ARISTOTLE UNIVERSITY OF THESSALONIKI DEPARTMENT OF ECONOMICS M.Sc. LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Master Thesis
“Identifying the optimal location for the facilitation of a retail store”
Author: Petrou Achilleas
Supervisor: Diamandidis Alexandros
Master Thesis submitted to the Department of Economics of Aristotle University of Thessaloniki in partial of fulfilment of the requirement for the degree of Master of Science in Logistics and Supply Chain Management
Thessaloniki, September 2020
Abstract The identification of the optimal location is of the outmost importance for each business due to the high expenses and long-term commitment. The case examined refers to the identification of the optimal location for the establishment of a retail store for a nuts company. The study area in which the examination take place is the Prefecture of Attica. The investigation contains different approaches encompasses subjectivity (Weighted factor rating method), objectivity (Load distance technique) and mixed subjectivity and objectivity (Analytical Hierarchy Process). Two different solutions obtained by the application of the processes allowing to decision makers evaluate the optimal one based on their preferences.
Keywords: facility location, retail store, nuts industry, analytical hierarchy process
Table of Contents 1 Introduction ...... 1
1.1 Introduction to facility location theory...... 1
1.2 Master thesis structure ...... 2
2 Classification of facility location models ...... 3
2.1 5–position classification scheme ...... 3
2.1.1 Models Classification based decision area...... 3
2.1.2 Classification based objective function ...... 4
2.2 Distance metrics in location theory ...... 7
2.2.1 Euclidean Distance...... 7
2.2.2 Rectilinear (Manhattan) Distance ...... 8
2.2.3 Highway Distance ...... 9
2.2.4 Great circle ...... 9
3 Fundamental Facility Location Problems ...... 11
3.1 MiniSum problems on the network ...... 11
3.1.1 P-Median problem ...... 11
3.1.2 Uncapacitated Facility Location Problem (UFLP) ...... 14
3.1.3 Capacitated Facility Location Problem (CFLP) ...... 16
3.2 P–Center problem ...... 17
3.3 Coverage Problem ...... 19
3.3.1 Location set covering problem (SCLP) ...... 20
3.3.2 Maximal covering location problem (MCLP) ...... 21
4 Modern Facility Location Problem ...... 23
4.1 Competitive Location Problem ...... 23
4.2 Hub location problem ...... 26
4.3 Undesirable location problems ...... 28
5 Solution techniques and methods apply in Facility Location Problems ...... 32
5.1 Weighted Factor Rating Method ...... 32
5.2 Analytical Hierarchy Process (AHP) ...... 32
5.3 Center of gravity...... 37
5.4 Load Distance Technique ...... 38
6 Case Study Presentation ...... 39
6.1 Overview of nuts industry ...... 39
6.1.1 The nutritional value of nuts ...... 39
6.1.2 Characteristics of nuts industry in Greece ...... 39
6.2 Presentation of Petrou Nuts Company ...... 41
6.2.1 Introduction ...... 41
6.2.2 Company’s structure ...... 42
6.2.3 Company’s characteristics ...... 44
6.2.4 Company’s Portfolio ...... 45
7 Facility Location Analysis ...... 49
7.1 Analytical Hierarchy Process (AHP) ...... 49
7.1.1 Introduction ...... 49
7.1.2 Classic Analytical Hierarchy Process ...... 49
7.1.3 Hybrid Analytical Hierarchy Process ...... 61
7.1.4 Sensitivity Analysis ...... 64
7.2 Weighted Factor Rating Method ...... 69
7.3 Load Distance Technique ...... 71
8 Conclusions ...... 73
Bibliography ...... 75
List of Figures
Figure 1: MiniMax model illustration {Source: Author} ...... 5 Figure 2: MiniSum Model illustration {Source: Author} ...... 6 Figure 3: Coverage Models illustration {Source: Author} ...... 7 Figure 4: Illustration of Euclidean distance among points 1 and 2...... 8 Figure 5: Illustration of Manhattan distance among points 1 and 2 ...... 8 Figure 6 Highway distance example calculated using mapping services ...... 9 Figure 7: Illustration of Great-Circle distance among r and s points ...... 10 Figure 8: A network consisted by 6 nodes and 30 origin-destination pairs (left); A hub-and- spoke network consisted by 1 hub, 5 spokes and 10 origin-destination pairs (right)...... 26 Figure 9: Solution process of the AHP location model {Source: (Yang & Lee, 1997)} ...... 37 Figure 10: Quantity produced by the main nuts trees in Greece, over time...... 40 Figure 11: Quantity of pistachios production (in tonnes) per year by dominant producing countries ...... 40 Figure 12: Quantity of almonds production (in tonnes) per year by dominant producing countries ...... 41 Figure 13: Company’s chart ...... 44 Figure 14: Hierarchy of the decision model developed ...... 51 Figure 15: Priorities of selected criteria ...... 53 Figure 16: Priorities of each potential site regarding each criterion ...... 57
