70 1214.98 2.10 0.00 0.00 0.00 11.00 1064.6 8.70% R108 12.00 1016.58 1.00 0.00 0.00 0.00 11.60 1047.71 1.10 0.00 0.00 0.00 10.00 932.1 9.06% R109 14.00 1269.60 1.00 0.00 0.00 0.00 14.20 1295.25 0.20 0.00 0.00 0.00 13.00 1146.9 10.70% R110 13.00 1196.43 1.00 0.00 0.00 0.00 13.70 1223.10 0.50 0.00 0.00 0.00 12.00 1068.0 12.03% R111 12.00 1132.15 1.00 0.00 0.00 0.00 13.00 1176.99 0.70 0.00 0.00 0.00 12.00 1048.7 7.96% R112 11.00 1038.54 1.00 0.00 0.00 0.00 12.30 1092.22 1.00 0.00 0.00 0.00 10.00 948.6 9.48%

R1-Avg. 14.67 1259.84 1.00 0.00 0.00 0.00 15.12 1295.88 0.92 0.00 0.00 0.00 13.25 1173.61 7.73%

RC101 17.00 1725.93 0.00 0.00 0.00 0.00 17.30 1749.85 0.00 0.00 0.00 0.00 15.00 1619.8 6.55% RC102 15.00 1566.16 0.00 0.00 0.00 0.00 15.50 1614.81 0.00 0.00 0.00 0.00 14.00 1457.4 7.46% RC103 14.00 1411.76 0.00 0.00 0.00 0.00 14.00 1431.16 0.10 0.00 0.00 0.00 11.00 1258.0 12.22% RC104 11.00 1196.21 1.00 0.00 0.00 0.00 12.10 1270.48 1.30 0.00 0.00 0.00 10.00 1132.3 5.64% RC105 17.00 1631.33 0.00 0.00 0.00 0.00 17.50 1679.08 0.00 0.00 0.00 0.00 15.00 1513.7 7.77% RC106 14.00 1455.42 1.00 0.00 0.00 0.00 14.10 1479.75 1.50 0.00 0.00 0.00 13.00 1372.7 6.03% RC107 14.00 1335.62 1.00 0.00 0.00 0.00 13.60 1394.42 1.30 0.00 0.00 0.00 12.00 1207.8 10.58% RC108 12.00 1233.19 3.00 0.00 0.00 0.00 12.70 1276.22 3.00 0.00 0.00 0.00 11.00 1114.2 10.68%

RC1-Avg. 14.25 1444.45 0.75 0.00 0.00 0.00 14.60 1486.97 0.90 0.00 0.00 0.00 12.63 1334.49 8.37%

C201 3.00 591.56 28.00 0.00 0.00 0.00 3.00 594.55 24.80 0.00 0.00 0.00 3.00 589.1 0.42% C202 4.00 632.05 19.00 0.00 0.00 0.00 4.30 662.25 18.40 0.00 0.00 0.00 3.00 589.1 7.29% C203 3.00 631.06 20.00 0.00 0.00 0.00 4.30 670.38 15.10 0.00 0.00 0.00 3.00 588.7 7.20% C204 3.00 614.54 32.00 0.00 0.00 0.00 4.10 670.45 20.30 0.00 0.00 0.00 3.00 588.1 4.50% C205 3.00 609.36 27.00 0.00 0.00 0.00 3.50 620.81 24.50 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 26.00 0.00 0.00 0.00 4.20 638.38 20.30 0.00 0.00 0.00 3.00 586.0 0.43% C207 4.00 620.45 26.00 0.00 0.00 0.00 4.50 651.02 19.60 0.00 0.00 0.00 3.00 585.8 5.91% C208 3.00 588.32 40.00 0.00 0.00 0.00 3.20 593.83 31.30 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.25 609.48 27.25 0.00 0.00 0.00 3.89 637.71 21.79 0.00 0.00 0.00 3.00 587.38 3.76%

R201 7.00 1187.54 8.00 0.00 0.00 0.00 6.80 1261.91 7.40 0.00 0.00 0.00 8.00 1143.2 3.88% R202 7.00 1099.26 6.00 0.00 0.00 0.00 6.80 1122.52 7.90 0.00 0.00 0.00 8.00 1029.6 6.77% R203 5.00 917.78 22.00 0.00 0.00 0.00 5.00 986.88 16.50 0.00 0.00 0.00 6.00 870.8 5.39% R204 4.00 809.37 23.00 0.00 0.00 0.00 4.00 836.39 33.30 0.00 0.00 0.00 5.00 731.3 10.68% R205 6.00 1040.65 10.00 0.00 0.00 0.00 5.00 1087.45 13.80 0.00 0.00 0.00 5.00 949.8 9.57% R206 5.00 958.51 15.00 0.00 0.00 0.00 4.30 987.93 20.60 0.00 0.00 0.00 5.00 875.9 9.43% R207 5.00 877.66 16.00 0.00 0.00 0.00 3.70 925.42 34.20 0.00 0.00 0.00 3.00 794.0 10.54% R208 4.00 740.37 28.00 0.00 0.00 0.00 3.50 788.52 39.70 0.00 0.00 0.00 3.00 701.2 5.59% R209 5.00 925.85 9.00 0.00 0.00 0.00 5.00 962.12 17.70 0.00 0.00 0.00 5.00 854.8 8.31% R210 6.00 979.71 15.00 0.00 0.00 0.00 5.70 1017.81 10.40 0.00 0.00 0.00 6.00 900.5 8.80% R211 4.00 832.32 9.00 0.00 0.00 0.00 4.70 877.89 20.20 0.00 0.00 0.00 4.00 746.7 11.47%

R2-Avg. 5.27 942.64 14.64 0.00 0.00 0.00 4.95 986.80 20.15 0.00 0.00 0.00 5.27 872.53 8.22%

RC201 9.00 1337.84 10.00 0.00 0.00 0.00 8.00 1386.61 10.10 0.00 0.00 0.00 9.00 1261.8 6.03% RC202 8.00 1158.19 13.00 0.00 0.00 0.00 7.30 1229.97 10.60 0.00 0.00 0.00 8.00 1092.3 6.03% RC203 5.00 1045.62 8.00 0.00 0.00 0.00 5.30 1119.11 14.00 0.00 0.00 0.00 5.00 923.7 13.20% RC204 4.00 856.47 15.00 0.00 0.00 0.00 3.80 895.05 35.90 0.00 0.00 0.00 4.00 783.5 9.31% RC205 8.00 1217.46 5.00 0.00 0.00 0.00 7.40 1307.86 11.10 0.00 0.00 0.00 7.00 1154.0 5.50% RC206 6.00 1142.65 10.00 0.00 0.00 0.00 5.40 1227.19 14.00 0.00 0.00 0.00 7.00 1051.1 8.71% RC207 6.00 1014.20 5.00 0.00 0.00 0.00 5.60 1093.29 10.90 0.00 0.00 0.00 6.00 962.9 5.33% RC208 4.00 879.50 21.00 0.00 0.00 0.00 4.30 950.41 18.70 0.00 0.00 0.00 4.00 776.5 13.26%

RC2-Avg. 6.25 1081.49 10.88 0.00 0.00 0.00 5.89 1151.19 15.66 0.00 0.00 0.00 6.25 1000.73 8.42%

77 Appendix B

Table B23.: Detailed Test Result TS with Tabu Tenure =8

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 5.00 0.00 0.00 0.00 10.00 828.94 2.40 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 828.94 4.00 0.00 0.00 0.00 10.60 941.40 2.70 0.00 0.00 0.00 10.00 827.3 0.20% C103 11.00 908.86 1.00 0.00 0.00 0.00 11.20 1006.29 2.00 0.00 0.00 0.00 10.00 826.3 9.99% C104 11.00 914.21 4.00 0.00 0.00 0.00 10.50 1000.63 2.20 0.00 0.00 0.00 10.00 822.9 11.10% C105 10.00 828.94 1.00 0.00 0.00 0.00 11.00 912.23 1.10 0.00 0.00 0.00 10.00 827.3 0.20% C106 11.00 860.21 1.00 0.00 0.00 0.00 11.30 912.95 1.00 0.00 0.00 0.00 10.00 827.3 3.98% C107 10.00 828.94 2.00 0.00 0.00 0.00 10.30 876.18 1.50 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 828.94 5.00 0.00 0.00 0.00 11.40 936.21 3.20 0.00 0.00 0.00 10.00 827.3 0.20% C109 10.00 828.94 4.00 0.00 0.00 0.00 10.10 886.40 2.10 0.00 0.00 0.00 10.00 827.3 0.20%

C1-Avg. 10.33 850.77 3.00 0.00 0.00 0.00 10.71 922.36 2.02 0.00 0.00 0.00 10.00 826.70 2.92%

R101 21.00 1679.13 1.00 0.00 0.00 0.00 21.40 1696.01 0.90 0.00 0.00 0.00 20.00 1637.7 2.53% R102 19.00 1501.31 0.00 0.00 0.00 0.00 19.60 1543.30 0.70 0.01 0.00 0.00 18.00 1466.6 2.37% R103 16.00 1298.84 0.00 0.00 0.00 0.00 16.80 1341.62 0.70 0.00 0.00 0.00 14.00 1208.7 7.46% R104 13.00 1054.17 3.00 0.00 0.00 0.00 13.40 1087.72 2.50 0.00 0.00 0.00 11.00 971.5 8.51% R105 17.00 1440.98 1.00 0.00 0.00 0.00 17.10 1494.25 1.50 0.00 0.00 0.00 15.00 1355.3 6.32% R106 15.00 1298.29 0.00 0.00 0.00 0.00 15.50 1348.10 0.40 0.00 0.00 0.00 13.00 1234.6 5.16% R107 12.00 1149.78 1.00 0.00 0.00 0.00 13.40 1202.32 0.50 0.00 0.00 0.00 11.00 1064.6 8.00% R108 12.00 1026.74 2.00 0.00 0.00 0.00 11.90 1054.67 1.40 0.00 0.00 0.00 10.00 932.1 10.15% R109 14.00 1262.95 0.00 0.00 0.00 0.00 14.40 1297.36 0.00 0.00 0.00 0.00 13.00 1146.9 10.12% R110 13.00 1171.96 1.00 0.00 0.00 0.00 13.30 1215.49 0.40 0.00 0.00 0.00 12.00 1068.0 9.73% R111 13.00 1135.57 0.00 0.00 0.00 0.00 13.20 1185.44 0.70 0.00 0.00 0.00 12.00 1048.7 8.28% R112 11.00 1011.04 3.00 0.00 0.00 0.00 11.80 1070.01 1.40 0.00 0.00 0.00 10.00 948.6 6.58%

R1-Avg. 14.67 1252.56 1.00 0.00 0.00 0.00 15.15 1294.69 0.93 0.00 0.00 0.00 13.25 1173.61 7.10%

RC101 16.00 1708.83 2.00 0.00 0.00 0.00 17.10 1744.48 2.00 0.00 0.00 0.00 15.00 1619.8 5.50% RC102 15.00 1534.68 2.00 0.00 0.00 0.00 15.80 1606.23 2.00 0.00 0.00 0.00 14.00 1457.4 5.30% RC103 13.00 1400.85 2.00 0.00 0.00 0.00 14.10 1445.99 2.10 0.00 0.00 0.00 11.00 1258.0 11.36% RC104 12.00 1186.96 4.00 0.00 0.00 0.00 11.90 1248.43 1.80 0.00 0.00 0.00 10.00 1132.3 4.83% RC105 17.00 1639.07 0.00 0.00 0.00 0.00 17.80 1698.93 0.70 0.00 0.00 0.00 15.00 1513.7 8.28% RC106 14.00 1482.06 3.00 0.00 0.00 0.00 14.20 1499.04 2.20 0.00 0.00 0.00 13.00 1372.7 7.97% RC107 14.00 1371.49 2.00 0.00 0.00 0.00 14.00 1412.23 2.50 0.00 0.00 0.00 12.00 1207.8 13.55% RC108 12.00 1226.10 3.00 0.00 0.00 0.00 12.90 1297.81 2.90 0.00 0.00 0.00 11.00 1114.2 10.04%

RC1-Avg. 14.13 1443.76 2.25 0.00 0.00 0.00 14.73 1494.14 2.03 0.00 0.00 0.00 12.63 1334.49 8.35%

C201 3.00 591.56 23.00 0.00 0.00 0.00 3.00 594.55 31.10 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 591.56 28.00 0.00 0.00 0.00 4.30 652.47 21.80 0.00 0.00 0.00 3.00 589.1 0.42% C203 4.00 629.69 11.00 0.00 0.00 0.00 4.40 666.80 14.40 0.00 0.00 0.00 3.00 588.7 6.96% C204 5.00 643.92 17.00 0.00 0.00 0.00 4.40 696.07 16.10 0.00 0.00 0.00 3.00 588.1 9.49% C205 3.00 609.36 45.00 0.00 0.00 0.00 3.50 617.57 28.00 0.00 0.00 0.00 3.00 586.4 3.92% C206 4.00 609.70 47.00 0.00 0.00 0.00 4.40 645.34 21.20 0.00 0.00 0.00 3.00 586.0 4.04% C207 3.00 588.29 48.00 0.00 0.00 0.00 4.00 620.33 30.90 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 25.00 0.00 0.00 0.00 3.20 593.83 29.40 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.50 606.55 30.50 0.00 0.00 0.00 3.90 635.87 24.11 0.00 0.00 0.00 3.00 587.38 3.26%

R201 8.00 1191.94 7.00 0.00 0.00 0.00 7.30 1224.31 8.90 0.00 0.00 0.00 8.00 1143.2 4.26% R202 8.00 1088.81 9.00 0.00 0.00 0.00 7.00 1135.11 10.40 0.00 0.00 0.00 8.00 1029.6 5.75% R203 5.00 939.80 22.00 0.00 0.00 0.00 4.70 1020.91 26.10 0.00 0.00 0.00 6.00 870.8 7.92% R204 4.00 794.17 11.00 0.00 0.00 0.00 4.00 834.05 37.70 0.00 0.00 0.00 5.00 731.3 8.60% R205 6.00 1022.23 16.00 0.00 0.00 0.00 5.20 1073.28 21.40 0.00 0.00 0.00 5.00 949.8 7.63% R206 4.00 950.04 16.00 0.00 0.00 0.00 4.80 1002.22 24.00 0.00 0.00 0.00 5.00 875.9 8.46% R207 5.00 877.74 78.00 0.00 0.00 0.00 3.80 932.99 65.90 0.00 0.00 0.00 3.00 794.0 10.55% R208 4.00 738.60 73.00 0.00 0.00 0.00 3.50 786.42 71.50 0.00 0.00 0.00 3.00 701.2 5.33% R209 5.00 936.01 33.00 0.00 0.00 0.00 4.90 987.48 30.80 0.00 0.00 0.00 5.00 854.8 9.50% R210 5.00 974.37 35.00 0.00 0.00 0.00 5.40 1016.88 24.90 0.00 0.00 0.00 6.00 900.5 8.20% R211 5.00 834.33 12.00 0.00 0.00 0.00 4.30 893.09 49.10 0.00 0.00 0.00 4.00 746.7 11.74%

R2-Avg. 5.36 940.73 28.36 0.00 0.00 0.00 4.99 991.52 33.70 0.00 0.00 0.00 5.27 872.53 7.99%

RC201 8.00 1332.55 4.00 0.00 0.00 0.00 9.00 1401.71 7.80 0.00 0.00 0.00 9.00 1261.8 5.61% RC202 7.00 1139.68 6.00 0.00 0.00 0.00 7.10 1226.11 10.60 0.00 0.00 0.00 8.00 1092.3 4.34% RC203 7.00 980.15 23.00 0.00 0.00 0.00 5.50 1110.10 23.80 0.00 0.00 0.00 5.00 923.7 6.11% RC204 4.00 835.06 58.00 0.00 0.00 0.00 4.20 859.11 34.00 0.00 0.00 0.00 4.00 783.5 6.58% RC205 7.00 1216.84 15.00 0.00 0.00 0.00 7.30 1304.51 13.90 0.00 0.00 0.00 7.00 1154.0 5.45% RC206 6.00 1151.55 14.00 0.00 0.00 0.00 5.60 1193.37 16.90 0.00 0.00 0.00 7.00 1051.1 9.56% RC207 6.00 1053.45 21.00 0.00 0.00 0.00 5.60 1114.22 21.90 0.00 0.00 0.00 6.00 962.9 9.40% RC208 5.00 903.31 30.00 0.00 0.00 0.00 4.70 953.45 37.20 0.00 0.00 0.00 4.00 776.5 16.33%

RC2-Avg. 6.25 1076.57 21.38 0.00 0.00 0.00 6.13 1145.32 20.76 0.00 0.00 0.00 6.25 1000.73 7.92%

78 B.1. Computational Experiments

Table B24.: Detailed Test Result TS with Tabu Tenure =9

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 4.00 0.00 0.00 0.00 10.00 828.94 3.80 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 831.53 3.00 0.00 0.00 0.00 10.60 930.15 2.10 0.00 0.00 0.00 10.00 827.3 0.51% C103 10.00 828.07 4.00 0.00 0.00 0.00 10.70 972.59 2.30 0.00 0.00 0.00 10.00 826.3 0.21% C104 11.00 932.06 5.00 0.00 0.00 0.00 10.30 1032.82 3.50 0.00 0.00 0.00 10.00 822.9 13.27% C105 10.00 828.94 1.00 0.00 0.00 0.00 11.40 927.38 1.00 0.00 0.00 0.00 10.00 827.3 0.20% C106 10.00 828.94 1.00 0.00 0.00 0.00 10.70 882.62 1.60 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 2.00 0.00 0.00 0.00 10.40 896.92 2.00 0.00 0.00 0.00 10.00 827.3 0.20% C108 11.00 886.77 1.00 0.00 0.00 0.00 11.20 957.48 1.00 0.00 0.00 0.00 10.00 827.3 7.19% C109 11.00 860.82 1.00 0.00 0.00 0.00 10.30 905.23 1.10 0.00 0.00 0.00 10.00 827.3 4.05%

C1-Avg. 10.33 850.55 2.44 0.00 0.00 0.00 10.62 926.01 2.04 0.00 0.00 0.00 10.00 826.70 2.89%

R101 20.00 1658.16 0.00 0.00 0.00 0.00 21.40 1688.45 0.30 0.00 0.00 0.00 20.00 1637.7 1.25% R102 19.00 1511.72 0.00 0.00 0.00 0.00 19.40 1531.97 0.90 0.00 0.00 0.00 18.00 1466.6 3.08% R103 16.00 1280.04 0.00 0.00 0.00 0.00 16.50 1321.33 0.60 0.00 0.00 0.00 14.00 1208.7 5.90% R104 13.00 1061.35 1.00 0.00 0.00 0.00 13.40 1096.16 0.70 0.00 0.00 0.00 11.00 971.5 9.25% R105 17.00 1457.88 1.00 0.13 0.00 0.00 17.30 1498.01 0.50 0.01 0.00 0.00 15.00 1355.3 7.57% R106 15.00 1298.16 1.00 0.00 0.00 0.00 15.00 1346.16 0.80 0.00 0.00 0.00 13.00 1234.6 5.15% R107 13.00 1144.75 1.00 0.00 0.00 0.00 13.60 1201.23 0.50 0.00 0.00 0.00 11.00 1064.6 7.53% R108 11.00 1017.82 1.00 0.00 0.00 0.00 11.50 1046.60 1.00 0.00 0.00 0.00 10.00 932.1 9.20% R109 14.00 1246.30 1.00 0.00 0.00 0.00 14.40 1311.71 1.30 0.00 0.00 0.00 13.00 1146.9 8.67% R110 13.00 1185.05 0.00 0.00 0.00 0.00 13.60 1226.57 1.00 0.00 0.00 0.00 12.00 1068.0 10.96% R111 13.00 1152.30 2.00 0.00 0.00 0.00 13.60 1190.07 1.60 0.00 0.00 0.00 12.00 1048.7 9.88% R112 11.00 1019.10 6.00 0.00 0.00 0.00 11.90 1078.95 3.60 0.00 0.00 0.00 10.00 948.6 7.43%

R1-Avg. 14.58 1252.72 1.17 0.01 0.00 0.00 15.13 1294.77 1.07 0.00 0.00 0.00 13.25 1173.61 7.15%

