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Jorge Lusi Oyola Mendoza Essays on Stochastic and Multi-Objective Jorge Lusi Oyola Mendoza Essays on stochastic and multi-objective capacitated vehicle routing problems PhD theses in Logistics 2016:2 Essays on stochastic and multi-objective capacitated vehicle routing problems Jorge Luis Oyola Mendoza A dissertation submitted to Molde University College - Specialized University in Logistics for the degree of Philosophiae Doctor PhD theses in Logistics 2016:2 Molde University College - Specialized University in Logistics Molde, Norway 2016 Jorge Luis Oyola Mendoza Essays on stochastic and multi-objective capacitated vehicle routing problems © Jorge Luis Oyola Mendoza 2016 PhD theses in Logistics 2016:2 Molde University College - Specialized University in Logistics P.O.Box 2110 NO-6402 Molde, Norway www.himolde.no This dissertation can be ordered from Molde University College Library [email protected] Printing Molde University College ISBN: 978-82-7962-209-3 ISSN: 0809-9588 Preface This document is submitted as partial fulfillment of the requirements for the degree of Philosophiae Doctor (PhD) in Logistics at Molde University College - Specialized University in Logistics, Molde, Norway. This work was conducted from September 2010 until February 2016. Late Professor Arne Løkketangen from Molde University College was the main supervisor until June 2013. Associate Professor Halvard Arntzen from Molde University College was co-supervisor during this period. In June 2013 Professor Arntzen was appointed as main supervisor and Professor David L. Woodruff from University of California, Davis was appointed as co-supervisor. The main subject of this thesis is multi-objective vehicle routing problems. Both deterministic and stochastic versions of such problems have been studied. Routing planning is considered to be a multi-criteria process, therefore optimizing several meaningful objectives simultaneously may provide decision makers with better evidence to support their choices. The work presented in this PhD thesis has been evaluated by a committee consisting of Professor Rafael Mart´ı from University of Valencia, Spain, Associate Professor Sin C. Ho from Aarhus University, Denmark, and Associate Professor Arild Hoff from Molde University College - Specialized University in Logistics, Norway. Acknowledgments First and foremost I would like to thank my previous supervisor, late Professor Arne Løkketangen. Perhaps he was even more confident than me in the eventual success of this work. He gave me the opportunity to work with him during my master degree program and later during the Phd program. The experience of working with him was invaluable. I am equally thankful to my current supervisor, Associate Professor Halvard Artnzen, for his patience suggestions, constructive criticisms and quest for precision. I owe many thanks to Professor David L. Woodruff whose guidance and encouragement had an unquestionable impact in the completion of this work. I am also grateful to the library, IT center, faculty members and administrative personnel at Molde University College. The de facto coordinator, Irene Sætre, Jens Erik Østergaard, Rickard Romfo, Bente Lindset and Johan Oppen in particular deserve to be mentioned. I will always appreciate the support received from the Jaime Ben´ıtez Tobon´ Foundation. This achievement still is a result of that support and I will never be able to pay back. I also wish to thank all who had the (mis)fortune of being part of the A288 club, including the latest members, Kiros, Evellyn and Pipe. But specially to the great team of 2014-2015: Primo, Poncho, Chapul´ın and The Sundance Kid (aka Butch Cassidy). I met many people during all this years in Molde. I would like to thank all of them, specially those who despite the fact of knowing me better somehow became my friends. A special mention goes to Yuri Redutskiy, Sergei Teryokhin, Jianyong Jin, Øivind Opdal and Bella Nujen. In the last stage of this process, my supervisor had limited availability. I wish to extend many thanks to Aksel for, sometimes reluctantly, allowing stochastic time windows for Associate Professor Artnzen to supervise my progress. Special Thanks go to Jana Hajasova, her unconditional support and friendship are very much appreciated. I would also like to thank people who were there for me, even when I was unable to do the same. Finally I would like to thank Delia Barros for always trying to see the best of me. To my friends and family who even at the distance have made me feel close to them. And to Lidis, of course. Molde, Norway Jorge Luis Oyola Mendoza April, 2016 Contents Preface iii Acknowledgments v Introduction 1 The Vehicle Routing Problem . .1 Multi-objective optimization . .2 The Stochastic Vehicle Routing Problem . .3 Solution methods for VRPs . .3 Scientific contribution . .6 Summary of the papers . .6 Bibliography . .9 Paper 1 An Attribute Based Similarity Function for VRP Decision Support 17 Paper 2 GRASP-ASP: An algorithm for the CVRP with route balancing 37 Paper 3 The stochastic vehicle routing problem, a literature review 61 Paper 4 The CVRP with route