List of Tables
Table 1: Indicative fields used AHP method ...... 33 Table 2 : Relative importance scale matrix for AHP models ...... 35 Table 3: Indicative pairwise comparison between selected criteria ...... 35 Table 4: Pairwise comparison matrix example ...... 36 Table 5: Indicative list of Petrou Nuts clientele...... 44 Table 6: Types of roasted nuts Petrou Nuts Company offers ...... 48 Table 7: Pairwise comparison matrix ...... 52 Table 8: Sum of the columns of pairwise comparison matrix (Table 7) ...... 52 Table 9: Normalized pairwise comparison matrix ...... 52 Table 10: Consistency matrix ...... 54 Table 11: Consistency Ratio (CR) of the pairwise comparison between selected criteria ...... 55 Table 12: Location pairwise comparison regarding accessibility to consumers...... 55 Table 13: Location pairwise comparison regarding consumers’ behavior ...... 55 Table 14: Location pairwise comparison regarding attractiveness of the city...... 55 Table 15: Location pairwise comparison regarding the touristic character of the city ...... 56 Table 16: Location pairwise comparison regarding familiarity with differentiated products . 56 Table 17: Location pairwise comparison regarding average rent per square ...... 56 Table 18: Location pairwise comparison regarding purchasing power of the area ...... 56 Table 19: Location pairwise comparison regarding number of competitors ...... 56 Table 20: Location pairwise comparison regarding the accessibility to the distributor ...... 57 Table 21: Consistency matrix regarding accessibility to customers’ criterion ...... 58 Table 22: Consistency matrix regarding consumers’ behavior criterion ...... 58 Table 23: Consistency matrix regarding attractiveness of the city criterion ...... 58 Table 24: Consistency matrix regarding touristic destination criterion ...... 58 Table 25: Consistency matrix regarding familiarity with differentiated products criterion .... 58 Table 26: Consistency matrix regarding average rent per square criterion ...... 59 Table 27: Consistency matrix regarding purchasing power of the area criterion ...... 59 Table 28: Consistency matrix regarding number of customers’ criterion ...... 59 Table 29: Consistency matrix regarding accessibility to distributor criterion ...... 59 Table 30: Consistency Index per criterion ...... 59 Table 31: Consistency ratio per criterion ...... 60 Table 32: Overall priority ranking per candidate location ...... 60
Table 33:Location criteria ...... 61 Table 34: Location comparison regarding quantitative criteria ...... 62 Table 35: Priorities of each potential site regarding qualitative criteria ...... 62 Table 36: Weighted values for each criterion and candidate location ...... 63 Table 37 Priorities of each candidate location regarding quantitative criteria ...... 63 Table 38: Overall rating of candidate locations ...... 64 Table 39: Priorities of criteria in the initial analysis for scenario 1...... 65 Table 40: Overall ratings for scenario 1 ...... 65 Table 41: New priorities obtained by the modifications in scenario 2 ...... 66 Table 42: Consistency Ratio (CR) for examined scenarios ...... 67 Table 43: Overall ranking of the candidate locations for scenario 2 ...... 67 Table 44: Overall ratings per candidate location for scenario 3 ...... 68 Table 46: Consistency Ratio (CR) for scenario 4 ...... 69 Table 47: Overall rating per candidate location for scenario 4 ...... 69 Table 48: Indicators and their corresponding weighted factor ...... 70 Table 49: Location comparison based on each criterion ...... 70 Table 50: Weighted Factor Rating Method results ...... 70 Table 51: Coordinates of both candidate locations and distributor’s facility ...... 71 Table 52: Different types of distance measures used in the analysis ...... 71 Table 53: Transportation cost per unit of product ...... 72 Table 54: Load – Distance technique values per distance type ...... 72
List of Pictures
Picture 1: Company’s plant in the city of Agia ...... 42 Picture 2: Privately owned cultivation of hazelnuts ...... 43 Picture 3: Hazelnut paste (left), pistachios paste (right) ...... 45 Picture 4: Salted caramelized pistachios ...... 46 Picture 5: Organic pistachios packages for retail use (left), privately-owned bio cultivation of hazelnuts (right) ...... 47 Picture 6: Caramelized hazelnuts packages for retail use (left), international crystal taste award (right) ...... 47 Picture 7: Salted nuts ...... 47 Picture 8: Blanched diced almonds (left), blanched diced hazelnuts (right) ...... 48