RC101 17.00 1701.56 1.00 0.00 0.00 0.00 17.40 1743.14 0.80 0.01 0.00 0.00 15.00 1619.8 5.05% RC102 15.00 1570.94 1.00 0.00 0.00 0.00 16.30 1640.11 1.00 0.01 0.00 0.00 14.00 1457.4 7.79% RC103 14.00 1421.08 1.00 0.00 0.00 0.00 14.40 1441.30 1.00 0.00 0.00 0.00 11.00 1258.0 12.96% RC104 11.00 1189.14 2.00 0.00 0.00 0.00 11.90 1261.48 1.40 0.00 0.00 0.00 10.00 1132.3 5.02% RC105 17.00 1599.49 1.00 0.00 0.00 0.00 17.60 1668.10 0.90 0.00 0.00 0.00 15.00 1513.7 5.67% RC106 14.00 1475.15 1.00 0.00 0.00 0.00 14.00 1494.72 1.00 0.00 0.00 0.00 13.00 1372.7 7.46% RC107 14.00 1334.04 1.00 0.00 0.00 0.00 13.90 1406.34 1.00 0.00 0.00 0.00 12.00 1207.8 10.45% RC108 13.00 1235.52 1.00 0.00 0.00 0.00 12.80 1284.49 1.10 0.00 0.00 0.00 11.00 1114.2 10.89%

RC1-Avg. 10.00 1357.40 5.00 0.00 0.00 0.00 8.40 1406.35 7.40 0.01 0.00 0.00 12.63 1334.49 8.16%

C201 3.00 591.56 53.00 0.00 0.00 0.00 3.00 597.55 42.50 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 591.56 31.00 0.00 0.00 0.00 4.10 640.32 33.50 0.00 0.00 0.00 3.00 589.1 0.42% C203 4.00 629.68 14.00 0.00 0.00 0.00 4.70 688.86 15.20 0.00 0.00 0.00 3.00 588.7 6.96% C204 4.00 655.09 17.00 0.00 0.00 0.00 4.30 684.37 17.50 0.00 0.00 0.00 3.00 588.1 11.39% C205 3.00 609.36 44.00 0.00 0.00 0.00 3.60 617.30 56.10 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 49.00 0.00 0.00 0.00 4.10 623.78 40.10 0.00 0.00 0.00 3.00 586.0 0.43% C207 3.00 588.29 22.00 0.00 0.00 0.00 4.00 633.36 28.10 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 49.00 0.00 0.00 0.00 3.20 593.94 51.40 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.25 605.29 34.88 0.00 0.00 0.00 3.88 634.93 35.55 0.00 0.00 0.00 3.00 587.38 3.05%

R201 7.00 1220.14 8.00 0.00 0.00 0.00 7.10 1276.01 8.60 0.00 0.00 0.00 8.00 1143.2 6.73% R202 7.00 1083.86 9.00 0.00 0.00 0.00 6.80 1123.95 14.30 0.00 0.00 0.00 8.00 1029.6 5.27% R203 6.00 938.77 26.00 0.00 0.00 0.00 5.30 996.45 38.60 0.00 0.00 0.00 6.00 870.8 7.81% R204 5.00 763.54 23.00 0.00 0.00 0.00 4.20 830.77 51.20 0.00 0.00 0.00 5.00 731.3 4.41% R205 7.00 1043.68 14.00 0.00 0.00 0.00 5.80 1092.67 19.90 0.00 0.00 0.00 5.00 949.8 9.88% R206 5.00 939.69 22.00 0.00 0.00 0.00 4.70 987.51 26.10 0.00 0.00 0.00 5.00 875.9 7.28% R207 4.00 858.13 46.00 0.00 0.00 0.00 3.90 919.93 46.70 0.00 0.00 0.00 3.00 794.0 8.08% R208 4.00 737.91 90.00 0.00 0.00 0.00 3.40 777.66 87.00 0.00 0.00 0.00 3.00 701.2 5.24% R209 5.00 921.52 20.00 0.00 0.00 0.00 4.70 985.33 27.20 0.00 0.00 0.00 5.00 854.8 7.81% R210 6.00 955.11 20.00 0.00 0.00 0.00 5.70 1018.03 17.70 0.00 0.00 0.00 6.00 900.5 6.06% R211 4.00 823.93 50.00 0.00 0.00 0.00 4.30 873.27 32.60 0.00 0.00 0.00 4.00 746.7 10.34%

R2-Avg. 5.45 935.12 29.82 0.00 0.00 0.00 5.08 989.23 33.63 0.00 0.00 0.00 5.27 872.53 7.17%

RC201 10.00 1357.40 5.00 0.00 0.00 0.00 8.40 1406.35 7.40 0.01 0.00 0.00 9.00 1261.8 7.58% RC202 8.00 1144.07 11.00 0.00 0.00 0.00 7.00 1201.59 11.80 0.00 0.00 0.00 8.00 1092.3 4.74% RC203 6.00 1028.11 17.00 0.00 0.00 0.00 5.20 1078.21 20.10 0.00 0.00 0.00 5.00 923.7 11.30% RC204 4.00 832.45 21.00 0.00 0.00 0.00 3.70 896.44 33.80 0.00 0.00 0.00 4.00 783.5 6.25% RC205 8.00 1215.25 6.00 0.00 0.00 0.00 7.30 1301.10 9.30 0.00 0.00 0.00 7.00 1154.0 5.31% RC206 5.00 1159.04 16.00 0.00 0.00 0.00 5.80 1191.47 14.70 0.00 0.00 0.00 7.00 1051.1 10.27% RC207 5.00 1060.26 18.00 0.00 0.00 0.00 5.80 1103.89 14.30 0.00 0.00 0.00 6.00 962.9 10.11% RC208 5.00 924.53 16.00 0.00 0.00 0.00 4.10 980.75 24.00 0.00 0.00 0.00 4.00 776.5 19.06%

RC2-Avg. 6.38 1090.14 13.75 0.00 0.00 0.00 5.91 1144.98 16.93 0.00 0.00 0.00 6.25 1000.73 9.33%

79 Appendix B

Table B25.: Detailed Test Result TS with Tabu Tenure =10

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 2.00 0.00 0.00 0.00 10.00 828.94 2.00 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 832.61 2.00 0.00 0.00 0.00 10.50 923.33 2.10 0.00 0.00 0.00 10.00 827.3 0.64% C103 10.00 880.14 2.00 0.00 0.00 0.00 10.80 946.91 4.10 0.00 0.00 0.00 10.00 826.3 6.52% C104 10.00 870.59 2.00 0.00 0.00 0.00 10.40 983.37 2.30 0.00 0.00 0.00 10.00 822.9 5.79% C105 10.00 828.94 2.00 0.00 0.00 0.00 11.20 908.08 1.90 0.00 0.00 0.00 10.00 827.3 0.20% C106 11.00 895.42 1.00 0.00 0.00 0.00 11.30 925.96 1.80 0.00 0.00 0.00 10.00 827.3 8.23% C107 10.00 828.94 2.00 0.00 0.00 0.00 10.10 848.09 2.00 0.00 0.00 0.00 10.00 827.3 0.20% C108 11.00 885.09 2.00 0.00 0.00 0.00 11.40 939.16 1.90 0.00 0.00 0.00 10.00 827.3 6.98% C109 10.00 828.94 2.00 0.00 0.00 0.00 10.10 898.75 2.00 0.00 0.00 0.00 10.00 827.3 0.20%

C1-Avg. 10.22 853.29 1.89 0.00 0.00 0.00 10.64 911.40 2.23 0.00 0.00 0.00 10.00 826.70 3.22%

R101 21.00 1668.29 1.00 0.00 0.00 0.00 21.50 1700.03 0.60 0.00 0.00 0.00 20.00 1637.7 1.87% R102 18.00 1487.34 1.00 0.00 0.00 0.00 19.40 1532.73 1.00 0.01 0.00 0.00 18.00 1466.6 1.41% R103 16.00 1307.03 2.00 0.00 0.00 0.00 16.80 1344.76 1.80 0.00 0.00 0.00 14.00 1208.7 8.14% R104 13.00 1059.91 2.00 0.00 0.00 0.00 13.40 1111.23 2.40 0.00 0.00 0.00 11.00 971.5 9.10% R105 17.00 1425.92 1.00 0.00 0.00 0.00 17.00 1486.52 1.50 0.00 0.00 0.00 15.00 1355.3 5.21% R106 15.00 1313.14 2.00 0.00 0.00 0.00 15.40 1349.81 1.90 0.00 0.00 0.00 13.00 1234.6 6.36% R107 13.00 1150.30 3.00 0.00 0.00 0.00 13.40 1194.68 2.40 0.00 0.00 0.00 11.00 1064.6 8.05% R108 10.00 998.38 3.00 0.00 0.00 0.00 11.40 1035.15 3.00 0.00 0.00 0.00 10.00 932.1 7.11% R109 15.00 1269.88 2.00 0.00 0.00 0.00 14.30 1308.67 1.50 0.00 0.00 0.00 13.00 1146.9 10.72% R110 13.00 1193.64 2.00 0.00 0.00 0.00 13.00 1223.99 1.60 0.00 0.00 0.00 12.00 1068.0 11.76% R111 13.00 1130.48 1.00 0.00 0.00 0.00 13.00 1172.36 1.00 0.00 0.00 0.00 12.00 1048.7 7.80% R112 11.00 1020.22 3.00 0.00 0.00 0.00 12.00 1082.86 1.30 0.00 0.00 0.00 10.00 948.6 7.55%

R1-Avg. 14.58 1252.04 1.92 0.00 0.00 0.00 15.05 1295.23 1.67 0.00 0.00 0.00 13.25 1173.61 7.09%

RC101 17.00 1688.94 2.00 0.00 0.00 0.00 17.20 1745.49 1.30 0.00 0.00 0.00 15.00 1619.8 4.27% RC102 15.00 1570.58 2.00 0.00 0.00 0.00 15.70 1627.00 1.90 0.00 0.00 0.00 14.00 1457.4 7.77% RC103 13.00 1392.37 2.00 0.00 0.00 0.00 14.00 1430.88 1.80 0.00 0.00 0.00 11.00 1258.0 10.68% RC104 12.00 1195.37 2.00 0.00 0.00 0.00 11.80 1250.19 2.70 0.00 0.00 0.00 10.00 1132.3 5.57% RC105 17.00 1658.32 1.00 0.00 0.00 0.00 17.70 1693.29 0.60 0.00 0.00 0.00 15.00 1513.7 9.55% RC106 15.00 1472.61 2.00 0.00 0.00 0.00 14.30 1501.13 1.80 0.00 0.00 0.00 13.00 1372.7 7.28% RC107 13.00 1319.22 1.00 0.00 0.00 0.00 13.70 1389.99 1.70 0.00 0.00 0.00 12.00 1207.8 9.23% RC108 12.00 1213.98 2.00 0.00 0.00 0.00 12.70 1283.54 1.00 0.00 0.00 0.00 11.00 1114.2 8.96%

RC1-Avg. 14.25 1438.92 1.75 0.00 0.00 0.00 14.64 1490.19 1.60 0.00 0.00 0.00 12.63 1334.49 7.91%

C201 3.00 591.56 38.00 0.00 0.00 0.00 3.00 591.56 43.60 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 591.56 34.00 0.00 0.00 0.00 4.10 666.06 25.30 0.00 0.00 0.00 3.00 589.1 0.42% C203 3.00 610.99 30.00 0.00 0.00 0.00 4.10 655.16 20.00 0.00 0.00 0.00 3.00 588.7 3.79% C204 4.00 623.06 24.00 0.00 0.00 0.00 4.20 686.92 23.40 0.00 0.00 0.00 3.00 588.1 5.94% C205 3.00 609.36 50.00 0.00 0.00 0.00 3.40 618.75 40.00 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 41.00 0.00 0.00 0.00 4.10 634.36 29.00 0.00 0.00 0.00 3.00 586.0 0.43% C207 3.00 588.29 51.00 0.00 0.00 0.00 4.30 640.98 26.50 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 35.00 0.00 0.00 0.00 3.20 591.60 41.40 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.13 598.95 37.88 0.00 0.00 0.00 3.80 635.67 31.15 0.00 0.00 0.00 3.00 587.38 1.97%

R201 8.00 1234.57 9.00 0.00 0.00 0.00 8.00 1275.03 11.60 0.00 0.00 0.00 8.00 1143.2 7.99% R202 7.00 1095.26 22.00 0.00 0.00 0.00 7.10 1131.21 13.90 0.00 0.00 0.00 8.00 1029.6 6.38% R203 5.00 930.86 37.00 0.00 0.00 0.00 5.20 982.63 28.30 0.00 0.00 0.00 6.00 870.8 6.90% R204 4.00 799.67 32.00 0.00 0.00 0.00 4.00 832.14 34.40 0.00 0.00 0.00 5.00 731.3 9.35% R205 8.00 1028.76 8.00 0.00 0.00 0.00 5.50 1068.95 12.30 0.00 0.00 0.00 5.00 949.8 8.31% R206 5.00 937.26 8.00 0.00 0.00 0.00 5.00 981.78 18.00 0.00 0.00 0.00 5.00 875.9 7.01% R207 4.00 873.59 29.00 0.00 0.00 0.00 3.90 920.81 39.80 0.00 0.00 0.00 3.00 794.0 10.02% R208 4.00 750.18 36.00 0.00 0.00 0.00 4.00 790.20 51.10 0.00 0.00 0.00 3.00 701.2 6.98% R209 5.00 946.21 16.00 0.00 0.00 0.00 4.80 991.08 25.40 0.00 0.00 0.00 5.00 854.8 10.69% R210 6.00 945.07 15.00 0.00 0.00 0.00 5.40 996.63 17.00 0.00 0.00 0.00 6.00 900.5 4.95% R211 4.00 829.32 15.00 0.00 0.00 0.00 4.50 874.18 30.60 0.00 0.00 0.00 4.00 746.7 11.06%

R2-Avg. 5.45 942.79 20.64 0.00 0.00 0.00 5.22 985.88 25.67 0.00 0.00 0.00 5.27 872.53 8.15%

RC201 8.00 1353.79 4.00 0.00 0.00 0.00 7.80 1416.39 7.50 0.00 0.00 0.00 9.00 1261.8 7.29% RC202 6.00 1149.14 5.00 0.00 0.00 0.00 7.20 1214.50 12.00 0.00 0.00 0.00 8.00 1092.3 5.20% RC203 6.00 987.54 13.00 0.00 0.00 0.00 5.20 1092.96 17.70 0.00 0.00 0.00 5.00 923.7 6.91% RC204 4.00 843.23 33.00 0.00 0.00 0.00 3.70 912.31 40.50 0.00 0.00 0.00 4.00 783.5 7.62% RC205 8.00 1251.71 6.00 0.00 0.00 0.00 7.20 1358.93 7.70 0.00 0.00 0.00 7.00 1154.0 8.47% RC206 5.00 1149.34 8.00 0.00 0.00 0.00 5.70 1200.49 14.10 0.00 0.00 0.00 7.00 1051.1 9.35% RC207 7.00 1064.58 6.00 0.00 0.00 0.00 5.70 1095.09 16.40 0.00 0.00 0.00 6.00 962.9 10.56% RC208 5.00 847.04 12.00 0.00 0.00 0.00 4.60 936.07 19.50 0.00 0.00 0.00 4.00 776.5 9.08%

RC2-Avg. 6.13 1080.80 10.88 0.00 0.00 0.00 5.89 1153.34 16.93 0.00 0.00 0.00 6.25 1000.73 8.06%

80 B.1. Computational Experiments

Table B26.: Detailed Test Result TS with Tabu Tenure =11

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 2.00 0.00 0.00 0.00 10.00 828.94 1.40 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 828.94 2.00 0.00 0.00 0.00 10.80 915.64 1.40 0.00 0.00 0.00 10.00 827.3 0.20% C103 11.00 899.47 1.00 0.00 0.00 0.00 10.90 1003.81 1.60 0.00 0.00 0.00 10.00 826.3 8.85% C104 10.00 864.30 1.00 0.00 0.00 0.00 10.60 930.85 1.20 0.00 0.00 0.00 10.00 822.9 5.03% C105 10.00 828.94 3.00 0.00 0.00 0.00 11.10 921.39 2.40 0.00 0.00 0.00 10.00 827.3 0.20% C106 10.00 828.94 4.00 0.00 0.00 0.00 11.30 899.66 2.20 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 1.00 0.00 0.00 0.00 10.10 883.67 2.10 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 828.94 1.00 0.00 0.00 0.00 11.10 917.86 1.10 0.00 0.00 0.00 10.00 827.3 0.20% C109 10.00 831.85 1.00 0.00 0.00 0.00 10.20 896.15 1.30 0.00 0.00 0.00 10.00 827.3 0.55%

C1-Avg. 10.11 841.03 1.78 0.00 0.00 0.00 10.68 910.89 1.63 0.00 0.00 0.00 10.00 826.70 1.74%

R101 20.00 1681.11 0.00 0.00 0.00 0.00 21.40 1689.41 0.30 0.00 0.00 0.00 20.00 1637.7 2.65% R102 19.00 1519.42 1.00 0.00 0.00 0.00 19.60 1536.58 1.10 0.00 0.00 0.00 18.00 1466.6 3.60% R103 15.00 1289.27 1.00 0.00 0.00 0.00 16.60 1328.22 1.40 0.00 0.00 0.00 14.00 1208.7 6.67% R104 13.00 1061.04 3.00 0.00 0.00 0.00 13.30 1100.57 2.70 0.00 0.00 0.00 11.00 971.5 9.22% R105 16.00 1466.77 1.00 0.00 0.00 0.00 17.00 1485.39 1.30 0.00 0.00 0.00 15.00 1355.3 8.22% R106 14.00 1299.12 2.00 0.00 0.00 0.00 14.80 1335.09 1.50 0.00 0.00 0.00 13.00 1234.6 5.23% R107 13.00 1176.57 0.00 0.00 0.00 0.00 13.50 1191.45 0.30 0.00 0.00 0.00 11.00 1064.6 10.52% R108 11.00 1016.18 2.00 0.00 0.00 0.00 12.00 1051.37 1.80 0.00 0.00 0.00 10.00 932.1 9.02% R109 14.00 1266.97 2.00 0.00 0.00 0.00 14.20 1301.84 1.80 0.00 0.00 0.00 13.00 1146.9 10.47% R110 13.00 1149.17 3.00 0.00 0.00 0.00 13.30 1237.91 2.40 0.00 0.00 0.00 12.00 1068.0 7.60% R111 13.00 1141.42 2.00 0.00 0.00 0.00 13.40 1189.35 2.10 0.00 0.00 0.00 12.00 1048.7 8.84% R112 11.00 1031.65 1.00 0.00 0.00 0.00 11.80 1077.07 1.80 0.00 0.00 0.00 10.00 948.6 8.76%

R1-Avg. 14.33 1258.22 1.50 0.00 0.00 0.00 15.08 1293.69 1.54 0.00 0.00 0.00 13.25 1173.61 7.57%

RC101 17.00 1706.69 2.00 0.00 0.00 0.00 17.50 1746.04 1.50 0.00 0.00 0.00 15.00 1619.8 5.36% RC102 16.00 1583.92 1.00 0.00 0.00 0.00 15.70 1619.45 0.90 0.00 0.00 0.00 14.00 1457.4 8.68% RC103 13.00 1370.16 2.00 0.00 0.00 0.00 13.80 1422.14 1.20 0.00 0.00 0.00 11.00 1258.0 8.92% RC104 12.00 1220.52 3.00 0.00 0.00 0.00 12.10 1277.75 2.90 0.00 0.00 0.00 10.00 1132.3 7.79% RC105 17.00 1645.41 1.00 0.00 0.00 0.00 17.40 1682.62 1.00 0.00 0.00 0.00 15.00 1513.7 8.70% RC106 14.00 1473.21 2.00 0.00 0.00 0.00 14.30 1498.70 1.90 0.00 0.00 0.00 13.00 1372.7 7.32% RC107 13.00 1342.33 2.00 0.00 0.00 0.00 13.70 1392.88 2.10 0.00 0.00 0.00 12.00 1207.8 11.14% RC108 12.00 1230.15 2.00 0.00 0.00 0.00 12.70 1282.44 1.60 0.00 0.00 0.00 11.00 1114.2 10.41%

RC1-Avg. 14.25 1446.55 1.88 0.00 0.00 0.00 14.65 1490.25 1.64 0.00 0.00 0.00 12.63 1334.49 8.54%