balancing and stochastic demand 109 Paper 5 The CVRP with soft time windows and stochastic travel times 153 Introduction Introduction The vehicle routing problem (VRP) is one of the most studied subjects in Operations Research (Braekers et al., 2016). Such interest may be due to its wide range of applications in solving real-life problems. Examples of such applications are: milk collection, milk delivery, distribution of ready-made concrete, furniture distribution, city logistics, retail distribution, green logistics (Koc¸ et al., 2016); cash transportation, garbage collection, social legislation for drivers’ working hours, school bus routing, shipment of hazardous material (Braekers et al., 2016); allocation of work- force, vendor-managed distribution systems, courier service, emergency service, taxi cab service, after-sales service, e-commerce (Lin et al., 2014); livestock collection (Oppen and Løkketangen, 2008); beer, wine, and spirits distribution (Erera et al., 2009); road network monitoring (Chen et al., 2014). The vehicle routing problem (VRP) was proposed in 1959 by Dantzig and Ramser (1959) as a generalization of the traveling salesman problem, though the name used back then was “the truck dispatching problem”. Due to the shape of a solution to the problem, the name “clover leaf problem” was also suggested. The term “vehicle routing” did not appear in the literature until the early 1970s (Eksioglu et al., 2009). The theme of this thesis is the development of solution methods for different versions of stochastic and multi-objective VRPs. The following parts of this introduction define the general concepts used in the thesis, the scientific contribution of this research, the summary of papers that compose it and suggest avenues for further research. The Vehicle Routing Problem Different versions of the vehicle routing problem have been proposed, such as the basic version of the capacitated vehicle routing problem (CVRP) (Toth and Vigo, 2002a). Various authors have defined this version of the problem, e.g. Toth and Vigo (1998) and Cordeau et al. (2002), who begin with an undirected graph G = V; E , where V = v ; v ; : : : ; v is the vertex set, and f g f 0 1 ng E = (v ; v ): v ; v V; i < j is the edge set. v represents the depot, and the other vertices f i j i j 2 g 0 represent the customers, each having a non-negative demand, qi. The set E has an associated cost matrix cij, representing the cost of traveling from vertex i to vertex j and cij = cji, in the symmetric case. A fleet of m vehicles with equal capacity Q is based at the depot. The optimal solution to the problem is the one that minimizes the total routing cost, the total demand of the customers in one route is not greater than Q, every customer is visited once by just one vehicle, and each tour includes the depot. Several other versions can be found, depending on considerations and/or constraints included in the problem, e.g. the vehicle routing problem with time windows (VRPTW), vehicle routing problem with pickups and deliveries (VRPPD), vehicle routing problem with backhauling (VRPB) and vehicle routing problem with distance constraints (DCVRP) (Toth and Vigo, 2002a). Essays on stochastic and multi-objective capacitated vehicle routing problems Multi-objective optimization More than two thousands years ago Sun Tzu considered planning to be a multi-criteria process, at least in the context of war (Sawyer and Sawyer, 1994). Such philosophy initially applied to warfare has been applied to other areas, such as business and politics, for several decades (Dimovski et al., 2012). In particular, it is considered that transportation planning is intrinsically a multi-objective decision process (Current and Min, 1986). Therefore considering several meaningful objectives simultaneously may lead to better plans. In a multi-objective optimization problem several functions are optimized (minimized or maximized) subject to the same set of constraints. Without loss of generality, it can be assumed that all objec- tive function are minimized. This problem then can be stated as min F (x) = (f (x); f (x); : : : ; f (x)); s:t: x D; (1) 1 2 n 2 with the number of objective functions being n 2; the decision variable vector x = (x ; x ; : : : ; x ); ≥ 1 2 r the feasible solution space D; and F (x) is the objective vector (Jozefowiez et al., 2007). The development of mathematical programming by Kantorovich and Dantzig, in the 1930s and 1940s respectively, provided the right environment for the establishment of multi-objective math- ematical programming. Even though mathematical programming does not directly solve multi- objective optimization problems, it was proposed to use weights to combine the objective functions into a weighted single objective function (Koksalan¨ et al., 2011). The multi-objective vehicle routing problem started to gain popularity in the 1980s (Jozefowiez et al., 2008). The different objective functions in a multi-objective problem are usually conflicting. Because of this, it is common that no single optimal solution is able to minimize all the objectives of the problem.
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