Master Thesis: “Identifying the optimal location for the facilitation of a retail store”
1 Introduction
1.1 Introduction to facility location theory Although the problem of the selection of optimal location for the establishment of a facility concerns the scientific community for many centuries, substantive solutions given only a few decades recently, starting with the early studies of Von Thϋnen and Weber. Based on the fact that the development and operation of a new facility, is costly and vulnerable in a number of unpredictable factors, the selection of the location for the establishment of a facility it’s a crucial a decision , that plays a key role in the strategic planning of a firm, either private or public. The decision-making process concerning such a long-term investment is particularly complex, and therefore the challenge for businesses who attempt to solve this problem, is significant. Until nowadays there is no a specific mathematical model that meet the needs of every facility location problem. As mentioned before, von Thϋnen was a farmer and economist that introduced a model regarding the distribution of agricultural land use around a city, depending the cultivation type. His model set the city in the center and, while four rings, each one with different agricultural activity surrounds the city. In his model, he attempt to achieve a balance among transportation and rental costs. As closest to city the less the transportation costs the higher the rental cost and vice versa. Respectively, Weber was one of the first researches that attempt to provide solution on the problem, assuming that the optimal location for the establishment of a facility is the one that minimized the cost of the business. However, he did not take into consideration many factors affecting the final decision. A factor that set constraints in the further evolution of the facility location theory was the significant shortcomings in the mathematical science of that period. After the insertion of Operational Research as a science and the updates in the mathematical science, researches has in their possession valuable tools that assist them in their effort to examine location problem under multiple approaches. Facility location decision is a problem that met in many occasions in real life. Either the decision refers to private initiative, such as the allocation of warehouse, a plant or a retail store, or the allocation of facilities of public interest such as a fire station, a hospital or public services, the approach remains the same. The only differentiation is the constraints that taken into consideration in each occasion. In public interest facilities though, decisions affected by
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Master Thesis: “Identifying the optimal location for the facilitation of a retail store”
governmental policies that does not necessarily meet the optimal solution, which may lead to increase the operational costs, as well as, at reduced efficiency in service provision.
1.2 Master thesis structure This master thesis consists of eight chapters. In the first chapter a few a words about facility location theory discussed, as well as the structure of this master thesis provided. Following, in chapter two a presentation of the most significant classification of facility location models provided, while a presentation of some distance metrics, widely used in facility location models analyzed too. In chapter three a presentation of the most representative facility location problems, with their respective formulation as they identified in the international literature, is provided. In chapter four, three quite new concepts in the facility location theory provided. A presentation of competitive, hub and undesirable location problems, with their respective formulations provided. In chapter five, an analysis of the most widely applied, solution techniques and methods in the location theory provided. In chapter six, a presentation of the case study examined in the framework of this master thesis provided. First, a discussion of the importance in including nuts in diet, as well as the characteristics of nuts industry in Greece provided. Second, a presentation of the company examined also provided. Chapter seven, is the most important chapter as the analysis, through three different techniques and methods takes place, aiming to assist company to select the optimal location for the establishment of their new retail store. Finally, in chapter eight, a discussion of the results obtained by the application of the techniques and methods used, provided.