C201 3.00 591.56 28.00 0.00 0.00 0.00 3.00 591.56 29.50 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 591.56 31.00 0.00 0.00 0.00 4.30 662.41 19.60 0.00 0.00 0.00 3.00 589.1 0.42% C203 3.00 621.21 21.00 0.00 0.00 0.00 4.10 666.57 18.20 0.00 0.00 0.00 3.00 588.7 5.52% C204 4.00 638.36 13.00 0.00 0.00 0.00 4.30 688.96 18.10 0.00 0.00 0.00 3.00 588.1 8.55% C205 3.00 609.36 31.00 0.00 0.00 0.00 3.90 624.58 27.50 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 20.00 0.00 0.00 0.00 4.50 644.80 25.00 0.00 0.00 0.00 3.00 586.0 0.43% C207 3.00 588.29 30.00 0.00 0.00 0.00 4.10 630.02 23.10 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 72.00 0.00 0.00 0.00 3.10 595.76 59.30 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.13 602.14 30.75 0.00 0.00 0.00 3.91 638.08 27.54 0.00 0.00 0.00 3.00 587.38 2.51%

R201 10.00 1222.68 10.00 0.00 0.00 0.00 7.80 1256.78 13.00 0.00 0.00 0.00 8.00 1143.2 6.95% R202 7.00 1086.28 7.00 0.00 0.00 0.00 6.70 1141.60 14.40 0.00 0.00 0.00 8.00 1029.6 5.51% R203 5.00 947.11 24.00 0.00 0.00 0.00 5.20 967.40 27.80 0.00 0.00 0.00 6.00 870.8 8.76% R204 5.00 758.93 63.00 0.00 0.00 0.00 4.30 828.20 47.80 0.00 0.00 0.00 5.00 731.3 3.78% R205 5.00 987.56 20.00 0.00 0.00 0.00 4.70 1059.70 26.20 0.00 0.00 0.00 5.00 949.8 3.98% R206 4.00 930.85 58.00 0.00 0.00 0.00 4.80 1024.17 27.10 0.00 0.00 0.00 5.00 875.9 6.27% R207 5.00 861.42 37.00 0.00 0.00 0.00 3.90 913.27 40.80 0.00 0.00 0.00 3.00 794.0 8.49% R208 3.00 738.68 103.00 0.00 0.00 0.00 3.60 771.66 61.90 0.00 0.00 0.00 3.00 701.2 5.34% R209 6.00 953.13 30.00 0.00 0.00 0.00 5.30 991.44 25.50 0.00 0.00 0.00 5.00 854.8 11.50% R210 6.00 987.83 35.00 0.00 0.00 0.00 5.90 1022.49 32.30 0.00 0.00 0.00 6.00 900.5 9.70% R211 5.00 836.19 12.00 0.00 0.00 0.00 4.00 895.97 50.40 0.00 0.00 0.00 4.00 746.7 11.98%

R2-Avg. 5.55 937.33 36.27 0.00 0.00 0.00 5.11 988.42 33.38 0.00 0.00 0.00 5.27 872.53 7.48%

RC201 9.00 1352.89 10.00 0.00 0.00 0.00 8.60 1396.74 10.70 0.00 0.00 0.00 9.00 1261.8 7.22% RC202 8.00 1162.39 10.00 0.00 0.00 0.00 7.00 1220.51 12.90 0.00 0.00 0.00 8.00 1092.3 6.42% RC203 6.00 976.30 14.00 0.00 0.00 0.00 5.20 1066.27 22.20 0.00 0.00 0.00 5.00 923.7 5.69% RC204 4.00 830.07 16.00 0.00 0.00 0.00 3.50 915.18 47.40 0.00 0.00 0.00 4.00 783.5 5.94% RC205 8.00 1209.19 13.00 0.00 0.00 0.00 7.40 1292.91 14.10 0.00 0.00 0.00 7.00 1154.0 4.78% RC206 7.00 1127.51 19.00 0.00 0.00 0.00 6.00 1197.21 23.30 0.00 0.00 0.00 7.00 1051.1 7.27% RC207 5.00 1081.23 25.00 0.00 0.00 0.00 5.50 1119.27 20.40 0.00 0.00 0.00 6.00 962.9 12.29% RC208 5.00 865.70 37.00 0.00 0.00 0.00 4.60 937.46 36.80 0.00 0.00 0.00 4.00 776.5 11.49%

RC2-Avg. 6.50 1075.66 18.00 0.00 0.00 0.00 5.98 1143.19 23.48 0.00 0.00 0.00 6.25 1000.73 7.64%

81 Appendix B

Table B27.: Detailed Test Result TS with Tabu Tenure =12

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 4.00 0.00 0.00 0.00 10.00 828.94 1.70 0.00 0.00 0.00 10.00 827.3 0.20% C102 11.00 855.51 3.00 0.00 0.00 0.00 10.40 935.32 1.80 0.00 0.00 0.00 10.00 827.3 3.41% C103 10.00 862.98 4.00 0.00 0.00 0.00 10.60 959.69 3.20 0.00 0.00 0.00 10.00 826.3 4.44% C104 10.00 869.50 3.00 0.00 0.00 0.00 10.30 976.30 3.30 0.00 0.00 0.00 10.00 822.9 5.66% C105 10.00 828.94 4.00 0.00 0.00 0.00 11.10 916.05 3.50 0.00 0.00 0.00 10.00 827.3 0.20% C106 11.00 894.68 4.00 0.00 0.00 0.00 11.50 936.79 3.00 0.00 0.00 0.00 10.00 827.3 8.14% C107 10.00 828.94 1.00 0.00 0.00 0.00 10.20 843.24 1.10 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 864.93 1.00 0.00 0.00 0.00 11.40 929.32 2.50 0.00 0.00 0.00 10.00 827.3 4.55% C109 10.00 828.94 1.00 0.00 0.00 0.00 10.10 874.07 1.60 0.00 0.00 0.00 10.00 827.3 0.20%

C1-Avg. 10.22 851.48 2.78 0.00 0.00 0.00 10.62 911.08 2.41 0.00 0.00 0.00 10.00 826.70 3.00%

R101 22.00 1667.66 1.00 0.00 0.00 0.00 21.40 1690.24 0.50 0.00 0.00 0.00 20.00 1637.7 1.83% R102 19.00 1491.49 1.00 0.00 0.00 0.00 19.10 1517.08 1.00 0.02 0.00 0.00 18.00 1466.6 1.70% R103 17.00 1320.67 1.00 0.00 0.00 0.00 16.90 1335.33 0.90 0.00 0.00 0.00 14.00 1208.7 9.26% R104 12.00 1082.07 4.00 0.00 0.00 0.00 13.60 1111.96 2.40 0.00 0.00 0.00 11.00 971.5 11.38% R105 16.00 1448.88 2.00 0.00 0.00 0.00 16.90 1478.31 1.00 0.00 0.00 0.00 15.00 1355.3 6.90% R106 15.00 1328.08 0.00 0.00 0.00 0.00 15.60 1358.59 0.10 0.00 0.00 0.00 13.00 1234.6 7.57% R107 13.00 1181.80 2.00 0.00 0.00 0.00 13.80 1212.77 1.70 0.00 0.00 0.00 11.00 1064.6 11.01% R108 12.00 1037.60 3.00 0.00 0.00 0.00 11.90 1062.33 2.60 0.00 0.00 0.00 10.00 932.1 11.32% R109 14.00 1267.38 2.00 0.00 0.00 0.00 14.40 1294.88 1.40 0.00 0.00 0.00 13.00 1146.9 10.50% R110 13.00 1174.99 1.00 0.00 0.00 0.00 13.50 1224.48 1.30 0.00 0.00 0.00 12.00 1068.0 10.02% R111 13.00 1137.28 3.00 0.00 0.00 0.00 13.10 1176.65 2.00 0.00 0.00 0.00 12.00 1048.7 8.45% R112 12.00 1047.72 1.00 0.00 0.00 0.00 12.00 1076.61 1.00 0.00 0.00 0.00 10.00 948.6 10.45%

R1-Avg. 14.83 1265.47 1.75 0.00 0.00 0.00 15.18 1294.94 1.33 0.00 0.00 0.00 13.25 1173.61 8.37%

RC101 17.00 1720.75 0.00 0.00 0.00 0.00 17.40 1755.40 0.00 0.00 0.00 0.00 15.00 1619.8 6.23% RC102 15.00 1541.94 2.00 0.00 0.00 0.00 15.60 1614.59 1.90 0.00 0.00 0.00 14.00 1457.4 5.80% RC103 14.00 1419.86 2.00 0.00 0.00 0.00 14.20 1453.69 2.00 0.00 0.00 0.00 11.00 1258.0 12.87% RC104 12.00 1208.39 2.00 0.00 0.00 0.00 12.10 1263.30 2.80 0.00 0.00 0.00 10.00 1132.3 6.72% RC105 18.00 1621.98 1.00 0.00 0.00 0.00 17.60 1675.23 1.30 0.00 0.00 0.00 15.00 1513.7 7.15% RC106 14.00 1439.18 2.00 0.00 0.00 0.00 13.90 1486.31 1.50 0.00 0.00 0.00 13.00 1372.7 4.84% RC107 13.00 1343.58 2.00 0.00 0.00 0.00 13.60 1388.30 2.00 0.00 0.00 0.00 12.00 1207.8 11.24% RC108 12.00 1207.25 1.00 0.00 0.00 0.00 12.80 1271.22 0.90 0.00 0.00 0.00 11.00 1114.2 8.35%

RC1-Avg. 14.38 1437.87 1.50 0.00 0.00 0.00 14.65 1488.51 1.55 0.00 0.00 0.00 12.63 1334.49 7.90%

C201 3.00 591.56 63.00 0.00 0.00 0.00 3.00 591.56 54.80 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 611.08 63.00 0.00 0.00 0.00 4.20 647.24 43.90 0.00 0.00 0.00 3.00 589.1 3.73% C203 3.00 617.80 39.00 0.00 0.00 0.00 4.00 663.49 39.50 0.00 0.00 0.00 3.00 588.7 4.94% C204 4.00 654.61 49.00 0.00 0.00 0.00 4.10 696.80 38.50 0.00 0.00 0.00 3.00 588.1 11.31% C205 3.00 609.36 55.00 0.00 0.00 0.00 3.60 616.41 49.80 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 60.00 0.00 0.00 0.00 3.90 618.24 38.60 0.00 0.00 0.00 3.00 586.0 0.43% C207 3.00 588.29 40.00 0.00 0.00 0.00 3.70 618.22 43.40 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 70.00 0.00 0.00 0.00 3.20 592.61 54.60 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.13 606.19 54.88 0.00 0.00 0.00 3.71 630.57 45.39 0.00 0.00 0.00 3.00 587.38 3.20%

R201 9.00 1220.26 18.00 0.00 0.00 0.00 7.50 1269.47 12.00 0.00 0.00 0.00 8.00 1143.2 6.74% R202 6.00 1088.78 15.00 0.00 0.00 0.00 6.80 1138.36 19.80 0.00 0.00 0.00 8.00 1029.6 5.75% R203 5.00 928.40 50.00 0.00 0.00 0.00 5.30 992.07 40.80 0.00 0.00 0.00 6.00 870.8 6.61% R204 5.00 757.62 52.00 0.00 0.00 0.00 4.30 836.48 56.80 0.00 0.00 0.00 5.00 731.3 3.60% R205 6.00 1014.86 21.00 0.00 0.00 0.00 5.10 1115.12 28.40 0.00 0.00 0.00 5.00 949.8 6.85% R206 5.00 940.05 21.00 0.00 0.00 0.00 4.50 981.77 31.00 0.00 0.00 0.00 5.00 875.9 7.32% R207 4.00 839.65 58.00 0.00 0.00 0.00 4.00 924.50 46.50 0.00 0.00 0.00 3.00 794.0 5.75% R208 4.00 754.38 44.00 0.00 0.00 0.00 3.40 779.42 65.40 0.00 0.00 0.00 3.00 701.2 7.58% R209 5.00 911.61 14.00 0.00 0.00 0.00 4.70 966.45 22.10 0.00 0.00 0.00 5.00 854.8 6.65% R210 6.00 977.82 11.00 0.00 0.00 0.00 5.40 1015.45 16.20 0.00 0.00 0.00 6.00 900.5 8.59% R211 4.00 824.21 21.00 0.00 0.00 0.00 3.80 883.17 42.30 0.00 0.00 0.00 4.00 746.7 10.38%

R2-Avg. 5.36 932.51 29.55 0.00 0.00 0.00 4.98 991.12 34.66 0.00 0.00 0.00 5.27 872.53 6.89%

RC201 8.00 1321.51 8.00 0.00 0.00 0.00 8.60 1398.77 10.00 0.00 0.00 0.00 9.00 1261.8 4.73% RC202 8.00 1139.55 14.00 0.00 0.00 0.00 7.70 1211.41 11.40 0.00 0.00 0.00 8.00 1092.3 4.33% RC203 6.00 1015.41 17.00 0.00 0.00 0.00 5.30 1088.26 24.10 0.00 0.00 0.00 5.00 923.7 9.93% RC204 4.00 858.42 20.00 0.00 0.00 0.00 4.00 885.95 44.80 0.00 0.00 0.00 4.00 783.5 9.56% RC205 7.00 1264.27 10.00 0.00 0.00 0.00 7.30 1316.77 12.10 0.00 0.00 0.00 7.00 1154.0 9.56% RC206 7.00 1148.24 22.00 0.00 0.00 0.00 5.90 1218.59 24.00 0.00 0.00 0.00 7.00 1051.1 9.24% RC207 6.00 1031.50 20.00 0.00 0.00 0.00 5.70 1111.06 20.90 0.00 0.00 0.00 6.00 962.9 7.12% RC208 5.00 904.30 33.00 0.00 0.00 0.00 4.50 952.73 30.60 0.00 0.00 0.00 4.00 776.5 16.46%

RC2-Avg. 6.38 1085.40 18.00 0.00 0.00 0.00 6.13 1147.94 22.24 0.00 0.00 0.00 6.25 1000.73 8.87%

82 B.1. Computational Experiments

Table B28.: Detailed Test Result TS with Random Tabu Tenure =[1,10]

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 4.00 0.00 0.00 0.00 10.00 828.94 2.00 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 858.43 1.00 0.00 0.00 0.00 10.70 925.71 1.00 0.00 0.00 0.00 10.00 827.3 3.76% C103 10.00 881.53 1.00 0.00 0.00 0.00 10.90 952.94 1.90 0.00 0.00 0.00 10.00 826.3 6.68% C104 10.00 892.14 4.00 0.00 0.00 0.00 10.10 996.57 2.00 0.00 0.00 0.00 10.00 822.9 8.41% C105 10.00 828.94 1.00 0.00 0.00 0.00 11.10 921.58 1.00 0.00 0.00 0.00 10.00 827.3 0.20% C106 11.00 864.93 3.00 0.00 0.00 0.00 11.40 919.63 2.70 0.00 0.00 0.00 10.00 827.3 4.55% C107 10.00 828.94 1.00 0.00 0.00 0.00 10.00 852.63 1.40 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 828.94 2.00 0.00 0.00 0.00 11.20 920.41 1.80 0.00 0.00 0.00 10.00 827.3 0.20% C109 10.00 849.98 5.00 0.00 0.00 0.00 10.30 910.26 3.40 0.00 0.00 0.00 10.00 827.3 2.74%

C1-Avg. 10.11 851.42 2.44 0.00 0.00 0.00 10.63 914.30 1.91 0.00 0.00 0.00 10.00 826.70 2.99%

R101 20.00 1657.41 0.00 0.00 0.00 0.00 21.20 1690.48 0.50 0.00 0.00 0.00 20.00 1637.7 1.20% R102 19.00 1494.60 1.00 0.00 0.00 0.00 19.00 1527.03 0.50 0.02 0.00 0.00 18.00 1466.6 1.91% R103 16.00 1279.40 0.00 0.00 0.00 0.00 16.80 1337.45 0.00 0.00 0.00 0.00 14.00 1208.7 5.85% R104 13.00 1066.39 1.00 0.00 0.00 0.00 13.30 1103.98 1.60 0.00 0.00 0.00 11.00 971.5 9.77% R105 17.00 1455.81 0.00 0.00 0.00 0.00 16.90 1498.49 0.00 0.00 0.00 0.00 15.00 1355.3 7.42% R106 15.00 1302.56 0.00 0.00 0.00 0.00 15.30 1338.30 0.80 0.00 0.00 0.00 13.00 1234.6 5.50% R107 13.00 1172.15 3.00 0.00 0.00 0.00 13.30 1208.49 2.00 0.00 0.00 0.00 11.00 1064.6 10.10% R108 11.00 1012.12 4.00 0.00 0.00 0.00 11.70 1038.42 2.50 0.00 0.00 0.00 10.00 932.1 8.58% R109 14.00 1272.42 1.00 0.00 0.00 0.00 14.30 1305.15 1.70 0.00 0.00 0.00 13.00 1146.9 10.94% R110 14.00 1202.13 3.00 0.00 0.00 0.00 13.50 1253.51 2.10 0.00 0.00 0.00 12.00 1068.0 12.56% R111 13.00 1136.11 1.00 0.00 0.00 0.00 13.00 1177.70 1.00 0.00 0.00 0.00 12.00 1048.7 8.34% R112 12.00 1043.32 1.00 0.00 0.00 0.00 12.00 1068.94 2.40 0.00 0.00 0.00 10.00 948.6 9.99%

R1-Avg. 14.75 1257.87 1.25 0.00 0.00 0.00 15.03 1295.66 1.26 0.00 0.00 0.00 13.25 1173.61 7.68%

RC101 17.00 1704.02 0.00 0.00 0.00 0.00 17.30 1761.04 0.10 0.00 0.00 0.00 15.00 1619.8 5.20% RC102 16.00 1548.85 1.00 0.00 0.00 0.00 15.70 1613.00 1.20 0.00 0.00 0.00 14.00 1457.4 6.27% RC103 14.00 1425.43 1.00 0.00 0.00 0.00 14.40 1454.71 1.10 0.00 0.00 0.00 11.00 1258.0 13.31% RC104 11.00 1189.41 4.00 0.00 0.00 0.00 12.10 1255.56 2.20 0.00 0.00 0.00 10.00 1132.3 5.04% RC105 17.00 1640.08 2.00 0.00 0.00 0.00 18.30 1703.42 1.10 0.00 0.00 0.00 15.00 1513.7 8.35% RC106 14.00 1495.54 1.00 0.00 0.00 0.00 14.20 1510.58 1.00 0.00 0.00 0.00 13.00 1372.7 8.95% RC107 13.00 1305.49 1.00 0.00 0.00 0.00 13.90 1379.58 1.30 0.00 0.00 0.00 12.00 1207.8 8.09% RC108 12.00 1230.67 1.00 0.00 0.00 0.00 13.10 1290.07 0.60 0.00 0.00 0.00 11.00 1114.2 10.45%

RC1-Avg. 14.25 1442.44 1.38 0.00 0.00 0.00 14.88 1496.00 1.08 0.00 0.00 0.00 12.63 1334.49 8.21%

C201 3.00 591.56 45.00 0.00 0.00 0.00 3.00 591.56 63.50 0.00 0.00 0.00 3.00 589.1 0.42% C202 4.00 623.96 38.00 0.00 0.00 0.00 4.20 650.26 40.20 0.00 0.00 0.00 3.00 589.1 5.92% C203 3.00 621.21 40.00 0.00 0.00 0.00 4.30 649.66 29.70 0.00 0.00 0.00 3.00 588.7 5.52% C204 4.00 673.73 25.00 0.00 0.00 0.00 4.20 702.55 34.20 0.00 0.00 0.00 3.00 588.1 14.56% C205 3.00 609.36 29.00 0.00 0.00 0.00 3.50 618.95 54.00 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 49.00 0.00 0.00 0.00 4.40 631.59 35.60 0.00 0.00 0.00 3.00 586.0 0.43% C207 4.00 611.64 33.00 0.00 0.00 0.00 4.10 637.08 28.30 0.00 0.00 0.00 3.00 585.8 4.41% C208 3.00 588.32 60.00 0.00 0.00 0.00 3.10 589.96 43.70 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.38 613.53 39.88 0.00 0.00 0.00 3.85 633.95 41.15 0.00 0.00 0.00 3.00 587.38 4.45%