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2 Classification of facility location models
2.1 5–position classification scheme A classification of the needs each facility location problem has to deal with has been presented by Hamacher et. al. (1997). The aim of this work has to define a scheme in order to caver the needs need to address each facility location problem. A comprehensive list of 5 positions have introduced and presented as follows. 1. In each facility location, the firstc thing need to be declared is the type and the number of required facilities that will be established. 2. An important element that need to be declared it the type of the decision space under which the examination will be conducted. The definition of whether the problem concerns a continuous or discrete problem need to be addressed in this position. 3. The definition of constraints regarding problems specifications need also to be addressed. For example, existing constraints regarding available budget or capacity restrictions need to be addressed. 4. An important factor that is crucial to be defined, concerns relation between existing and new facilities, expressed either as distance or as cost function. 5. Finally, after the synthetization of the problem it is necessary to be defined the objective of the problem. Hamacher’s work of 5-position scheme is consider as the first one applicable scheme that refers to all of the location problems. However, researchers, regarding specific location problems, have introduced equivalent job. Handler and Mirchandani have introduced a 4-position classification in 1979 concerning center problems (Handler & Mirchandani, 1979). Respectively, a 5-position scheme concerning competitive models has been introduced in 1993, incorporating factors such as pricing policy and customers’ behavior (Eiselt, Laporte, & Thisse, 1993). 2.1.1 Models Classification based decision area. A model categorization has been provided by Re Velle et. al. regarding the decision area of the problem (ReVelle, Eiselt, & Daskin, 2008). More specifically, classification includes four categories, which are presented as follows: • Continuous models The aim of this type of modes is the minimization of the demand-weighted total cost. Concerning facilities, there are no constraints regarding the space, as they usually can be
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located abstractly in the demand area. However, demand is consider that has its origin in discrete location. As an indicative example of continuous problem can be considered the Weber problem, where by using the Euclidean distance as metric, the minimization of the distance between facility and demand discrete location is the final objective. • Discrete models In contrast with continuous models, discrete modes are taking as a fact that both the location of the facility and customers demand has its origin in discrete location. In most of the cases, the approach used for the solution of that kind of problems refer to in integer or mixed-integer programming, while additional they consider as NP-hard. Discrete models are considered as the most applied models in real life applications. • Network models Network models, as their name indicates, they composed by a set of nodes and sections. Both facilities and demand are considered as located in a node, while connection between nodes is provided only by sections. For the solution of that kind of models usually integer programming techniques used. • Analytic models The main characteristics of analytic models is the assumptions that taking into consideration in model’s application. An example of the assumptions is that the total cost for the establishment of a facility, is fixed, no matter the distance with the demand area that serves. Due to their simplicity and the extended use of assumptions, analytic models their application in real-life location problems is limited. 2.1.2 Classification based objective function Eiselt and Marianov in 2011 through their research, provide a classification of facility location problems based the category of the objective function. The common characteristics that taken as granted, is that all categories refer to desirable facilities, as well distance between facilities and demand points. Finally the main goal of them is to satisfy as much of the demand as possible by reducing at the same time the costs occurred. The classification, incudes three types of models as follows: • MiniMax models The objective of that type of models is to provide an acceptable level of accessibility to all customers. Indicative type of facilities that included in that type are hospital, social services etc. Although, accessibility offered to everyone MiniMax model cannot fit to the needs of any type of facility. The fact that, the objective is the minimization of the maximum distance to
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offer accessibility to all customers has as a consequence, the reduction of the efficiency level as increase the total average distance of the network.
Figure 1: MiniMax model illustration {Source: Author}
• MiniSum models In contrast with MiniMax models, MiniSum models objective is to minimize the total distance between all of the demand nodes in the network and the assigned facility. The approach of this type of model is to locate the facility as close as possible in the majority of demand points, in order to achieve higher level of accessibility. Although the total distance between facility/demand points is the minimum possible, deviations may occurred, when a demand point is located away from the general set of demand points get ‘penalized’ in terms of accessibility as the distance from the facility increase significantly.
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Figure 2: MiniSum Model illustration {Source: Author}
• Coverage models Coverage models follows a different approach comparing MiniMax and MiniSum models. The objective of those models is to establish a facility in such a way in order to be accessible in as much demand points as possible. The accessibility is expressed in terms of distance or travel time that customer/demand point consider as acceptable in order to reach the facility. A representation of coverage models is provided in Figure 3.
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Figure 3: Coverage Models illustration {Source: Author}
2.2 Distance metrics in location theory As has been recognized in the 5-position scheme introduced by Hamacher et. al., the definition of the distance in facility location theory plays a significant role in the analysis process. There are numerous of ways for the calculation of the distance regarding the needs, in .each occasion. There are different approaches in distance calculation regarding the scope of each interest. For example in daily basis activities, such as travelling, highway distance it is a more suitable indicator for the traveler. Different types of distances recognized in the literature, and presented as follows. 2.2.1 Euclidean Distance First, the Euclidean distance; as shown in Figure 4: Illustration of Euclidean distance among points 1 and 2, is the straight-line distance, or shortest possible path, between two points and is easy to calculate by knowing the coordinates of the two desired points. The calculation of the Euclidean distance points 1 and 2 provided as follows:
푑12 = √(푥2 − 푥1)^2 + (푦2 − 푦1)^2 (2.1) where,
푑12, the rectilinear distance among facilities located in points 1 and 2
푥1, 푦1 and 푥2, 푦2 coordinates of the facilities located in points 1 and 2 respectively.
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Figure 4: Illustration of Euclidean distance among points 1 and 2
2.2.2 Rectilinear (Manhattan) Distance Second, the rectilinear distance; that is the distance between two points with a series of 90- degree turs, as along city blocks. It has to be mentioned that rectilinear distance is also known as Manhattan distance in the international literature. An illustration of the Manhattan distance is presented in Figure 5: Illustration of Manhattan distance among points 1 and 2
The calculation of the rectilinear distance between points 1 and 2 provided as follows:
푑12 = |푥1 − 푥2| + |푦1 − 푦2| (2.2) where,
푑12, the rectilinear distance among facilities located in points 1 and 2
푥1, 푦1 and 푥2, 푦2 coordinates of the facilities located in points 1 and 2 accordingly
Figure 5: Illustration of Manhattan distance among points 1 and 2
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2.2.3 Highway Distance Final, the so-called Highway distance, that is the actual distance need to be travelled through the traffic network to travel from an origin to a destination point. The calculation of this type of distance easily can be achieved using mapping services such as google maps, openstreetmap, etc. Highway distance is the most representative and commonly used type of distance in daily base applications, an illustration of which is presented in Figure 6.
Figure 6 Highway distance example calculated using mapping services
2.2.4 Great circle Great circle distance is considered as the length between two points located in the surface of a sphere. An example of great circles on the Earth is all the meridians of longitude. In real life applications when the shortest distance between two points in the surface of the Earth, is the curve length that forms part of a great circle. The calculation of Great Circle distances can be calculated by the use of the following formulation. 훥휑 훥휆 푑 = 2 ∗ 푅 ∗ 푎푟푐 sin (√sin2 ( ) + cos 휑 ∗ cos 휑 ∗ sin2 ( )) (2.3) 2 푟 푠 2 where,
• 휑푟, 휆푟 and 휑푠, 휆푠: latitude and longitude coordinates of points r and s respectively
• 훥휑 and 훥휆: the absolute difference of respective coordinates of points r and s • 푅: the radius of the sphere. In real life computations where Earth represents the sphere, R is equal to 6.371km.