R201 9.00 1212.02 9.00 0.00 0.00 0.00 7.30 1257.15 13.10 0.00 0.00 0.00 8.00 1143.2 6.02% R202 6.00 1102.61 23.00 0.00 0.00 0.00 6.90 1141.52 15.20 0.00 0.00 0.00 8.00 1029.6 7.09% R203 5.00 943.02 15.00 0.00 0.00 0.00 4.80 1023.64 24.70 0.00 0.00 0.00 6.00 870.8 8.29% R204 3.00 807.40 80.00 0.00 0.00 0.00 4.00 837.11 51.80 0.00 0.00 0.00 5.00 731.3 10.41% R205 6.00 1036.19 383.00 0.00 0.00 0.00 4.90 1093.43 582.80 0.00 0.00 0.00 5.00 949.8 9.10% R206 4.00 954.40 41.00 0.00 0.00 0.00 4.10 980.82 29.40 0.00 0.00 0.00 5.00 875.9 8.96% R207 4.00 868.03 14.00 0.00 0.00 0.00 3.80 924.56 36.30 0.00 0.00 0.00 3.00 794.0 9.32% R208 4.00 771.10 41.00 0.00 0.00 0.00 3.40 805.64 41.60 0.00 0.00 0.00 3.00 701.2 9.97% R209 5.00 917.98 12.00 0.00 0.00 0.00 4.50 999.56 20.60 0.00 0.00 0.00 5.00 854.8 7.39% R210 5.00 1007.23 11.00 0.00 0.00 0.00 5.20 1042.67 18.90 0.00 0.00 0.00 6.00 900.5 11.85% R211 5.00 825.27 15.00 0.00 0.00 0.00 4.40 858.62 23.90 0.00 0.00 0.00 4.00 746.7 10.52%

R2-Avg. 5.09 949.57 58.55 0.00 0.00 0.00 4.85 996.79 78.03 0.00 0.00 0.00 5.27 872.53 8.99%

RC201 7.00 1318.84 8.00 0.00 0.00 0.00 8.00 1406.52 4.60 0.00 0.00 0.00 9.00 1261.8 4.52% RC202 8.00 1176.10 8.00 0.00 0.00 0.00 7.20 1245.16 11.50 0.00 0.00 0.00 8.00 1092.3 7.67% RC203 6.00 995.88 10.00 0.00 0.00 0.00 5.10 1079.08 18.00 0.00 0.00 0.00 5.00 923.7 7.81% RC204 4.00 835.36 27.00 0.00 0.00 0.00 4.00 884.74 31.60 0.00 0.00 0.00 4.00 783.5 6.62% RC205 7.00 1251.98 10.00 0.00 0.00 0.00 7.20 1326.50 11.50 0.00 0.00 0.00 7.00 1154.0 8.49% RC206 7.00 1147.93 12.00 0.00 0.00 0.00 5.80 1201.73 15.10 0.00 0.00 0.00 7.00 1051.1 9.21% RC207 6.00 1068.15 18.00 0.00 0.00 0.00 5.40 1122.84 13.40 0.00 0.00 0.00 6.00 962.9 10.93% RC208 4.00 868.62 17.00 0.00 0.00 0.00 4.00 968.08 22.20 0.00 0.00 0.00 4.00 776.5 11.86%

RC2-Avg. 6.13 1082.86 13.75 0.00 0.00 0.00 5.84 1154.33 15.99 0.00 0.00 0.00 6.25 1000.73 8.39%

83 Appendix B

Table B29.: Detailed Test Result TS with Random Tabu Tenure =[11,20]

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 4.00 0.00 0.00 0.00 10.00 828.94 3.20 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 835.09 3.00 0.00 0.00 0.00 10.60 913.25 3.10 0.00 0.00 0.00 10.00 827.3 0.94% C103 11.00 868.39 2.00 0.00 0.00 0.00 11.10 973.72 1.50 0.00 0.00 0.00 10.00 826.3 5.09% C104 11.00 915.67 3.00 0.00 0.00 0.00 10.40 1010.47 2.90 0.00 0.00 0.00 10.00 822.9 11.27% C105 10.00 828.94 2.00 0.00 0.00 0.00 11.30 926.01 2.60 0.00 0.00 0.00 10.00 827.3 0.20% C106 11.00 861.80 2.00 0.00 0.00 0.00 11.10 906.42 2.30 0.00 0.00 0.00 10.00 827.3 4.17% C107 10.00 828.94 1.00 0.00 0.00 0.00 10.10 879.07 1.00 0.00 0.00 0.00 10.00 827.3 0.20% C108 11.00 861.24 4.00 0.00 0.00 0.00 11.30 920.90 2.30 0.00 0.00 0.00 10.00 827.3 4.10% C109 10.00 831.85 5.00 0.00 0.00 0.00 10.60 924.56 3.70 0.00 0.00 0.00 10.00 827.3 0.55%

C1-Avg. 10.44 851.21 2.89 0.00 0.00 0.00 10.72 920.37 2.51 0.00 0.00 0.00 10.00 826.70 2.97%

R101 20.00 1663.23 1.00 0.00 0.00 0.00 21.30 1688.98 0.90 0.00 0.00 0.00 20.00 1637.7 1.56% R102 19.00 1493.67 1.00 0.12 0.00 0.00 19.40 1529.54 0.70 0.02 0.00 0.00 18.00 1466.6 1.85% R103 16.00 1302.28 1.00 0.00 0.00 0.00 16.50 1330.49 1.40 0.00 0.00 0.00 14.00 1208.7 7.74% R104 13.00 1068.79 3.00 0.00 0.00 0.00 13.40 1097.40 2.40 0.00 0.00 0.00 11.00 971.5 10.01% R105 17.00 1441.17 2.00 0.00 0.00 0.00 17.10 1498.62 1.70 0.00 0.00 0.00 15.00 1355.3 6.34% R106 14.00 1296.83 2.00 0.00 0.00 0.00 15.10 1346.60 1.90 0.00 0.00 0.00 13.00 1234.6 5.04% R107 14.00 1164.76 2.00 0.00 0.00 0.00 13.90 1210.40 0.80 0.00 0.00 0.00 11.00 1064.6 9.41% R108 11.00 1028.59 3.00 0.00 0.00 0.00 11.60 1045.23 1.30 0.00 0.00 0.00 10.00 932.1 10.35% R109 14.00 1277.74 2.00 0.00 0.00 0.00 14.30 1298.05 1.30 0.00 0.00 0.00 13.00 1146.9 11.41% R110 13.00 1183.59 1.00 0.00 0.00 0.00 13.20 1235.27 0.40 0.00 0.00 0.00 12.00 1068.0 10.82% R111 13.00 1127.65 1.00 0.00 0.00 0.00 13.20 1173.23 0.90 0.00 0.00 0.00 12.00 1048.7 7.53% R112 12.00 1046.95 1.00 0.00 0.00 0.00 12.00 1090.93 1.00 0.00 0.00 0.00 10.00 948.6 10.37%

R1-Avg. 14.67 1257.94 1.67 0.01 0.00 0.00 15.08 1295.40 1.23 0.00 0.00 0.00 13.25 1173.61 7.70%

RC101 17.00 1698.64 1.00 0.00 0.00 0.00 17.40 1748.40 0.60 0.00 0.00 0.00 15.00 1619.8 4.87% RC102 15.00 1569.82 1.00 0.00 0.00 0.00 15.90 1625.08 1.60 0.00 0.00 0.00 14.00 1457.4 7.71% RC103 14.00 1415.10 2.00 0.00 0.00 0.00 14.00 1440.48 1.40 0.00 0.00 0.00 11.00 1258.0 12.49% RC104 12.00 1209.58 2.00 0.00 0.00 0.00 12.10 1272.79 2.30 0.00 0.00 0.00 10.00 1132.3 6.83% RC105 17.00 1624.98 1.00 0.00 0.00 0.00 17.70 1666.76 1.20 0.00 0.00 0.00 15.00 1513.7 7.35% RC106 14.00 1448.10 1.00 0.00 0.00 0.00 14.20 1504.26 2.20 0.00 0.00 0.00 13.00 1372.7 5.49% RC107 14.00 1339.32 8.00 0.00 0.00 0.00 13.60 1403.31 2.40 0.00 0.00 0.00 12.00 1207.8 10.89% RC108 12.00 1185.53 1.00 0.00 0.00 0.00 12.60 1282.87 1.30 0.00 0.00 0.00 11.00 1114.2 6.40%

RC1-Avg. 14.38 1436.38 2.13 0.00 0.00 0.00 14.69 1492.99 1.63 0.00 0.00 0.00 12.63 1334.49 7.75%

C201 3.00 591.56 43.00 0.00 0.00 0.00 3.00 600.54 50.80 0.00 0.00 0.00 3.00 589.1 0.42% C202 4.00 620.49 33.00 0.00 0.00 0.00 4.40 665.35 32.90 0.00 0.00 0.00 3.00 589.1 5.33% C203 3.00 621.21 41.00 0.00 0.00 0.00 4.30 678.03 31.10 0.00 0.00 0.00 3.00 588.7 5.52% C204 4.00 656.57 25.00 0.00 0.00 0.00 4.00 677.25 37.90 0.00 0.00 0.00 3.00 588.1 11.64% C205 3.00 609.36 60.00 0.00 0.00 0.00 3.80 622.51 52.00 0.00 0.00 0.00 3.00 586.4 3.92% C206 4.00 621.01 23.00 0.00 0.00 0.00 4.30 641.12 38.00 0.00 0.00 0.00 3.00 586.0 5.98% C207 3.00 588.29 49.00 0.00 0.00 0.00 4.20 637.62 34.30 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 76.00 0.00 0.00 0.00 3.30 596.88 54.60 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.38 612.10 43.75 0.00 0.00 0.00 3.91 639.91 41.45 0.00 0.00 0.00 3.00 587.38 4.21%

R201 8.00 1202.71 4.00 0.00 0.00 0.00 7.50 1249.42 5.70 0.00 0.00 0.00 8.00 1143.2 5.21% R202 6.00 1116.57 7.00 0.00 0.00 0.00 6.60 1139.72 7.80 0.00 0.00 0.00 8.00 1029.6 8.45% R203 6.00 951.07 9.00 0.00 0.00 0.00 5.10 988.33 18.10 0.00 0.00 0.00 6.00 870.8 9.22% R204 5.00 783.33 27.00 0.00 0.00 0.00 4.30 826.24 39.90 0.00 0.00 0.00 5.00 731.3 7.11% R205 6.00 1030.04 19.00 0.00 0.00 0.00 5.10 1081.57 15.10 0.00 0.00 0.00 5.00 949.8 8.45% R206 5.00 968.03 14.00 0.00 0.00 0.00 4.70 1010.00 15.90 0.00 0.00 0.00 5.00 875.9 10.52% R207 4.00 880.08 34.00 0.00 0.00 0.00 3.50 936.05 46.60 0.00 0.00 0.00 3.00 794.0 10.84% R208 4.00 745.03 24.00 0.00 0.00 0.00 3.90 769.07 32.00 0.00 0.00 0.00 3.00 701.2 6.25% R209 6.00 917.84 13.00 0.00 0.00 0.00 5.30 965.69 19.70 0.00 0.00 0.00 5.00 854.8 7.37% R210 6.00 966.96 7.00 0.00 0.00 0.00 5.40 1006.42 11.40 0.00 0.00 0.00 6.00 900.5 7.38% R211 5.00 843.28 13.00 0.00 0.00 0.00 4.90 902.70 17.20 0.00 0.00 0.00 4.00 746.7 12.93%

R2-Avg. 5.55 945.90 15.55 0.00 0.00 0.00 5.12 988.66 20.85 0.00 0.00 0.00 5.27 872.53 8.52%

RC201 10.00 1341.71 5.00 0.00 0.00 0.00 8.60 1403.64 4.30 0.00 0.00 0.00 9.00 1261.8 6.33% RC202 8.00 1187.52 5.00 0.00 0.00 0.00 6.80 1240.61 8.60 0.00 0.00 0.00 8.00 1092.3 8.72% RC203 5.00 996.84 8.00 0.00 0.00 0.00 5.40 1045.55 12.30 0.00 0.00 0.00 5.00 923.7 7.92% RC204 4.00 817.46 20.00 0.00 0.00 0.00 4.20 862.36 22.40 0.00 0.00 0.00 4.00 783.5 4.33% RC205 8.00 1238.66 3.00 0.00 0.00 0.00 7.60 1314.46 5.00 0.00 0.00 0.00 7.00 1154.0 7.34% RC206 6.00 1149.75 8.00 0.00 0.00 0.00 5.90 1191.92 10.00 0.00 0.00 0.00 7.00 1051.1 9.39% RC207 6.00 1045.62 10.00 0.00 0.00 0.00 6.00 1097.44 9.40 0.00 0.00 0.00 6.00 962.9 8.59% RC208 4.00 866.61 31.00 0.00 0.00 0.00 4.30 940.28 38.20 0.00 0.00 0.00 4.00 776.5 11.60%

RC2-Avg. 6.38 1080.52 11.25 0.00 0.00 0.00 6.10 1137.03 13.78 0.00 0.00 0.00 6.25 1000.73 8.03%

84 B.1. Computational Experiments

Table B30.: Detailed Test Result TS on Intensiﬁcation with Or-Opt

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 5.00 0.00 0.00 0.00 10.00 828.94 2.60 0.00 0.00 0.00 10.00 827.3 0.20% C102 11.00 871.23 3.00 0.00 0.00 0.00 10.60 958.39 4.10 0.00 0.00 0.00 10.00 827.3 5.31% C103 10.00 835.56 5.00 0.00 0.00 0.00 11.00 953.81 3.00 0.00 0.00 0.00 10.00 826.3 1.12% C104 10.00 913.39 12.00 0.00 0.00 0.00 10.30 998.59 4.10 0.00 0.00 0.00 10.00 822.9 11.00% C105 10.00 828.94 2.00 0.00 0.00 0.00 11.30 915.66 2.40 0.00 0.00 0.00 10.00 827.3 0.20% C106 10.00 828.94 4.00 0.00 0.00 0.00 10.90 896.56 3.70 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 2.00 0.00 0.00 0.00 10.20 874.36 1.10 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 828.94 5.00 0.00 0.00 0.00 11.00 923.98 2.80 0.00 0.00 0.00 10.00 827.3 0.20% C109 10.00 829.70 4.00 0.00 0.00 0.00 10.30 885.52 3.70 0.00 0.00 0.00 10.00 827.3 0.29%

C1-Avg. 10.11 843.84 4.67 0.00 0.00 0.00 10.62 915.09 3.06 0.00 0.00 0.00 10.00 826.70 2.08%

R101 20.00 1663.24 0.00 0.00 0.00 0.00 21.50 1692.75 0.00 0.00 0.00 0.00 20.00 1637.7 1.56% R102 19.00 1502.56 0.00 0.00 0.00 0.00 19.50 1528.33 0.00 0.01 0.00 0.00 18.00 1466.6 2.45% R103 16.00 1309.32 0.00 0.00 0.00 0.00 16.60 1337.83 0.50 0.00 0.00 0.00 14.00 1208.7 8.32% R104 13.00 1080.07 1.00 0.00 0.00 0.00 13.80 1114.45 1.00 0.00 0.00 0.00 11.00 971.5 11.18% R105 17.00 1439.00 0.00 0.00 0.00 0.00 16.60 1468.18 0.60 0.00 0.00 0.00 15.00 1355.3 6.18% R106 14.00 1301.11 3.00 0.00 0.00 0.00 15.30 1335.95 1.70 0.00 0.00 0.00 13.00 1234.6 5.39% R107 13.00 1159.74 1.00 0.00 0.00 0.00 13.60 1194.85 1.00 0.00 0.00 0.00 11.00 1064.6 8.94% R108 11.00 1028.30 1.00 0.00 0.00 0.00 11.80 1072.23 1.00 0.00 0.00 0.00 10.00 932.1 10.32% R109 14.00 1276.82 0.00 0.00 0.00 0.00 14.20 1297.96 0.60 0.00 0.00 0.00 13.00 1146.9 11.33% R110 14.00 1181.77 1.00 0.00 0.00 0.00 13.50 1234.78 1.00 0.00 0.00 0.00 12.00 1068.0 10.65% R111 13.00 1153.39 1.00 0.00 0.00 0.00 13.50 1183.18 1.80 0.00 0.00 0.00 12.00 1048.7 9.98% R112 12.00 1035.06 2.00 0.00 0.00 0.00 12.00 1080.32 1.80 0.00 0.00 0.00 10.00 948.6 9.11%

R1-Avg. 14.67 1260.87 0.83 0.00 0.00 0.00 15.16 1295.07 0.92 0.00 0.00 0.00 13.25 1173.61 7.95%

RC101 17.00 1708.49 0.00 0.00 0.00 0.00 17.10 1754.81 0.00 0.02 0.00 0.00 15.00 1619.8 5.48% RC102 15.00 1592.83 1.00 0.00 0.00 0.00 16.00 1621.18 0.40 0.00 0.00 0.00 14.00 1457.4 9.29% RC103 14.00 1414.06 2.00 0.00 0.00 0.00 14.10 1450.29 1.60 0.00 0.00 0.00 11.00 1258.0 12.41% RC104 11.00 1198.13 1.00 0.00 0.00 0.00 12.00 1259.64 1.10 0.00 0.00 0.00 10.00 1132.3 5.81% RC105 17.00 1630.62 0.00 0.00 0.00 0.00 18.10 1702.15 0.00 0.00 0.00 0.00 15.00 1513.7 7.72% RC106 14.00 1471.82 1.00 0.00 0.00 0.00 14.30 1495.14 1.20 0.00 0.00 0.00 13.00 1372.7 7.22% RC107 13.00 1312.27 1.00 0.00 0.00 0.00 13.50 1393.08 1.00 0.00 0.00 0.00 12.00 1207.8 8.65% RC108 13.00 1258.75 1.00 0.00 0.00 0.00 12.70 1302.41 1.00 0.00 0.00 0.00 11.00 1114.2 12.97%

RC1-Avg. 14.25 1448.37 0.88 0.00 0.00 0.00 14.73 1497.34 0.79 0.00 0.00 0.00 12.63 1334.49 8.69%

C201 3.00 591.56 65.00 0.00 0.00 0.00 3.00 603.54 60.90 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 591.56 24.00 0.00 0.00 0.00 4.30 658.62 29.80 0.00 0.00 0.00 3.00 589.1 0.42% C203 4.00 624.28 47.00 0.00 0.00 0.00 4.70 671.22 23.60 0.00 0.00 0.00 3.00 588.7 6.04% C204 4.00 634.40 23.00 0.00 0.00 0.00 4.50 695.24 19.50 0.00 0.00 0.00 3.00 588.1 7.87% C205 3.00 609.36 46.00 0.00 0.00 0.00 3.00 609.36 45.80 0.00 0.00 0.00 3.00 586.4 3.92% C206 4.00 604.87 33.00 0.00 0.00 0.00 4.30 640.77 27.30 0.00 0.00 0.00 3.00 586.0 3.22% C207 4.00 614.17 51.00 0.00 0.00 0.00 4.60 652.68 26.90 0.00 0.00 0.00 3.00 585.8 4.84% C208 3.00 588.32 32.00 0.00 0.00 0.00 3.00 588.32 41.10 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.50 607.31 40.13 0.00 0.00 0.00 3.93 639.97 34.36 0.00 0.00 0.00 3.00 587.38 3.39%

R201 7.00 1225.17 11.00 0.00 0.00 0.00 6.90 1273.97 10.80 0.00 0.00 0.00 8.00 1143.2 7.17% R202 7.00 1089.69 16.00 0.00 0.00 0.00 6.30 1160.67 14.70 0.00 0.00 0.00 8.00 1029.6 5.84% R203 5.00 942.33 13.00 0.00 0.00 0.00 5.00 971.46 26.40 0.00 0.00 0.00 6.00 870.8 8.21% R204 4.00 798.23 46.00 0.00 0.00 0.00 4.10 842.76 32.10 0.00 0.00 0.00 5.00 731.3 9.15% R205 5.00 1005.31 19.00 0.00 0.00 0.00 4.80 1084.12 21.90 0.00 0.00 0.00 5.00 949.8 5.84% R206 4.00 962.68 25.00 0.00 0.00 0.00 4.20 1001.70 33.00 0.00 0.00 0.00 5.00 875.9 9.91% R207 3.00 870.23 46.00 0.00 0.00 0.00 3.10 912.62 56.60 0.00 0.00 0.00 3.00 794.0 9.60% R208 4.00 755.91 38.00 0.00 0.00 0.00 3.50 781.98 50.00 0.00 0.00 0.00 3.00 701.2 7.80% R209 4.00 926.01 35.00 0.00 0.00 0.00 4.30 989.74 26.00 0.00 0.00 0.00 5.00 854.8 8.33% R210 5.00 983.09 22.00 0.00 0.00 0.00 5.00 1029.88 22.10 0.00 0.00 0.00 6.00 900.5 9.17% R211 5.00 852.83 31.00 0.00 0.00 0.00 4.30 887.22 27.20 0.00 0.00 0.00 4.00 746.7 14.21%

R2-Avg. 4.82 946.50 27.45 0.00 0.00 0.00 4.68 994.19 29.16 0.00 0.00 0.00 5.27 872.53 8.66%

RC201 8.00 1311.74 5.00 0.00 0.00 0.00 8.30 1395.13 6.40 0.00 0.00 0.00 9.00 1261.8 3.96% RC202 7.00 1142.52 12.00 0.00 0.00 0.00 6.60 1226.00 10.80 0.00 0.00 0.00 8.00 1092.3 4.60% RC203 5.00 1036.68 24.00 0.00 0.00 0.00 5.10 1101.92 19.90 0.00 0.00 0.00 5.00 923.7 12.23% RC204 4.00 824.04 22.00 0.00 0.00 0.00 3.50 902.07 44.20 0.00 0.00 0.00 4.00 783.5 5.17% RC205 9.00 1265.83 12.00 0.00 0.00 0.00 6.70 1323.67 12.90 0.00 0.00 0.00 7.00 1154.0 9.69% RC206 6.00 1134.09 11.00 0.00 0.00 0.00 5.40 1200.71 16.10 0.00 0.00 0.00 7.00 1051.1 7.90% RC207 6.00 1060.92 24.00 0.00 0.00 0.00 5.50 1125.36 17.20 0.00 0.00 0.00 6.00 962.9 10.18% RC208 5.00 890.39 16.00 0.00 0.00 0.00 4.20 946.22 24.90 0.00 0.00 0.00 4.00 776.5 14.67%

RC2-Avg. 6.25 1083.28 15.75 0.00 0.00 0.00 5.66 1152.64 19.05 0.00 0.00 0.00 6.25 1000.73 8.55%

85 Appendix B

Table B31.: Detailed Test Result TS on Intensiﬁcation with S/F Heuristic

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 2.00 0.00 0.00 0.00 10.00 828.94 2.50 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 835.40 1.00 0.00 0.00 0.00 10.50 965.81 2.50 0.00 0.00 0.00 10.00 827.3 0.98% C103 10.00 842.33 3.00 0.00 0.00 0.00 10.70 961.75 2.60 0.00 0.00 0.00 10.00 826.3 1.94% C104 10.00 931.43 1.00 0.00 0.00 0.00 10.50 1011.95 2.00 0.00 0.00 0.00 10.00 822.9 13.19% C105 10.00 828.94 1.00 0.00 0.00 0.00 11.10 912.67 1.40 0.00 0.00 0.00 10.00 827.3 0.20% C106 10.00 828.94 2.00 0.00 0.00 0.00 10.80 890.59 1.80 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 4.00 0.00 0.00 0.00 10.00 914.72 2.70 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 866.66 2.00 0.00 0.00 0.00 11.00 922.22 2.00 0.00 0.00 0.00 10.00 827.3 4.76% C109 10.00 852.02 3.00 0.00 0.00 0.00 10.00 886.61 2.50 0.00 0.00 0.00 10.00 827.3 2.99%

C1-Avg. 10.00 849.29 2.11 0.00 0.00 0.00 10.51 921.70 2.22 0.00 0.00 0.00 10.00 826.70 2.74%

R101 21.00 1675.59 0.00 0.00 0.00 0.00 21.10 1692.68 0.10 0.00 0.00 0.00 20.00 1637.7 2.31% R102 19.00 1495.86 0.00 0.00 0.00 0.00 19.30 1523.62 0.00 0.04 0.00 0.00 18.00 1466.6 2.00% R103 16.00 1307.68 1.00 0.00 0.00 0.00 16.80 1339.62 0.40 0.00 0.00 0.00 14.00 1208.7 8.19% R104 13.00 1064.69 1.00 0.00 0.00 0.00 13.30 1087.94 1.60 0.00 0.00 0.00 11.00 971.5 9.59% R105 16.00 1401.16 1.00 0.00 0.00 0.00 16.90 1480.84 0.60 0.00 0.00 0.00 15.00 1355.3 3.38% R106 15.00 1308.47 1.00 0.00 0.00 0.00 14.80 1335.93 1.30 0.00 0.00 0.00 13.00 1234.6 5.98% R107 13.00 1156.76 2.00 0.00 0.00 0.00 13.50 1201.35 1.30 0.00 0.00 0.00 11.00 1064.6 8.66% R108 12.00 1025.41 3.00 0.00 0.00 0.00 11.80 1054.20 1.30 0.00 0.00 0.00 10.00 932.1 10.01% R109 14.00 1265.85 1.00 0.00 0.00 0.00 14.50 1309.05 1.30 0.00 0.00 0.00 13.00 1146.9 10.37% R110 13.00 1205.01 1.00 0.00 0.00 0.00 13.10 1224.26 1.20 0.00 0.00 0.00 12.00 1068.0 12.83% R111 13.00 1136.40 1.00 0.00 0.00 0.00 13.20 1184.88 1.00 0.00 0.00 0.00 12.00 1048.7 8.36% R112 12.00 1045.98 2.00 0.00 0.00 0.00 11.90 1074.90 1.30 0.00 0.00 0.00 10.00 948.6 10.27%

R1-Avg. 14.75 1257.41 1.17 0.00 0.00 0.00 15.02 1292.44 0.95 0.00 0.00 0.00 13.25 1173.61 7.66%

RC101 17.00 1733.49 10.00 0.00 0.00 0.00 17.20 1764.85 2.30 0.00 0.00 0.00 15.00 1619.8 7.02% RC102 15.00 1532.28 1.00 0.00 0.00 0.00 16.20 1622.23 0.30 0.00 0.00 0.00 14.00 1457.4 5.14% RC103 14.00 1416.10 1.00 0.00 0.00 0.00 14.20 1446.50 1.20 0.00 0.00 0.00 11.00 1258.0 12.57% RC104 11.00 1201.56 3.00 0.00 0.00 0.00 12.00 1256.42 1.30 0.00 0.00 0.00 10.00 1132.3 6.12% RC105 17.00 1620.54 0.00 0.00 0.00 0.00 17.80 1686.50 0.30 0.00 0.00 0.00 15.00 1513.7 7.06% RC106 14.00 1478.67 2.00 0.00 0.00 0.00 13.90 1507.68 1.20 0.00 0.00 0.00 13.00 1372.7 7.72% RC107 13.00 1357.70 1.00 0.00 0.00 0.00 13.60 1402.87 1.20 0.00 0.00 0.00 12.00 1207.8 12.41% RC108 12.00 1226.44 2.00 0.00 0.00 0.00 12.50 1280.05 2.20 0.00 0.00 0.00 11.00 1114.2 10.07%

RC1-Avg. 14.13 1445.85 2.50 0.00 0.00 0.00 14.68 1495.89 1.25 0.00 0.00 0.00 12.63 1334.49 8.51%

C201 3.00 591.56 49.00 0.00 0.00 0.00 3.00 594.55 46.80 0.00 0.00 0.00 3.00 589.1 0.42% C202 3.00 591.56 28.00 0.00 0.00 0.00 4.00 650.41 28.40 0.00 0.00 0.00 3.00 589.1 0.42% C203 3.00 621.21 29.00 0.00 0.00 0.00 4.10 661.44 22.50 0.00 0.00 0.00 3.00 588.7 5.52% C204 4.00 664.63 15.00 0.00 0.00 0.00 4.10 710.91 27.20 0.00 0.00 0.00 3.00 588.1 13.01% C205 3.00 609.36 47.00 0.00 0.00 0.00 3.00 609.36 42.40 0.00 0.00 0.00 3.00 586.4 3.92% C206 3.00 588.49 53.00 0.00 0.00 0.00 4.00 641.62 31.30 0.00 0.00 0.00 3.00 586.0 0.43% C207 3.00 588.29 44.00 0.00 0.00 0.00 3.80 620.48 37.00 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 54.00 0.00 0.00 0.00 3.00 588.32 50.20 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.13 605.43 39.88 0.00 0.00 0.00 3.63 634.64 35.73 0.00 0.00 0.00 3.00 587.38 3.07%

R201 7.00 1214.81 15.00 0.00 0.00 0.00 6.60 1272.03 11.10 0.00 0.00 0.00 8.00 1143.2 6.26% R202 6.00 1109.57 20.00 0.00 0.00 0.00 6.70 1146.64 13.80 0.00 0.00 0.00 8.00 1029.6 7.77% R203 6.00 930.59 10.00 0.00 0.00 0.00 4.80 975.89 23.20 0.00 0.00 0.00 6.00 870.8 6.87% R204 4.00 798.45 25.00 0.00 0.00 0.00 3.90 841.39 48.70 0.00 0.00 0.00 5.00 731.3 9.18% R205 5.00 1050.60 26.00 0.00 0.00 0.00 4.50 1102.49 24.30 0.00 0.00 0.00 5.00 949.8 10.61% R206 4.00 955.76 23.00 0.00 0.00 0.00 3.90 1010.30 32.40 0.00 0.00 0.00 5.00 875.9 9.12% R207 3.00 877.46 59.00 0.00 0.00 0.00 3.30 932.21 55.20 0.00 0.00 0.00 3.00 794.0 10.51% R208 4.00 744.97 41.00 0.00 0.00 0.00 3.60 777.17 65.70 0.00 0.00 0.00 3.00 701.2 6.24% R209 5.00 948.10 18.00 0.00 0.00 0.00 4.50 991.48 27.50 0.00 0.00 0.00 5.00 854.8 10.92% R210 5.00 988.63 15.00 0.00 0.00 0.00 5.00 1025.82 18.30 0.00 0.00 0.00 6.00 900.5 9.79% R211 5.00 829.25 16.00 0.00 0.00 0.00 3.90 885.35 37.00 0.00 0.00 0.00 4.00 746.7 11.06%

R2-Avg. 4.91 949.84 24.36 0.00 0.00 0.00 4.61 996.43 32.47 0.00 0.00 0.00 5.27 872.53 8.94%

RC201 8.00 1379.87 10.00 0.00 0.00 0.00 8.70 1423.54 5.90 0.00 0.00 0.00 9.00 1261.8 9.36% RC202 7.00 1166.19 17.00 0.00 0.00 0.00 7.30 1225.61 10.30 0.00 0.00 0.00 8.00 1092.3 6.76% RC203 6.00 1033.15 21.00 0.00 0.00 0.00 5.00 1137.65 22.70 0.00 0.00 0.00 5.00 923.7 11.85% RC204 4.00 821.06 26.00 0.00 0.00 0.00 3.60 907.26 45.20 0.00 0.00 0.00 4.00 783.5 4.79% RC205 7.00 1258.97 8.00 0.00 0.00 0.00 6.80 1346.42 9.80 0.01 0.00 0.00 7.00 1154.0 9.10% RC206 5.00 1137.30 15.00 0.00 0.00 0.00 4.80 1209.28 19.10 0.00 0.00 0.00 7.00 1051.1 8.20% RC207 5.00 1096.87 10.00 0.00 0.00 0.00 5.20 1157.11 17.70 0.00 0.00 0.00 6.00 962.9 13.91% RC208 5.00 850.61 21.00 0.00 0.00 0.00 4.60 985.98 31.30 0.00 0.00 0.00 4.00 776.5 9.54%

RC2-Avg. 5.88 1093.00 16.00 0.00 0.00 0.00 5.75 1174.11 20.25 0.00 0.00 0.00 6.25 1000.73 9.19%

86 B.1. Computational Experiments

Table B32.: Detailed Test Result TS on Intensiﬁcation with C/R Heuristic

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 2.00 0.00 0.00 0.00 10.00 828.94 2.00 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 828.94 3.00 0.00 0.00 0.00 10.70 954.96 2.90 0.00 0.00 0.00 10.00 827.3 0.20% C103 11.00 854.70 5.00 0.00 0.00 0.00 10.80 969.23 3.40 0.00 0.00 0.00 10.00 826.3 3.44% C104 10.00 879.50 3.00 0.00 0.00 0.00 10.50 979.18 3.80 0.00 0.00 0.00 10.00 822.9 6.88% C105 11.00 894.59 4.00 0.00 0.00 0.00 11.70 958.57 3.30 0.00 0.00 0.00 10.00 827.3 8.13% C106 10.00 828.94 3.00 0.00 0.00 0.00 10.80 878.58 2.80 0.00 0.00 0.00 10.00 827.3 0.20% C107 10.00 828.94 3.00 0.00 0.00 0.00 10.10 881.17 3.00 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 828.94 3.00 0.00 0.00 0.00 11.20 912.48 2.30 0.00 0.00 0.00 10.00 827.3 0.20% C109 10.00 849.98 2.00 0.00 0.00 0.00 10.10 912.97 2.80 0.00 0.00 0.00 10.00 827.3 2.74%

C1-Avg. 10.22 847.05 3.11 0.00 0.00 0.00 10.66 919.56 2.92 0.00 0.00 0.00 10.00 826.70 2.46%

R101 21.00 1682.09 1.00 0.00 0.00 0.00 22.00 1702.55 1.00 0.00 0.00 0.00 20.00 1637.7 2.71% R102 19.00 1489.96 2.00 0.00 0.00 0.00 19.60 1539.80 1.70 0.00 0.00 0.00 18.00 1466.6 1.59% R103 16.00 1290.89 3.00 0.00 0.00 0.00 16.70 1335.32 2.80 0.00 0.00 0.00 14.00 1208.7 6.80% R104 13.00 1094.62 6.00 0.00 0.00 0.00 13.80 1117.84 4.90 0.00 0.00 0.00 11.00 971.5 12.67% R105 16.00 1437.95 2.00 0.00 0.00 0.00 17.20 1491.31 1.40 0.00 0.00 0.00 15.00 1355.3 6.10% R106 15.00 1308.72 3.00 0.00 0.00 0.00 15.10 1347.35 2.80 0.00 0.00 0.00 13.00 1234.6 6.00% R107 13.00 1165.15 4.00 0.00 0.00 0.00 13.40 1204.01 3.50 0.00 0.00 0.00 11.00 1064.6 9.44% R108 12.00 1018.57 5.00 0.00 0.00 0.00 11.90 1043.70 5.30 0.00 0.00 0.00 10.00 932.1 9.28% R109 14.00 1261.22 2.00 0.00 0.00 0.00 14.10 1290.33 2.20 0.00 0.00 0.00 13.00 1146.9 9.97% R110 12.00 1153.95 3.00 0.00 0.00 0.00 13.30 1214.21 2.60 0.00 0.00 0.00 12.00 1068.0 8.05% R111 13.00 1124.68 3.00 0.00 0.00 0.00 13.20 1168.42 3.10 0.00 0.00 0.00 12.00 1048.7 7.25% R112 12.00 1041.61 3.00 0.01 0.00 0.00 12.10 1075.04 3.60 0.00 0.00 0.00 10.00 948.6 9.80%

R1-Avg. 14.67 1255.78 3.08 0.00 0.00 0.00 15.20 1294.16 2.91 0.00 0.00 0.00 13.25 1173.61 7.47%

RC101 18.00 1704.54 1.00 0.00 0.00 0.00 17.50 1754.61 0.90 0.00 0.00 0.00 15.00 1619.8 5.23% RC102 15.00 1611.38 2.00 0.00 0.00 0.00 16.00 1640.12 1.60 0.00 0.00 0.00 14.00 1457.4 10.57% RC103 13.00 1391.41 2.00 0.00 0.00 0.00 13.90 1441.96 2.30 0.00 0.00 0.00 11.00 1258.0 10.60% RC104 12.00 1205.92 3.00 0.00 0.00 0.00 11.80 1268.04 3.20 0.00 0.00 0.00 10.00 1132.3 6.50% RC105 17.00 1628.47 1.00 0.00 0.00 0.00 17.90 1684.59 1.10 0.00 0.00 0.00 15.00 1513.7 7.58% RC106 15.00 1460.62 1.00 0.00 0.00 0.00 14.40 1497.66 1.00 0.00 0.00 0.00 13.00 1372.7 6.40% RC107 13.00 1317.43 1.00 0.00 0.00 0.00 13.40 1366.54 1.40 0.00 0.00 0.00 12.00 1207.8 9.08% RC108 13.00 1238.36 2.00 0.00 0.00 0.00 12.50 1287.60 1.80 0.00 0.00 0.00 11.00 1114.2 11.14%

RC1-Avg. 14.50 1444.77 1.63 0.00 0.00 0.00 14.68 1492.64 1.66 0.00 0.00 0.00 12.63 1334.49 8.39%

C201 3.00 591.56 60.00 0.00 0.00 0.00 3.00 594.55 50.40 0.00 0.00 0.00 3.00 589.1 0.42% C202 4.00 609.21 28.00 0.00 0.00 0.00 4.30 651.15 32.80 0.00 0.00 0.00 3.00 589.1 3.41% C203 4.00 630.12 31.00 0.00 0.00 0.00 4.20 651.15 25.90 0.00 0.00 0.00 3.00 588.7 7.04% C204 4.00 637.65 59.00 0.00 0.00 0.00 4.10 673.84 44.20 0.00 0.00 0.00 3.00 588.1 8.42% C205 3.00 609.36 119.00 0.00 0.00 0.00 3.60 621.14 100.00 0.00 0.00 0.00 3.00 586.4 3.92% C206 4.00 604.87 69.00 0.00 0.00 0.00 4.50 646.77 56.00 0.00 0.00 0.00 3.00 586.0 3.22% C207 3.00 588.29 110.00 0.00 0.00 0.00 3.90 628.15 57.50 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 97.00 0.00 0.00 0.00 3.10 590.66 96.80 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.50 607.42 71.63 0.00 0.00 0.00 3.84 632.18 57.95 0.00 0.00 0.00 3.00 587.38 3.41%

R201 7.00 1229.76 20.00 0.00 0.00 0.00 7.10 1272.57 16.40 0.00 0.00 0.00 8.00 1143.2 7.57% R202 7.00 1098.73 17.00 0.00 0.00 0.00 6.80 1142.62 25.50 0.00 0.00 0.00 8.00 1029.6 6.71% R203 6.00 932.66 30.00 0.00 0.00 0.00 4.90 996.84 40.70 0.00 0.00 0.00 6.00 870.8 7.10% R204 4.00 785.16 72.00 0.00 0.00 0.00 4.10 820.22 57.70 0.00 0.00 0.00 5.00 731.3 7.36% R205 5.00 1006.81 23.00 0.00 0.00 0.00 5.90 1074.46 25.00 0.00 0.00 0.00 5.00 949.8 6.00% R206 5.00 945.76 49.00 0.00 0.00 0.00 4.70 991.70 34.60 0.00 0.00 0.00 5.00 875.9 7.98% R207 3.00 882.17 76.00 0.00 0.00 0.00 3.70 917.98 61.80 0.00 0.00 0.00 3.00 794.0 11.10% R208 4.00 755.81 89.00 0.00 0.00 0.00 3.60 780.14 76.80 0.00 0.00 0.00 3.00 701.2 7.79% R209 5.00 895.16 24.00 0.00 0.00 0.00 5.10 954.54 23.50 0.00 0.00 0.00 5.00 854.8 4.72% R210 4.00 974.83 28.00 0.00 0.00 0.00 5.40 1007.68 25.00 0.00 0.00 0.00 6.00 900.5 8.25% R211 4.00 828.51 29.00 0.00 0.00 0.00 3.90 882.45 35.10 0.00 0.00 0.00 4.00 746.7 10.96%

R2-Avg. 4.91 939.58 41.55 0.00 0.00 0.00 5.02 985.56 38.37 0.00 0.00 0.00 5.27 872.53 7.78%

RC201 8.00 1343.54 3.00 0.00 0.00 0.00 8.00 1382.55 7.20 0.00 0.00 0.00 9.00 1261.8 6.48% RC202 7.00 1147.80 9.00 0.00 0.00 0.00 7.10 1206.31 10.20 0.00 0.00 0.00 8.00 1092.3 5.08% RC203 6.00 1014.43 19.00 0.00 0.00 0.00 5.70 1080.70 16.90 0.00 0.00 0.00 5.00 923.7 9.82% RC204 4.00 845.02 32.00 0.00 0.00 0.00 3.90 909.95 41.80 0.00 0.00 0.00 4.00 783.5 7.85% RC205 8.00 1221.63 4.00 0.00 0.00 0.00 7.50 1320.61 7.80 0.00 0.00 0.00 7.00 1154.0 5.86% RC206 5.00 1168.52 15.00 0.00 0.00 0.00 5.80 1218.95 15.10 0.00 0.00 0.00 7.00 1051.1 11.17% RC207 6.00 988.35 9.00 0.00 0.00 0.00 5.80 1082.02 11.50 0.00 0.00 0.00 6.00 962.9 2.64% RC208 4.00 831.54 28.00 0.00 0.00 0.00 4.80 909.07 25.30 0.00 0.00 0.00 4.00 776.5 7.09%

RC2-Avg. 6.00 1070.10 14.88 0.00 0.00 0.00 6.08 1138.77 16.98 0.00 0.00 0.00 6.25 1000.73 7.00%