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Figure 7: Illustration of Great-Circle distance among r and s points
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3 Fundamental Facility Location Problems
In this chapter, an analysis of the most widely known facility location problems and their respective formulation is presented. First, the analysis will be focused in the MiniSum problems on the network. After that an analysis of the p-center problem, the most indicative of minimax problems follows and finally an analysis of the coverage problems will complete the analysis. 3.1 MiniSum problems on the network
The objective of MiniSum problems is the minimization of the total distance between the demand points in the network and the candidate, for establishment, facility. A brief presentation of indicative problems included in this category is presented as follows. 3.1.1 P-Median problem
P- Median problem has been introduced by Hakimi (1964, 1965) as a weighted version of Webber problem and recognized as a wide used application in location science. The objective of the p-Median problem is the allocation of p facilities on a network, in a way that minimize the weighted-demand distance between demand nodes and established facilities. The cost for the satisfaction of the demand on the node i, can be calculated by multiplying the demand on node i with the corresponding distance among the demand node i with the nearest facility on the node i. Through his research, Jamshidi in 2009 identifies a number of key assumptions set frames to the median problem (Jamshidi, 2009): • Existence of Linear relationship between distance and cost
• Goods are stored in the facilities
• Time horizon is infinite
• Infinite capacity of the facilities
• Absence of initial set-up cost
• Problem is exogenous
• Facilities are the same
• Facilities are stationary
• Demand on the nodes is steady
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• The problem is considered as discrete
The formulation of p-Median problem as Daskin proposed is been provided as follows (Daskin M. S., 1995): Totals I: set of customers/demand on nodes J: set of the candidate locations
Parameters
ℎ푖: demand on node i (units of product per unit of time), ∀ i∊I
푐푖푗: distance among demand node i and the candidate location j, ∀ i∊I, j∊J p: number of facilities to be established
Decision Variables
1, if a facility established at the candidate location 푋푗 j 0, otherwise While, y-variable, defines which facility j satisfies demand as it is expressed by a customer i, as follows:
1, if demand on node i is satisfied from the facility on node j
푌푖푗 0, otherwise
Objective function
푚푖푛 ∑ ℎ푖푐푖푗푌푖푗 (3.1) i ∊ I j ∊ J Constraints
∑ 푌푖푗 = 1 ∀ i∊I (3.2) j ∊ J
푌푖푗 − 푋푗 = 0 ∀ i∊I, j∊J (3.3)
∑ 푋푗 = 푝 (3.4) j ∊ J
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푋푗 ∈ {0 , 1} ∀ j∊J (3.5)
푌푖푗 ∈ {0 , 1} ∀ i∊I, j∊J (3.6)
The objective function (3.1) as formulated above, aims to minimize the demand-weighted total cost. As demand-weighted cost is considered the sum of transport costs for products transferred to customers through the established facilities. Constraint (3.2) refers to the fact that each customer can be served by exactly one facility, while constraint (3.3) states that demand can be satisfied only through the established facilities. The exact number of facilities is going to be established in the area is captured through the constraint (3.4). Final, the last two constraints (3.5) and (3.6) states all variables are binary. The main assumption, in which the above formulations is based, is that facilities can be established only on the existing demand nodes of the network. If this assumption doesn’t take as granted then the p-median problem becomes NP-hard. Hakimi in his research prove that at least one optimal solution can be found by locating facilities on existing nodes on the network. Going one step further Daskin and Mass, (Daskin & Maass, 2015) support that locating p+1 facilities from the beginning brings better or at least the same solutions compared to p ones. An extension of the p-median problem has been introduced by Balinski (Balinski M. , 1965), in which the aim is to minimize the sum of the costs for both facility location and transportation. Many techniques and procedures supporting the optimal solution of NP-hard p-median problem has been identified until nowadays. Through their work Daskin and Maass, (Daskin & Maass, 2015) identify a number of heuristics algorithms for the p-Median problem on a network. The identified algorithms include a Myopic or Greedy adding algorithm. The algorithm is based on a repetitive process where all of the facilities are examined using the demand-weighted total distance for the insertion of each facility on the network. Furthermore, Marananza (Marananza, 1963) has proposed a Neighborhood improvement algorithm, while Teitz and Bart introduce an Exchange algorithm (Teitz & Bart, 1968). Additionally, Daskin and Mass (Daskin & Maass, 2015) in their review provides an analysis of the Lagrangian relaxation algorithm regarding to the p-median problem. As they highlight Lagrangian relaxation has a couple of benefits compared to any heuristic approach has been presented. The first advantage of the Lagrangian procedure is the acquisition of upper and lower bounds on the objective function value. Second, Lagrangian procedure can easily integrated in a branch-and-bound algorithm in order to achieve optimal solutions.