87 Appendix B

Table B33.: Detailed Test Result TS on Intensiﬁcation and Diversiﬁcation

Best Solutions Avg Solutions Optimal Solution Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 3.00 0.00 0.00 0.00 10.00 839.29 5.30 0.00 0.00 0.00 10.00 827.3 0.20% C102 10.00 828.94 8.00 0.00 0.00 0.00 10.70 969.49 5.80 0.00 0.00 0.00 10.00 827.3 0.20% C103 10.00 833.95 10.00 0.00 0.00 0.00 10.90 943.90 7.10 0.00 0.00 0.00 10.00 826.3 0.93% C104 10.00 883.67 6.00 0.00 0.00 0.00 10.30 993.61 7.20 0.00 0.00 0.00 10.00 822.9 7.39% C105 10.00 828.94 3.00 0.00 0.00 0.00 10.90 901.11 5.20 0.00 0.00 0.00 10.00 827.3 0.20% C106 10.00 854.31 4.00 0.00 0.00 0.00 11.20 907.64 5.10 0.00 0.00 0.00 10.00 827.3 3.27% C107 10.00 828.94 3.00 0.00 0.00 0.00 10.20 879.71 4.70 0.00 0.00 0.00 10.00 827.3 0.20% C108 10.00 828.94 4.00 0.00 0.00 0.00 11.10 918.78 4.70 0.00 0.00 0.00 10.00 827.3 0.20% C109 10.00 828.94 4.00 0.00 0.00 0.00 10.20 872.96 3.70 0.00 0.00 0.00 10.00 827.3 0.20%

C1-Avg. 10.00 838.40 5.00 0.00 0.00 0.00 10.61 914.05 5.42 0.00 0.00 0.00 10.00 826.70 1.42%

R101 20.00 1672.87 1.00 0.00 0.00 0.00 21.30 1697.05 1.00 0.00 0.00 0.00 20.00 1637.7 2.15% R102 19.00 1513.16 2.00 0.00 0.00 0.00 19.20 1536.31 2.40 0.01 0.00 0.00 18.00 1466.6 3.17% R103 16.00 1277.87 3.00 0.00 0.00 0.00 16.20 1315.13 4.30 0.00 0.00 0.00 14.00 1208.7 5.72% R104 13.00 1070.71 6.00 0.00 0.00 0.00 13.00 1110.92 6.30 0.00 0.00 0.00 11.00 971.5 10.21% R105 16.00 1460.08 2.00 0.00 0.00 0.00 16.80 1489.84 2.00 0.01 0.00 0.00 15.00 1355.3 7.73% R106 15.00 1305.54 4.00 0.00 0.00 0.00 15.30 1347.07 3.60 0.00 0.00 0.00 13.00 1234.6 5.75% R107 13.00 1170.38 7.00 0.00 0.00 0.00 13.40 1195.35 5.10 0.00 0.00 0.00 11.00 1064.6 9.94% R108 12.00 1029.10 7.00 0.00 0.00 0.00 12.00 1070.33 6.60 0.00 0.00 0.00 10.00 932.1 10.41% R109 15.00 1279.75 4.00 0.00 0.00 0.00 14.80 1300.00 3.30 0.00 0.00 0.00 13.00 1146.9 11.58% R110 13.00 1179.89 5.00 0.00 0.00 0.00 13.60 1212.24 6.20 0.00 0.00 0.00 12.00 1068.0 10.48% R111 12.00 1119.81 15.00 0.00 0.00 0.00 13.20 1173.97 8.00 0.00 0.00 0.00 12.00 1048.7 6.78% R112 11.00 1023.71 4.00 0.00 0.00 0.00 11.80 1079.14 7.70 0.00 0.00 0.00 10.00 948.6 7.92%

R1-Avg. 14.58 1258.57 5.00 0.00 0.00 0.00 15.05 1293.95 4.71 0.00 0.00 0.00 13.25 1173.61 7.65%

RC101 17.00 1691.85 4.00 0.00 0.00 0.00 17.10 1736.18 3.90 0.00 0.00 0.00 15.00 1619.8 4.45% RC102 14.00 1556.20 6.00 0.00 0.00 0.00 15.70 1628.53 5.20 0.00 0.00 0.00 14.00 1457.4 6.78% RC103 14.00 1399.70 12.00 0.00 0.00 0.00 14.50 1462.54 7.80 0.00 0.00 0.00 11.00 1258.0 11.26% RC104 12.00 1202.49 7.00 0.00 0.00 0.00 12.00 1275.43 7.70 0.00 0.00 0.00 10.00 1132.3 6.20% RC105 17.00 1613.92 3.00 0.00 0.00 0.00 17.60 1682.98 2.40 0.01 0.00 0.00 15.00 1513.7 6.62% RC106 14.00 1454.41 3.00 0.00 0.00 0.00 14.50 1496.20 3.30 0.00 0.00 0.00 13.00 1372.7 5.95% RC107 14.00 1325.57 3.00 0.00 0.00 0.00 13.90 1381.05 3.50 0.00 0.00 0.00 12.00 1207.8 9.75% RC108 12.00 1236.10 4.00 0.00 0.00 0.00 12.40 1270.56 3.80 0.00 0.00 0.00 11.00 1114.2 10.94%

RC1-Avg. 14.25 1435.03 5.25 0.00 0.00 0.00 14.71 1491.68 4.70 0.00 0.00 0.00 12.63 1334.49 7.74%

C201 3.00 591.56 81.00 0.00 0.00 0.00 3.30 600.91 69.00 0.00 0.00 0.00 3.00 589.1 0.42% C202 4.00 612.77 65.00 0.00 0.00 0.00 4.20 647.93 51.00 0.00 0.00 0.00 3.00 589.1 4.02% C203 3.00 591.17 42.00 0.00 0.00 0.00 4.10 657.10 46.40 0.00 0.00 0.00 3.00 588.7 0.42% C204 4.00 675.99 44.00 0.00 0.00 0.00 4.20 706.69 43.10 0.00 0.00 0.00 3.00 588.1 14.94% C205 3.00 609.36 94.00 0.00 0.00 0.00 3.10 614.89 107.40 0.00 0.00 0.00 3.00 586.4 3.92% C206 4.00 615.52 72.00 0.00 0.00 0.00 4.70 662.13 75.80 0.00 0.00 0.00 3.00 586.0 5.04% C207 3.00 588.29 100.00 0.00 0.00 0.00 4.80 668.04 80.00 0.00 0.00 0.00 3.00 585.8 0.42% C208 3.00 588.32 138.00 0.00 0.00 0.00 3.30 594.89 128.00 0.00 0.00 0.00 3.00 585.8 0.43%

C2-Avg. 3.38 609.12 79.50 0.00 0.00 0.00 3.96 644.07 75.09 0.00 0.00 0.00 3.00 587.38 3.70%

R201 8.00 1183.04 25.00 0.00 0.00 0.00 7.60 1235.81 22.40 0.00 0.00 0.00 8.00 1143.2 3.48% R202 7.00 1099.96 25.00 0.00 0.00 0.00 6.80 1146.69 25.00 0.00 0.00 0.00 8.00 1029.6 6.83% R203 5.00 920.25 34.00 0.00 0.00 0.00 5.40 986.17 44.50 0.00 0.00 0.00 6.00 870.8 5.68% R204 4.00 799.40 77.00 0.00 0.00 0.00 4.20 833.04 77.00 0.00 0.00 0.00 5.00 731.3 9.31% R205 7.00 1025.30 30.00 0.00 0.00 0.00 5.70 1051.36 47.60 0.00 0.00 0.00 5.00 949.8 7.95% R206 5.00 937.62 47.00 0.00 0.00 0.00 4.90 979.05 53.40 0.00 0.00 0.00 5.00 875.9 7.05% R207 5.00 858.75 54.00 0.00 0.00 0.00 4.50 907.24 86.60 0.00 0.00 0.00 3.00 794.0 8.15% R208 5.00 730.57 63.00 0.00 0.00 0.00 4.20 788.03 84.30 0.00 0.00 0.00 3.00 701.2 4.19% R209 5.00 946.31 48.00 0.00 0.00 0.00 5.40 971.65 42.30 0.00 0.00 0.00 5.00 854.8 10.71% R210 6.00 965.01 29.00 0.00 0.00 0.00 6.40 1014.38 36.90 0.00 0.00 0.00 6.00 900.5 7.16% R211 5.00 811.29 28.00 0.00 0.00 0.00 5.00 865.67 54.50 0.00 0.00 0.00 4.00 746.7 8.65%

R2-Avg. 5.64 934.32 41.82 0.00 0.00 0.00 5.46 979.92 52.23 0.00 0.00 0.00 5.27 872.53 7.20%

RC201 11.00 1346.10 9.00 0.00 0.00 0.00 9.10 1380.46 11.20 0.01 0.00 0.00 9.00 1261.8 6.68% RC202 7.00 1120.21 15.00 0.00 0.00 0.00 7.40 1218.87 23.00 0.00 0.00 0.00 8.00 1092.3 2.56% RC203 6.00 987.32 31.00 0.00 0.00 0.00 6.00 1063.04 30.50 0.00 0.00 0.00 5.00 923.7 6.89% RC204 4.00 829.08 61.00 0.00 0.00 0.00 4.60 881.43 51.10 0.00 0.00 0.00 4.00 783.5 5.82% RC205 9.00 1229.11 9.00 0.00 0.00 0.00 7.80 1302.86 16.10 0.00 0.00 0.00 7.00 1154.0 6.51% RC206 6.00 1158.79 25.00 0.00 0.00 0.00 6.30 1194.99 31.90 0.00 0.00 0.00 7.00 1051.1 10.25% RC207 7.00 1061.29 15.00 0.00 0.00 0.00 6.20 1111.98 32.10 0.00 0.00 0.00 6.00 962.9 10.22% RC208 5.00 839.36 40.00 0.00 0.00 0.00 4.70 930.84 49.50 0.00 0.00 0.00 4.00 776.5 8.10%

RC2-Avg. 6.88 1071.41 25.63 0.00 0.00 0.00 6.51 1135.56 30.68 0.00 0.00 0.00 6.25 1000.73 7.13%

88 B.1. Computational Experiments

Table B34.: Detailed Test Result TS on Minimizing Number of Routes (toleranceV alue = 1.2)

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 19.00 0.00 0.00 0.00 10.00 828.94 16.00 0.00 0.00 0.00 10.00 828.94 0.00% C102 10.00 828.94 39.00 0.00 0.00 0.00 10.00 942.38 27.50 0.00 0.00 0.00 10.00 828.94 0.00% C103 10.00 950.29 42.00 0.00 0.00 0.00 10.00 1041.70 33.60 0.00 0.00 0.00 10.00 828.06 14.76% C104 10.00 922.73 54.00 0.00 0.00 0.00 10.00 1052.57 33.10 0.00 0.00 0.00 10.00 824.78 11.88% C105 10.00 828.94 27.00 0.00 0.00 0.00 10.40 865.38 30.70 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 34.00 0.00 0.00 0.00 10.20 873.69 29.70 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 29.00 0.00 0.00 0.00 10.00 922.29 30.50 0.00 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 36.00 0.00 0.00 0.00 10.10 869.68 40.20 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 828.94 34.00 0.00 0.00 0.00 10.00 855.34 31.40 0.00 0.00 0.00 10.00 828.94 0.00%

C1-Avg. 10.00 852.84 34.89 0.00 0.00 0.00 10.08 916.88 30.30 0.00 0.00 0.00 10.00 828.38 2.96%

R101 18.00 1731.38 22.00 0.88 0.00 0.00 19.30 1690.26 12.00 0.24 0.00 0.00 19.00 1650.80 4.88% R102 16.00 2184.90 14.00 7.14 0.00 0.00 17.40 1703.41 13.40 2.10 0.00 0.00 17.00 1486.12 47.02% R103 14.00 1260.41 28.00 0.00 0.00 0.00 14.90 1282.35 13.90 0.00 0.00 0.00 13.00 1292.68 -2.50% R104 10.00 1029.95 59.00 0.00 0.00 0.00 10.80 1068.34 30.90 0.00 0.00 0.00 9.00 1007.31 2.25% R105 14.00 1419.05 12.00 0.00 0.00 0.00 15.10 1455.74 11.80 0.03 0.00 0.00 14.00 1377.11 3.05% R106 13.00 1306.53 14.00 0.00 0.00 0.00 13.30 1336.89 14.40 0.00 0.00 0.00 12.00 1252.03 4.35% R107 11.00 1100.96 42.00 0.00 0.00 0.00 11.20 1185.56 34.70 0.00 0.00 0.00 10.00 1104.66 -0.33% R108 10.00 987.27 70.00 0.00 0.00 0.00 10.10 1033.32 57.70 0.00 0.00 0.00 9.00 960.88 2.75% R109 12.00 1222.20 38.00 0.00 0.00 0.00 12.50 1274.24 27.70 0.01 0.00 0.00 11.00 1194.73 2.30% R110 11.00 1140.93 38.00 0.00 0.00 0.00 11.50 1218.84 33.90 0.26 0.00 0.00 10.00 1118.84 1.97% R111 11.00 1145.84 46.00 0.00 0.00 0.00 11.80 1167.39 26.00 0.00 0.00 0.00 10.00 1096.72 4.48% R112 10.00 1010.78 14.00 0.00 0.00 0.00 10.20 1063.94 27.80 0.00 0.00 0.00 9.00 982.14 2.92%

R1-Avg. 12.50 1295.02 33.08 0.67 0.00 0.00 13.18 1290.02 25.35 0.22 0.00 0.00 11.92 1210.34 6.09%

RC101 15.00 1676.01 17.00 0.00 0.00 0.00 15.80 1753.52 17.20 0.24 0.00 0.00 14.00 1696.94 -1.23% RC102 13.00 1562.02 42.00 0.00 0.00 0.00 13.80 1644.02 23.50 0.65 0.00 0.00 12.00 1554.75 0.47% RC103 12.00 1358.16 41.00 0.00 0.00 0.00 12.10 1403.24 33.40 0.00 0.00 0.00 11.00 1261.67 7.65% RC104 10.00 1171.65 47.00 0.00 0.00 0.00 10.80 1263.83 35.50 0.24 0.00 0.00 10.00 1135.48 3.19% RC105 14.00 1630.65 30.00 0.24 0.00 0.00 14.90 1744.45 23.70 1.07 0.00 0.00 13.00 1629.44 0.07% RC106 13.00 1426.91 16.00 0.00 0.00 0.00 13.20 1473.66 20.00 0.00 0.00 0.00 11.00 1424.73 0.15% RC107 12.00 1306.08 32.00 0.00 0.00 0.00 12.00 1345.56 29.80 0.00 0.00 0.00 11.00 1230.48 6.14% RC108 11.00 1178.98 29.00 0.00 0.00 0.00 11.00 1252.55 33.20 0.19 0.00 0.00 10.00 1139.82 3.44%

RC1-Avg. 12.50 1413.81 31.75 0.03 0.00 0.00 12.95 1485.10 27.04 0.30 0.00 0.00 11.50 1384.16 2.48%

C201 3.00 591.56 366.00 0.00 0.00 0.00 3.00 603.54 301.30 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 505.00 0.00 0.00 0.00 3.00 623.32 439.20 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 600.54 656.00 0.00 0.00 0.00 3.00 631.88 476.40 0.00 0.00 0.00 3.00 591.17 1.59% C204 3.00 616.33 345.00 0.00 0.00 0.00 3.20 658.85 407.90 0.00 0.00 0.00 3.00 590.60 4.36% C205 3.00 609.36 235.00 0.00 0.00 0.00 3.00 609.36 289.50 0.00 0.00 0.00 3.00 588.88 3.48% C206 3.00 588.49 312.00 0.00 0.00 0.00 3.00 588.49 256.80 0.00 0.00 0.00 3.00 588.49 0.00% C207 3.00 588.29 157.00 0.00 0.00 0.00 3.00 588.63 230.70 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 228.00 0.00 0.00 0.00 3.00 588.32 238.50 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 596.81 350.50 0.00 0.00 0.00 3.03 611.55 330.04 0.00 0.00 0.00 3.00 589.86 1.18%

R201 4.00 1272.20 189.00 0.00 0.00 0.00 4.00 1335.79 256.80 0.00 0.00 0.00 4.00 1252.37 1.58% R202 3.00 1310.01 495.00 0.00 0.00 0.00 3.80 1218.37 313.70 0.00 0.00 0.00 3.00 1191.70 9.93% R203 3.00 1006.16 385.00 0.00 0.00 0.00 3.10 1060.87 297.90 0.00 0.00 0.00 3.00 939.50 7.10% R204 2.00 921.91 1524.00 0.00 0.00 0.00 2.80 869.69 647.10 0.00 0.00 0.00 2.00 825.52 11.68% R205 3.00 1107.53 509.00 0.00 0.00 0.00 3.40 1157.86 352.20 0.00 0.00 0.00 3.00 994.42 11.37% R206 3.00 983.92 595.00 0.00 0.00 0.00 3.20 1005.15 359.10 0.00 0.00 0.00 3.00 906.14 8.58% R207 3.00 867.09 391.00 0.00 0.00 0.00 3.00 961.15 565.00 0.00 0.00 0.00 2.00 890.61 -2.64% R208 2.00 754.77 1630.00 0.00 0.00 0.00 2.20 797.60 1115.40 0.00 0.00 0.00 2.00 726.82 3.85% R209 3.00 995.23 497.00 0.00 0.00 0.00 3.40 1048.63 427.20 0.00 0.00 0.00 3.00 909.16 9.47% R210 3.00 1049.60 476.00 0.00 0.00 0.00 3.20 1087.25 419.10 0.00 0.00 0.00 3.00 939.37 11.73% R211 3.00 854.83 565.00 0.00 0.00 0.00 3.20 898.96 468.00 0.00 0.00 0.00 2.00 885.71 -3.49%

R2-Avg. 2.91 1011.20 659.64 0.00 0.00 0.00 3.21 1040.12 474.68 0.00 0.00 0.00 2.73 951.03 6.29%

RC201 4.00 1543.14 299.00 0.00 0.00 0.00 4.30 1546.20 308.20 0.00 0.00 0.00 4.00 1406.94 9.68% RC202 4.00 1239.91 442.00 0.00 0.00 0.00 4.00 1352.26 337.80 0.00 0.00 0.00 3.00 1365.65 -9.21% RC203 3.00 1177.49 461.00 0.00 0.00 0.00 3.20 1227.67 495.40 0.06 0.00 0.00 3.00 1049.62 12.18% RC204 3.00 897.22 184.00 0.00 0.00 0.00 3.00 955.96 268.40 0.00 0.00 0.00 3.00 798.46 12.37% RC205 4.00 1439.79 127.00 0.00 0.00 0.00 4.00 1497.30 156.50 0.00 0.00 0.00 4.00 1297.65 10.95% RC206 3.00 1384.95 196.00 0.00 0.00 0.00 3.90 1277.59 135.80 0.00 0.00 0.00 3.00 1146.32 20.82% RC207 3.00 1172.82 437.00 0.00 0.00 0.00 3.50 1177.72 279.40 0.00 0.00 0.00 3.00 1061.14 10.52% RC208 3.00 907.89 527.00 0.00 0.00 0.00 3.10 1012.63 480.10 0.00 0.00 0.00 3.00 828.14 9.63%

RC2-Avg. 3.38 1220.40 334.13 0.00 0.00 0.00 3.63 1255.92 307.70 0.01 0.00 0.00 3.25 1119.24 9.62%

89 Appendix B

Table B35.: Detailed Test Result TS on Minimizing Number of Routes

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 14.00 0.00 0.00 0.00 10.00 828.94 14.60 0.00 0.00 0.00 10.00 828.94 0.00%

C102 10.00 831.53 47.00 0.00 0.00 0.00 10.00 912.79 30.40 0.00 0.00 0.00 10.00 828.94 0.31% C103 10.00 907.67 33.00 0.00 0.00 0.00 10.00 1051.47 29.40 0.00 0.00 0.00 10.00 828.06 9.61% C104 10.00 913.77 33.00 0.00 0.00 0.00 10.00 1029.22 31.70 0.00 0.00 0.00 10.00 824.78 10.79% C105 10.00 828.94 39.00 0.00 0.00 0.00 10.10 861.47 28.60 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 15.00 0.00 0.00 0.00 10.40 869.29 24.80 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 30.00 0.00 0.00 0.00 10.00 912.39 23.00 0.00 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 23.00 0.00 0.00 0.00 10.10 879.32 27.10 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 828.94 23.00 0.00 0.00 0.00 10.00 904.88 22.40 0.00 0.00 0.00 10.00 828.94 0.00%

C1-Avg. 10.00 847.40 28.56 0.00 0.00 0.00 10.07 916.64 25.78 0.00 0.00 0.00 10.00 828.38 2.30%

R101 19.00 1667.50 4.00 0.30 0.00 0.00 19.60 1683.33 3.50 0.18 0.00 0.00 19.00 1650.80 1.01% R102 16.00 2156.15 8.00 7.14 0.00 0.00 17.70 1629.80 6.80 1.31 0.00 0.00 17.00 1486.12 45.09% R103 14.00 1245.96 29.00 0.00 0.00 0.00 14.30 1281.82 21.10 0.00 0.00 0.00 13.00 1292.68 -3.61% R104 10.00 1040.20 63.00 0.00 0.00 0.00 10.70 1066.79 42.30 0.00 0.00 0.00 9.00 1007.31 3.27% R105 15.00 1408.86 21.00 0.00 0.00 0.00 15.10 1455.27 12.30 0.01 0.00 0.00 14.00 1377.11 2.31% R106 13.00 1304.18 14.00 0.00 0.00 0.00 13.70 1341.11 10.00 0.00 0.00 0.00 12.00 1252.03 4.17% R107 11.00 1152.34 43.00 0.00 0.00 0.00 11.60 1177.78 17.70 0.00 0.00 0.00 10.00 1104.66 4.32% R108 10.00 1011.48 21.00 0.00 0.00 0.00 10.20 1042.54 22.50 0.00 0.00 0.00 9.00 960.88 5.27% R109 12.00 1203.70 49.00 0.00 0.00 0.00 12.50 1274.92 21.40 0.00 0.00 0.00 11.00 1194.73 0.75% R110 11.00 1177.05 12.00 0.00 0.00 0.00 11.90 1193.15 13.40 0.00 0.00 0.00 10.00 1118.84 5.20% R111 12.00 1149.65 16.00 0.03 0.00 0.00 12.00 1186.64 14.80 0.01 0.00 0.00 10.00 1096.72 4.83% R112 10.00 1040.97 24.00 0.00 0.00 0.00 10.70 1053.96 19.60 0.00 0.00 0.00 9.00 982.14 5.99%

R1-Avg. 12.75 1296.50 25.33 0.62 0.00 0.00 13.33 1282.26 17.12 0.13 0.00 0.00 11.92 1210.34 6.55%

RC101 15.00 1780.68 18.00 0.51 0.00 0.00 16.10 1742.07 14.90 0.06 0.00 0.00 14.00 1696.94 4.93% RC102 14.00 1593.45 24.00 0.00 0.00 0.00 14.10 1659.89 18.00 0.58 0.00 0.00 12.00 1554.75 2.49% RC103 12.00 1332.02 12.00 0.00 0.00 0.00 12.10 1420.03 26.10 0.48 0.00 0.00 11.00 1261.67 5.58% RC104 10.00 1213.25 51.00 0.00 0.00 0.00 10.90 1232.36 31.80 0.00 0.00 0.00 10.00 1135.48 6.85% RC105 15.00 1613.77 20.00 0.00 0.00 0.00 15.20 1702.51 18.10 0.69 0.00 0.00 13.00 1629.44 -0.96% RC106 12.00 1415.96 33.00 0.00 0.00 0.00 12.90 1477.05 16.70 0.00 0.00 0.00 11.00 1424.73 -0.62% RC107 11.00 1389.54 30.00 0.00 0.00 0.00 12.00 1362.13 28.80 0.15 0.00 0.00 11.00 1230.48 12.93% RC108 11.00 1199.30 36.00 0.00 0.00 0.00 11.20 1243.93 29.40 0.00 0.00 0.00 10.00 1139.82 5.22%

RC1-Avg. 12.50 1442.25 28.00 0.06 0.00 0.00 13.06 1480.00 22.98 0.25 0.00 0.00 11.50 1384.16 4.55%

C201 3.00 591.56 220.00 0.00 0.00 0.00 3.00 600.54 147.30 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 275.00 0.00 0.00 0.00 3.00 629.86 229.80 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 600.21 389.00 0.00 0.00 0.00 3.10 647.82 275.30 0.00 0.00 0.00 3.00 591.17 1.53% C204 3.00 614.90 862.00 0.00 0.00 0.00 3.20 721.93 500.70 0.00 0.00 0.00 3.00 590.60 4.11% C205 3.00 609.36 384.00 0.00 0.00 0.00 3.00 609.36 415.80 0.00 0.00 0.00 3.00 588.88 3.48% C206 3.00 588.49 385.00 0.00 0.00 0.00 3.00 605.53 358.40 0.00 0.00 0.00 3.00 588.49 0.00% C207 3.00 588.29 474.00 0.00 0.00 0.00 3.00 588.29 448.30 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 379.00 0.00 0.00 0.00 3.00 588.32 357.30 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 596.59 421.00 0.00 0.00 0.00 3.04 623.96 341.61 0.00 0.00 0.00 3.00 589.86 1.14%

R201 4.00 1302.43 180.00 0.00 0.00 0.00 4.00 1351.37 205.80 0.00 0.00 0.00 4.00 1252.37 4.00% R202 4.00 1156.57 103.00 0.00 0.00 0.00 4.00 1204.09 125.60 0.00 0.00 0.00 3.00 1191.70 -2.95% R203 3.00 1012.73 163.00 0.00 0.00 0.00 3.20 1026.59 358.50 0.00 0.00 0.00 3.00 939.50 7.79% R204 2.00 937.36 719.00 0.00 0.00 0.00 2.90 841.58 377.70 0.00 0.00 0.00 2.00 825.52 13.55% R205 3.00 1065.91 374.00 0.00 0.00 0.00 3.20 1121.13 252.00 0.00 0.00 0.00 3.00 994.42 7.19% R206 3.00 1001.96 228.00 0.00 0.00 0.00 3.20 1033.15 204.60 0.00 0.00 0.00 3.00 906.14 10.57% R207 3.00 875.99 558.00 0.00 0.00 0.00 3.00 934.95 506.10 0.00 0.00 0.00 2.00 890.61 -1.64% R208 2.00 756.60 1349.00 0.00 0.00 0.00 2.30 796.66 1147.10 0.00 0.00 0.00 2.00 726.82 4.10% R209 3.00 977.98 447.00 0.00 0.00 0.00 3.10 1041.65 502.20 0.00 0.00 0.00 3.00 909.16 7.57% R210 3.00 1017.52 621.00 0.00 0.00 0.00 3.00 1072.56 435.00 0.00 0.00 0.00 3.00 939.37 8.32% R211 3.00 875.03 473.00 0.00 0.00 0.00 3.00 908.39 468.40 0.00 0.00 0.00 2.00 885.71 -1.21%

R2-Avg. 3.00 998.19 474.09 0.00 0.00 0.00 3.17 1030.19 416.64 0.00 0.00 0.00 2.73 951.03 5.21%

RC201 4.00 1515.38 193.00 0.00 0.00 0.00 4.10 1559.00 491.50 0.00 0.00 0.00 4.00 1406.94 7.71% RC202 4.00 1264.97 116.00 0.00 0.00 0.00 4.00 1313.73 268.00 0.00 0.00 0.00 3.00 1365.65 -7.37% RC203 3.00 1149.95 488.00 0.00 0.00 0.00 3.30 1189.44 402.30 0.00 0.00 0.00 3.00 1049.62 9.56% RC204 3.00 860.25 215.00 0.00 0.00 0.00 3.00 929.32 346.10 0.00 0.00 0.00 3.00 798.46 7.74% RC205 4.00 1443.15 198.00 0.00 0.00 0.00 4.00 1492.07 175.50 0.00 0.00 0.00 4.00 1297.65 11.21% RC206 3.00 1274.15 425.00 0.00 0.00 0.00 3.60 1286.33 292.20 0.00 0.00 0.00 3.00 1146.32 11.15% RC207 3.00 1153.52 707.00 0.00 0.00 0.00 3.50 1195.73 323.00 0.00 0.00 0.00 3.00 1061.14 8.71% RC208 3.00 905.08 458.00 0.00 0.00 0.00 3.20 958.91 407.10 0.00 0.00 0.00 3.00 828.14 9.29%

RC2-Avg. 3.38 1195.81 350.00 0.00 0.00 0.00 3.59 1240.57 338.21 0.00 0.00 0.00 3.25 1119.24 7.25%

90 B.1. Computational Experiments

Table B36.: Detailed Test Result TS on RIS

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 19.00 0.00 0.00 0.00 10.00 25547.10 27.40 245.99 0.00 0.00 10.00 828.94 0.00% C102 10.00 905.34 32.00 0.00 0.00 0.00 10.00 1044.28 31.00 0.00 0.00 0.00 10.00 828.94 9.22% C103 10.00 963.36 15.00 0.00 0.00 0.00 10.00 1076.31 21.20 0.00 0.00 0.00 10.00 828.06 16.34% C104 10.00 881.07 27.00 0.00 0.00 0.00 10.00 997.33 18.10 0.00 0.00 0.00 10.00 824.78 6.83% C105 10.00 828.94 30.00 0.00 0.00 0.00 10.30 855.55 16.80 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 29.00 0.00 0.00 0.00 10.20 866.41 28.00 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 30.00 0.00 0.00 0.00 10.00 2211.72 31.20 12.28 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 21.00 0.00 0.00 0.00 10.00 868.53 21.80 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 828.94 20.00 0.00 0.00 0.00 10.00 895.71 22.30 0.00 0.00 0.00 10.00 828.94 0.00%

C1-Avg. 10.00 858.16 24.78 0.00 0.00 0.00 10.06 3818.10 24.20 28.70 0.00 0.00 10.00 828.38 3.60%

R101 19.00 1672.78 6.00 0.30 0.00 0.00 19.60 1805.42 4.70 1.25 0.00 0.00 19.00 1650.80 1.33% R102 16.00 2066.25 5.00 6.32 0.00 0.00 17.50 1753.20 6.60 2.38 0.00 0.00 17.00 1486.12 39.04% R103 14.00 1279.83 14.00 0.00 0.00 0.00 14.80 1331.04 8.20 0.42 0.00 0.00 13.00 1292.68 -0.99% R104 10.00 1063.69 18.00 0.00 0.00 0.00 10.90 1071.00 15.90 0.00 0.00 0.00 9.00 1007.31 5.60% R105 15.00 1410.51 8.00 0.00 0.00 0.00 15.00 1453.30 7.60 0.00 0.00 0.00 14.00 1377.11 2.43% R106 13.00 1287.64 9.00 0.00 0.00 0.00 13.20 1366.12 9.50 0.25 0.00 0.00 12.00 1252.03 2.84% R107 11.00 1157.58 13.00 0.00 0.00 0.00 11.50 1180.05 11.00 0.00 0.00 0.00 10.00 1104.66 4.79% R108 10.00 1000.00 17.00 0.00 0.00 0.00 10.10 1027.37 16.60 0.00 0.00 0.00 9.00 960.88 4.07% R109 12.00 1201.32 13.00 0.00 0.00 0.00 12.50 1255.94 11.10 0.07 0.00 0.00 11.00 1194.73 0.55% R110 11.00 1178.26 25.00 0.00 0.00 0.00 11.90 1199.01 10.70 0.05 0.00 0.00 10.00 1118.80 5.31% R111 11.00 1203.88 13.00 0.00 0.00 0.00 11.90 1186.52 10.40 0.00 0.00 0.00 10.00 1096.72 9.77% R112 10.00 1031.10 25.00 0.00 0.00 0.00 10.60 1050.34 16.20 0.00 0.00 0.00 9.00 982.14 4.99%

R1-Avg. 12.67 1296.07 13.83 0.55 0.00 0.00 13.29 1306.61 10.71 0.37 0.00 0.00 11.92 1210.34 6.64%

RC101 15.00 1810.29 9.00 0.86 0.00 0.00 16.30 1779.29 7.20 0.28 0.00 0.00 14.00 1696.94 6.68% RC102 13.00 1798.43 31.00 2.23 0.00 0.00 14.10 1642.49 10.20 0.52 0.00 0.00 12.00 1554.75 15.67% RC103 12.00 1332.11 14.00 0.00 0.00 0.00 12.40 1402.59 10.30 0.22 0.00 0.00 11.00 1261.70 5.58% RC104 11.00 1178.64 10.00 0.00 0.00 0.00 11.10 1253.44 13.20 0.00 0.00 0.00 10.00 1135.48 3.80% RC105 15.00 1647.68 10.00 0.00 0.00 0.00 15.80 1701.86 6.30 0.63 0.00 0.00 13.00 1629.44 1.12% RC106 13.00 1476.74 7.00 0.00 0.00 0.00 13.40 1517.91 8.80 0.11 0.00 0.00 11.00 1424.73 3.65% RC107 12.00 1288.13 20.00 0.00 0.00 0.00 12.00 1362.12 15.00 0.00 0.00 0.00 11.00 1230.48 4.69% RC108 11.00 1207.18 15.00 0.00 0.00 0.00 11.30 1271.85 14.60 0.02 0.00 0.00 10.00 1139.82 5.91%

RC1-Avg. 12.75 1467.40 14.50 0.39 0.00 0.00 13.30 1491.44 10.70 0.22 0.00 0.00 11.50 1384.16 5.89%

C201 3.00 591.56 513.00 0.00 0.00 0.00 3.00 591.56 456.80 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 459.00 0.00 0.00 0.00 3.00 625.06 395.60 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 617.62 495.00 0.00 0.00 0.00 3.10 696.17 453.10 0.00 0.00 0.00 3.00 591.17 4.47% C204 3.00 614.88 432.00 0.00 0.00 0.00 3.10 662.18 416.20 0.00 0.00 0.00 3.00 590.60 4.11% C205 3.00 588.88 381.00 0.00 0.00 0.00 3.00 628.77 366.80 0.00 0.00 0.00 3.00 588.88 0.00% C206 3.00 588.49 232.00 0.00 0.00 0.00 3.00 588.49 288.50 0.00 0.00 0.00 3.00 588.50 0.00% C207 3.00 588.29 219.00 0.00 0.00 0.00 3.00 588.98 205.70 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 239.00 0.00 0.00 0.00 3.00 612.50 262.50 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 596.20 371.25 0.00 0.00 0.00 3.03 624.21 355.65 0.00 0.00 0.00 3.00 589.86 1.07%

R201 4.00 1261.65 168.00 0.00 0.00 0.00 4.00 1318.62 134.70 0.00 0.00 0.00 4.00 1252.37 0.74% R202 4.00 1175.24 219.00 0.00 0.00 0.00 4.00 1210.93 147.20 0.00 0.00 0.00 3.00 1191.70 -1.38% R203 3.00 1022.05 338.00 0.00 0.00 0.00 3.00 1068.28 236.40 0.00 0.00 0.00 3.00 939.50 8.79% R204 2.00 917.55 557.00 0.00 0.00 0.00 2.70 868.99 352.40 0.00 0.00 0.00 2.00 825.52 11.15% R205 3.00 1052.68 238.00 0.00 0.00 0.00 3.20 1170.65 204.20 0.00 0.00 0.00 3.00 994.42 5.86% R206 3.00 1018.29 249.00 0.00 0.00 0.00 3.00 1063.34 222.30 0.00 0.00 0.00 3.00 906.14 12.38% R207 3.00 882.35 170.00 0.00 0.00 0.00 3.00 987.70 274.40 0.00 0.00 0.00 2.00 890.60 -0.93% R208 2.00 801.91 525.00 0.00 0.00 0.00 2.20 812.23 554.50 0.00 0.00 0.00 2.00 726.82 10.33% R209 3.00 973.18 198.00 0.00 0.00 0.00 3.30 1052.51 192.90 0.00 0.00 0.00 3.00 909.16 7.04% R210 3.00 1040.55 325.00 0.00 0.00 0.00 3.10 1084.24 230.40 0.00 0.00 0.00 3.00 939.37 10.77% R211 3.00 868.97 250.00 0.00 0.00 0.00 3.00 918.89 220.60 0.00 0.00 0.00 2.00 885.71 -1.89%

R2-Avg. 3.00 1001.31 294.27 0.00 0.00 0.00 3.14 1050.58 251.82 0.00 0.00 0.00 2.73 951.03 5.71%

RC201 4.00 1483.79 99.00 0.00 0.00 0.00 4.00 1577.87 127.70 0.03 0.00 0.00 4.00 1406.94 5.46% RC202 4.00 1273.16 162.00 0.00 0.00 0.00 4.00 1345.46 170.50 0.00 0.00 0.00 3.00 1365.65 -6.77% RC203 3.00 1173.09 264.00 0.00 0.00 0.00 3.20 1204.22 232.70 0.00 0.00 0.00 3.00 1049.62 11.76% RC204 3.00 856.65 248.00 0.00 0.00 0.00 3.00 958.37 259.40 0.00 0.00 0.00 3.00 798.46 7.29% RC205 4.00 1442.11 115.00 0.00 0.00 0.00 4.00 1495.91 141.00 0.00 0.00 0.00 4.00 1297.70 11.13% RC206 3.00 1332.86 240.00 0.00 0.00 0.00 3.80 1305.08 164.00 0.00 0.00 0.00 3.00 1146.32 16.27% RC207 3.00 1173.00 221.00 0.00 0.00 0.00 3.40 1217.25 191.00 0.00 0.00 0.00 3.00 1061.14 10.54% RC208 3.00 919.03 216.00 0.00 0.00 0.00 3.10 977.11 212.20 0.00 0.00 0.00 3.00 828.14 10.98%

RC2-Avg. 3.38 1206.71 195.63 0.00 0.00 0.00 3.56 1260.16 187.31 0.00 0.00 0.00 3.25 1119.24 8.33%

91 Appendix B

Table B37.: Detailed Test Result TS on VRPTW

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 18.00 0.00 0.00 0.00 10.00 828.94 11.10 0.00 0.00 0.00 10.00 828.94 0.00% C102 10.00 860.62 9.00 0.00 0.00 0.00 10.00 949.80 15.70 0.00 0.00 0.00 10.00 828.94 3.82% C103 10.00 867.18 20.00 0.00 0.00 0.00 10.00 1051.06 19.60 0.00 0.00 0.00 10.00 828.06 4.72% C104 10.00 932.74 17.00 0.00 0.00 0.00 10.00 1014.16 24.90 0.00 0.00 0.00 10.00 824.78 13.09% C105 10.00 828.94 14.00 0.00 0.00 0.00 10.30 858.60 19.00 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 31.00 0.00 0.00 0.00 10.20 853.53 15.50 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 17.00 0.00 0.00 0.00 10.00 873.35 12.40 0.00 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 16.00 0.00 0.00 0.00 10.00 869.80 21.80 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 828.94 32.00 0.00 0.00 0.00 10.00 871.86 23.70 0.00 0.00 0.00 10.00 828.94 0.00%

C1-Avg. 10.00 848.24 19.33 0.00 0.00 0.00 10.06 907.90 18.19 0.00 0.00 0.00 10.00 828.38 2.40%

R101 20.00 1663.06 8.00 0.00 0.00 0.00 20.40 1678.99 7.70 0.00 0.00 0.00 19.00 1650.80 0.74% R102 18.00 1504.39 11.00 0.00 0.00 0.00 19.10 1519.51 8.50 0.00 0.00 0.00 17.00 1486.12 1.23% R103 14.00 1257.04 7.00 0.00 0.00 0.00 14.80 1279.37 13.20 0.00 0.00 0.00 13.00 1292.68 -2.76% R104 10.00 1044.72 23.00 0.00 0.00 0.00 10.30 1067.74 24.00 0.00 0.00 0.00 9.00 1007.31 3.71% R105 14.00 1462.13 9.00 0.00 0.00 0.00 15.30 1474.19 7.30 0.00 0.00 0.00 14.00 1377.11 6.17% R106 13.00 1267.69 19.00 0.00 0.00 0.00 13.50 1324.92 12.60 0.00 0.00 0.00 12.00 1252.03 1.25% R107 11.00 1139.61 23.00 0.00 0.00 0.00 11.50 1188.68 17.50 0.00 0.00 0.00 10.00 1104.66 3.16% R108 10.00 1023.85 47.00 0.00 0.00 0.00 10.00 1061.47 27.10 0.00 0.00 0.00 9.00 960.88 6.55% R109 12.00 1269.49 24.00 0.00 0.00 0.00 12.80 1302.00 17.50 0.00 0.00 0.00 11.00 1194.73 6.26% R110 11.00 1174.22 31.00 0.00 0.00 0.00 11.60 1212.95 22.80 0.00 0.00 0.00 10.00 1118.80 4.95% R111 11.00 1150.21 29.00 0.00 0.00 0.00 11.40 1195.03 27.50 0.00 0.00 0.00 10.00 1096.72 4.88% R112 10.00 1028.19 18.00 0.00 0.00 0.00 10.20 1055.66 27.00 0.00 0.00 0.00 9.00 982.14 4.69%

R1-Avg. 12.83 1248.72 20.75 0.00 0.00 0.00 13.41 1280.04 17.73 0.00 0.00 0.00 11.92 1210.34 3.40%

RC101 15.00 1716.71 5.00 0.00 0.00 0.00 16.40 1731.32 3.80 0.00 0.00 0.00 14.00 1696.94 1.17% RC102 14.00 1530.95 8.00 0.00 0.00 0.00 14.40 1588.88 6.10 0.00 0.00 0.00 12.00 1554.75 -1.53% RC103 12.00 1298.40 14.00 0.00 0.00 0.00 12.40 1387.59 11.90 0.00 0.00 0.00 11.00 1261.70 2.91% RC104 11.00 1197.46 11.00 0.00 0.00 0.00 11.00 1238.17 15.30 0.00 0.00 0.00 10.00 1135.48 5.46% RC105 15.00 1598.63 5.00 0.00 0.00 0.00 16.00 1624.17 6.60 0.00 0.00 0.00 13.00 1629.44 -1.89% RC106 12.00 1466.30 11.00 0.00 0.00 0.00 13.10 1493.72 7.20 0.00 0.00 0.00 11.00 1424.73 2.92% RC107 12.00 1300.27 9.00 0.00 0.00 0.00 12.10 1375.22 10.10 0.00 0.00 0.00 11.00 1230.48 5.67% RC108 11.00 1212.85 12.00 0.00 0.00 0.00 11.10 1237.41 16.40 0.00 0.00 0.00 10.00 1139.82 6.41%

RC1-Avg. 12.75 1415.20 9.38 0.00 0.00 0.00 13.31 1459.56 9.68 0.00 0.00 0.00 11.50 1384.16 2.64%

C201 3.00 591.56 196.00 0.00 0.00 0.00 3.00 594.55 156.20 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 278.00 0.00 0.00 0.00 3.00 622.23 257.50 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 600.21 163.00 0.00 0.00 0.00 3.00 656.48 217.10 0.00 0.00 0.00 3.00 591.17 1.53% C204 3.00 612.40 241.00 0.00 0.00 0.00 3.10 696.03 184.20 0.00 0.00 0.00 3.00 590.60 3.69% C205 3.00 609.36 200.00 0.00 0.00 0.00 3.00 609.36 130.60 0.00 0.00 0.00 3.00 588.88 3.48% C206 3.00 588.49 166.00 0.00 0.00 0.00 3.00 588.49 140.00 0.00 0.00 0.00 3.00 588.50 0.00% C207 3.00 588.29 138.00 0.00 0.00 0.00 3.00 588.29 275.90 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 251.00 0.00 0.00 0.00 3.00 588.32 270.60 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 596.27 204.13 0.00 0.00 0.00 3.01 617.97 204.01 0.00 0.00 0.00 3.00 589.86 1.09%

R201 4.00 1324.68 136.00 0.00 0.00 0.00 4.00 1374.30 180.70 0.00 0.00 0.00 4.00 1252.37 5.77% R202 3.00 1333.95 316.00 0.00 0.00 0.00 3.80 1216.21 205.70 0.00 0.00 0.00 3.00 1191.70 11.94% R203 3.00 1010.49 172.00 0.00 0.00 0.00 3.10 1054.17 328.00 0.00 0.00 0.00 3.00 939.50 7.56% R204 2.00 893.43 914.00 0.00 0.00 0.00 2.90 864.86 283.20 0.00 0.00 0.00 2.00 825.52 8.23% R205 3.00 1083.30 153.00 0.00 0.00 0.00 3.30 1154.49 149.10 0.00 0.00 0.00 3.00 994.42 8.94% R206 3.00 1006.66 202.00 0.00 0.00 0.00 3.00 1034.40 248.70 0.00 0.00 0.00 3.00 906.14 11.09% R207 2.00 966.85 540.00 0.00 0.00 0.00 2.90 953.36 227.30 0.00 0.00 0.00 2.00 890.60 8.56% R208 2.00 802.56 554.00 0.00 0.00 0.00 2.80 778.35 275.00 0.00 0.00 0.00 2.00 726.82 10.42% R209 3.00 976.18 318.00 0.00 0.00 0.00 3.40 1013.22 251.90 0.00 0.00 0.00 3.00 909.16 7.37% R210 3.00 1034.63 192.00 0.00 0.00 0.00 3.00 1085.55 186.80 0.00 0.00 0.00 3.00 939.37 10.14% R211 3.00 857.20 177.00 0.00 0.00 0.00 3.00 894.04 1151.10 0.00 0.00 0.00 2.00 885.71 -3.22%

R2-Avg. 2.82 1026.36 334.00 0.00 0.00 0.00 3.20 1038.45 317.05 0.00 0.00 0.00 2.73 951.03 7.89%

RC201 4.00 1465.72 101.00 0.00 0.00 0.00 4.20 1544.81 108.10 0.00 0.00 0.00 4.00 1406.94 4.18% RC202 4.00 1254.65 110.00 0.00 0.00 0.00 4.00 1368.49 132.60 0.00 0.00 0.00 3.00 1365.65 -8.13% RC203 3.00 1199.96 213.00 0.00 0.00 0.00 3.20 1220.14 166.20 0.00 0.00 0.00 3.00 1049.62 14.32% RC204 3.00 856.61 202.00 0.00 0.00 0.00 3.00 918.79 184.20 0.00 0.00 0.00 3.00 798.46 7.28% RC205 4.00 1368.17 146.00 0.00 0.00 0.00 4.00 1498.49 116.90 0.00 0.00 0.00 4.00 1297.70 5.43% RC206 3.00 1313.73 182.00 0.00 0.00 0.00 3.40 1328.12 153.00 0.00 0.00 0.00 3.00 1146.32 14.60% RC207 3.00 1169.40 189.00 0.00 0.00 0.00 3.70 1154.17 127.90 0.00 0.00 0.00 3.00 1061.14 10.20% RC208 3.00 929.98 167.00 0.00 0.00 0.00 3.20 987.35 146.40 0.00 0.00 0.00 3.00 828.14 12.30%

RC2-Avg. 3.38 1194.78 163.75 0.00 0.00 0.00 3.59 1252.54 141.91 0.00 0.00 0.00 3.25 1119.24 7.52%

92 B.1. Computational Experiments

Table B38.: Detailed Test Result TS-VRPSTW - Type b

Best Solutions Average Solutions

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth

C101 10.00 828.94 23.00 0.00 0.00 0.00 10.00 828.94 12.80 0.00 0.00 0.00 C102 10.00 1266.26 28.00 0.00 0.00 0.00 10.90 2881.42 19.80 13.20 0.00 0.00 C103 10.00 1631.99 36.00 0.00 0.00 0.00 10.00 2581.09 42.30 8.25 0.00 0.00 C104 10.00 1253.79 42.00 0.00 0.00 0.00 10.00 1380.98 26.30 0.00 0.00 0.00 C105 10.00 828.94 18.00 0.00 0.00 0.00 10.80 1859.43 19.30 6.51 0.00 0.00 C106 10.00 828.94 19.00 0.00 0.00 0.00 10.80 1154.28 15.40 0.00 0.00 0.00 C107 10.00 828.94 14.00 0.00 0.00 0.00 10.00 970.02 11.00 0.00 0.00 0.00 C108 10.00 828.94 24.00 0.00 0.00 0.00 10.40 1021.50 18.50 0.00 0.00 0.00 C109 10.00 870.78 17.00 0.00 0.00 0.00 10.00 939.84 18.70 0.00 0.00 0.00

C1-Avg. 10.00 1018.61 24.56 0.00 0.00 0.00 10.32 1513.06 20.46 3.11 0.00 0.00

R101 16.00 31763.10 7.00 295.95 0.00 0.00 16.60 34433.70 6.30 321.80 0.00 0.00 R102 14.00 12917.90 24.00 110.72 0.00 0.00 14.80 13018.50 10.50 110.72 0.00 0.00 R103 13.00 3555.40 22.00 19.33 0.00 0.00 13.00 4929.07 16.60 32.68 0.00 0.00 R104 11.00 1229.40 43.00 0.00 0.00 0.00 11.20 1337.82 31.70 0.61 0.00 0.00 R108 10.00 1075.13 23.00 0.00 0.00 0.00 10.10 1121.42 23.60 0.16 0.00 0.00 R109 13.00 2211.37 11.00 7.37 0.00 0.00 13.40 2434.20 16.40 9.23 0.00 0.00

R1-Avg. 12.83 8792.05 21.67 72.23 0.00 0.00 13.18 9545.79 17.52 79.20 0.00 0.00

RC101 14.00 18437.80 9.00 164.45 0.00 0.00 15.20 16981.50 10.30 148.21 0.00 0.00 RC102 14.00 2644.93 19.00 7.06 0.00 0.00 14.60 3609.50 15.80 15.74 0.00 0.00 RC103 12.00 1635.04 40.00 0.41 0.00 0.00 12.90 1736.08 19.00 0.67 0.00 0.00 RC104 11.00 1271.50 39.00 0.00 0.00 0.00 11.10 1379.23 29.50 0.00 0.00 0.00 RC106 12.00 3371.63 40.00 18.00 0.00 0.00 13.30 3056.64 21.10 13.44 0.00 0.00 RC108 11.00 1266.48 34.00 0.00 0.00 0.00 11.70 1356.92 27.20 0.00 0.00 0.00

RC1-Avg. 12.33 4771.23 30.17 31.65 0.00 0.00 13.13 4686.65 20.48 29.68 0.00 0.00

93 Appendix B

Table B39.: Detailed Test Result ILS with TO-NNB Heuristic and BF for the VRPSTW (toleranceV alue = 1.2)

Best Solutions Avg Solutions Best Known Sol. Best Gap

Violations Violations Problem NV Cost Time TW Ld Lgth NV Cost Time TW Ld Lgth NV Cost

C101 10.00 828.94 9.00 0.00 0.00 0.00 10.00 828.94 8.30 0.00 0.00 0.00 10.00 828.94 0.00% C102 10.00 834.64 6.00 0.00 0.00 0.00 10.00 975.47 5.90 0.00 0.00 0.00 10.00 828.94 0.69% C103 10.00 953.83 12.00 0.00 0.00 0.00 10.00 1037.23 9.50 0.00 0.00 0.00 10.00 828.06 15.19% C104 10.00 851.69 4.00 0.00 0.00 0.00 10.00 991.78 7.20 0.00 0.00 0.00 10.00 824.78 3.26% C105 10.00 828.94 5.00 0.00 0.00 0.00 10.30 857.73 6.80 0.00 0.00 0.00 10.00 828.94 0.00% C106 10.00 828.94 12.00 0.00 0.00 0.00 10.40 863.93 8.50 0.00 0.00 0.00 10.00 828.94 0.00% C107 10.00 828.94 10.00 0.00 0.00 0.00 10.00 884.66 8.00 0.00 0.00 0.00 10.00 828.94 0.00% C108 10.00 828.94 5.00 0.00 0.00 0.00 10.30 895.17 7.30 0.00 0.00 0.00 10.00 828.94 0.00% C109 10.00 828.94 4.00 0.00 0.00 0.00 10.00 874.89 9.20 0.00 0.00 0.00 10.00 828.94 0.00%

C1-Avg. 10.00 845.98 7.44 0.00 0.00 0.00 10.11 912.20 7.86 0.00 0.00 0.00 10.00 828.38 2.13%

R101 18.00 1670.60 7.00 0.30 0.00 0.00 19.60 1717.47 3.60 0.48 0.00 0.00 19.00 1650.80 1.20% R102 18.00 1512.23 1.00 0.42 0.00 0.00 18.40 1535.11 1.80 0.31 0.00 0.00 17.00 1486.12 1.76% R103 14.00 1267.29 8.00 0.00 0.00 0.00 14.90 1288.34 6.60 0.00 0.00 0.00 13.00 1292.68 -1.96% R104 10.00 1070.98 19.00 0.00 0.00 0.00 11.00 1063.41 8.10 0.00 0.00 0.00 9.00 1007.31 6.32% R105 15.00 1413.64 2.00 0.00 0.00 0.00 15.30 1471.72 2.20 0.27 0.00 0.00 14.00 1377.11 2.65% R106 12.00 1331.53 16.00 0.00 0.00 0.00 13.20 1310.71 7.60 0.06 0.00 0.00 12.00 1252.03 6.35% R107 11.00 1132.91 26.00 0.00 0.00 0.00 11.40 1172.62 13.50 0.01 0.00 0.00 10.00 1104.66 2.56% R108 10.00 973.26 13.00 0.00 0.00 0.00 10.00 1029.97 15.70 0.00 0.00 0.00 9.00 960.88 1.29% R109 12.00 1252.93 22.00 0.00 0.00 0.00 12.70 1301.51 13.00 0.09 0.00 0.00 11.00 1194.73 4.87% R110 12.00 1169.07 12.00 0.00 0.00 0.00 12.20 1212.87 7.20 0.00 0.00 0.00 10.00 1118.84 4.49% R111 11.00 1123.26 6.00 0.00 0.00 0.00 11.80 1143.01 3.60 0.00 0.00 0.00 10.00 1096.72 2.42% R112 10.00 1007.54 5.00 0.00 0.00 0.00 10.70 1043.05 4.10 0.00 0.00 0.00 9.00 982.14 2.59%

R1-Avg. 12.75 1243.77 11.42 0.06 0.00 0.00 13.43 1274.15 7.25 0.10 0.00 0.00 11.92 1210.34 2.88%

RC101 16.00 1726.11 6.00 0.00 0.00 0.00 16.40 1759.56 4.40 0.16 0.00 0.00 14.00 1696.94 1.72% RC102 13.00 1662.03 11.00 0.86 0.00 0.00 14.30 1583.59 6.00 0.20 0.00 0.00 12.00 1554.75 6.90% RC103 12.00 1344.50 10.00 0.00 0.00 0.00 12.50 1392.27 8.80 0.00 0.00 0.00 11.00 1261.67 6.57% RC104 10.00 1184.36 5.00 0.00 0.00 0.00 10.90 1241.57 7.50 0.22 0.00 0.00 10.00 1135.48 4.30% RC105 15.00 1632.21 8.00 0.00 0.00 0.00 15.20 1713.84 6.00 0.53 0.00 0.00 13.00 1629.44 0.17% RC106 12.00 1604.20 9.00 1.57 0.00 0.00 12.90 1519.34 7.00 0.47 0.00 0.00 11.00 1424.73 12.60% RC107 11.00 1514.48 14.00 2.14 0.00 0.00 12.10 1393.48 9.10 0.29 0.00 0.00 11.00 1230.48 23.08% RC108 11.00 1201.67 10.00 0.00 0.00 0.00 11.10 1242.72 10.40 0.00 0.00 0.00 10.00 1139.82 5.43%

RC1-Avg. 12.50 1483.70 9.13 0.57 0.00 0.00 13.18 1480.80 7.40 0.23 0.00 0.00 11.50 1384.16 7.60%

C201 3.00 591.56 60.00 0.00 0.00 0.00 3.00 591.56 71.70 0.00 0.00 0.00 3.00 591.56 0.00% C202 3.00 591.56 99.00 0.00 0.00 0.00 3.10 624.01 91.40 0.00 0.00 0.00 3.00 591.56 0.00% C203 3.00 600.21 149.00 0.00 0.00 0.00 3.20 656.50 119.00 0.00 0.00 0.00 3.00 591.17 1.53% C204 3.00 614.88 133.00 0.00 0.00 0.00 3.40 682.24 88.30 0.00 0.00 0.00 3.00 590.60 4.11% C205 3.00 609.36 95.00 0.00 0.00 0.00 3.00 609.36 117.10 0.00 0.00 0.00 3.00 588.88 3.48% C206 3.00 588.49 167.00 0.00 0.00 0.00 3.00 588.49 130.10 0.00 0.00 0.00 3.00 588.49 0.00% C207 3.00 588.29 83.00 0.00 0.00 0.00 3.00 598.87 106.00 0.00 0.00 0.00 3.00 588.29 0.00% C208 3.00 588.32 94.00 0.00 0.00 0.00 3.00 588.32 93.10 0.00 0.00 0.00 3.00 588.32 0.00%

C2-Avg. 3.00 596.58 110.00 0.00 0.00 0.00 3.09 617.42 102.09 0.00 0.00 0.00 3.00 589.86 1.14%

R201 4.00 1298.04 81.00 0.00 0.00 0.00 4.10 1356.94 116.90 0.00 0.00 0.00 4.00 1252.37 3.65% R202 4.00 1127.32 39.00 0.00 0.00 0.00 4.00 1193.12 94.20 0.00 0.00 0.00 3.00 1191.70 -5.40% R203 3.00 985.22 76.00 0.00 0.00 0.00 3.40 994.66 65.90 0.00 0.00 0.00 3.00 939.50 4.87% R204 2.00 944.09 442.00 0.00 0.00 0.00 2.90 851.91 244.50 0.00 0.00 0.00 2.00 825.52 14.36% R205 3.00 1095.09 125.00 0.00 0.00 0.00 3.70 1124.63 68.60 0.00 0.00 0.00 3.00 994.42 10.12% R206 3.00 987.03 144.00 0.00 0.00 0.00 3.20 1015.23 111.80 0.00 0.00 0.00 3.00 906.14 8.93% R207 3.00 906.59 83.00 0.00 0.00 0.00 3.00 939.68 122.40 0.00 0.00 0.00 2.00 890.61 1.79% R208 2.00 829.94 195.00 0.00 0.00 0.00 2.90 772.63 115.10 0.00 0.00 0.00 2.00 726.82 14.19% R209 3.00 1019.98 94.00 0.00 0.00 0.00 3.40 1025.41 90.10 0.00 0.00 0.00 3.00 909.16 12.19% R210 3.00 1035.06 90.00 0.00 0.00 0.00 3.60 1057.38 79.50 0.00 0.00 0.00 3.00 939.37 10.19% R211 3.00 843.00 93.00 0.00 0.00 0.00 3.20 885.40 101.40 0.00 0.00 0.00 2.00 885.71 -4.82%

R2-Avg. 3.00 1006.49 132.91 0.00 0.00 0.00 3.40 1019.73 110.04 0.00 0.00 0.00 2.73 951.03 6.37%

RC201 4.00 1549.61 49.00 0.00 0.00 0.00 4.10 1580.20 58.70 0.00 0.00 0.00 4.00 1406.94 10.14% RC202 4.00 1252.13 33.00 0.00 0.00 0.00 4.00 1323.87 50.90 0.00 0.00 0.00 3.00 1365.65 -8.31% RC203 3.00 1164.01 78.00 0.00 0.00 0.00 3.30 1221.99 75.80 0.00 0.00 0.00 3.00 1049.62 10.90% RC204 3.00 846.68 102.00 0.00 0.00 0.00 3.00 919.79 74.20 0.00 0.00 0.00 3.00 798.46 6.04% RC205 4.00 1409.18 67.00 0.00 0.00 0.00 4.00 1503.18 63.20 0.00 0.00 0.00 4.00 1297.65 8.59% RC206 3.00 1327.31 114.00 0.00 0.00 0.00 3.90 1244.27 68.80 0.00 0.00 0.00 3.00 1146.32 15.79% RC207 3.00 1196.09 161.00 0.00 0.00 0.00 3.90 1136.59 86.20 0.00 0.00 0.00 3.00 1061.14 12.72% RC208 3.00 950.34 123.00 0.00 0.00 0.00 3.50 976.17 91.40 0.00 0.00 0.00 3.00 828.14 14.76%

RC2-Avg. 3.38 1211.92 90.88 0.00 0.00 0.00 3.71 1238.26 71.15 0.00 0.00 0.00 3.25 1119.24 8.83%

94 List of Abbreviations

BF Best Fit CVRP Capacitated Vehicle Routing Problem CNV Cumulative Number of Vehicles CTC Cumulative Total Cost DA Deterministic Annealing FF First Fit HL HeuristicLab ILS Iterated Local Search JIT Just-In-Time LS Local Search NP Non-polynomial NV Number of Vehicles SA Simulated Annealing TO-NNB Time-Oriented Nearest Neighbor TS Tabu Search TSP Traveling Salesman Problem TT Tabu Tenure TW Time Window VNS Variable Neighborhood Search VRP Vehicle Routing Problem VRPTW Vehicle Routing Problem with (Hard) Time Windows VRPSTW Vehicle Routing Problem with Soft Time Windows

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