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3.1.2 Uncapacitated Facility Location Problem (UFLP)
In some problem categories the setup cost for the establishment of a facility is not the same among all the candidate locations as happens in the case of the p-median problem. In these cases, there is the necessity to introduce a new term in the objective function in order to differentiate fixed costs among the locations to be depicted. The insertion of this new term, led in the creation of a new category of discrete facility location problems. This category of problems is known as Uncapacitated Facility Location Problem. The main objective is the selection of the locations for the facilitation of unspecified number of facilities in order to satisfy the demand of a known number of customers, while at the same time achieve profit maximization. Fixed costs for the establishment of a facility is taken also under consideration. Additionally, a transport cost per unit is taken under consideration, for the expression of the transport cost between each candidate location and the demand node. Concluding, problem’s goal is the selection of the optimal location for the facilities to be established, as well as the identification of the optimal transport system among facilities and customers, so the total cost to be the minimum, while at the same time the demand is satisfied. As already has mentioned the problem belongs in the category of discrete facility location problems. The first attempts for the formulation of the problem have been made by Balinski and Wolf (Balinski & Wolf, 1963), Manne (Manne, 1964), Kuhne and Hamburger (Kuehn & Hamburger, 1963) and Stollsteimer (Stollsteimer, 1963). The formulation of the problem is been provided as follows:
Totals I: the total number of customers J: the total number of the candidate locations
Parameters
푓푗: the fixed costs for the establishment of the facility j. Fixed costs are being considered as non-negative.
푐푖푗: the cost for transporting a product from the facility j to customer i
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Decision Variables
1, if a facility established at the candidate location 푋푗 j 0, otherwise
1, if demand on node i is satisfied from a facility on node j 푌푖푗 0, otherwise
Objective function
푚푖푛 ∑ 푓푖푋푗 + ∑ ∑ ℎ푖푐푖푗푌푖푗 (3.7) 푗∈퐽 푗∈퐽 푖∈퐼
Constraints
∑ 푌푖푗 = 1 ∀ i∊I (3.8) j ∊ J
푌푖푗 ≤ 푋푗 ∀ i∊I, j∊J (3.9)
푋푗 ∈ {0 , 1} ∀ j∊J (3.10)
푌푖푗 ≥ 0 ∀ i∊I, j∊J (3.11)
As it is can be seen the objective function aims to minimize the both fixed facility and transportation costs. Concerning constraints, they have many similarities with those used in the P-median problem. Constraint (3.8) refers to the necessity of every demand node to be served, while (3.9) ensure that demand nodes can be served only from an established facility. Constraint (3.10) states that the variable Xj is binary and last constraint (3.11) ensure that the demand satisfied from the facilities is a non-negative value. Equivalent with previous, in case of weak formulation of the problem, the constraint (3.9) replaced as follows:
∑ 푌푖푗 ≤ 푚 푥푗 (3.12) j ∊ J
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It has to be mentioned that UFLP is NP-hard and many researches approach the problem under multiple scopes in order to obtain greater level of realism in the final solutions. Multiple methods offering solutions have been proposed such as Langrangian relaxation, DUALOC algorithm or heuristics. A brief discussion of those solutions is provided below. Kuehn and Hamburger (Kuehn & Hamburger, 1963) introduce one of the first heuristic solution approach focused on warehouse location. Additionally, Maranzana (Marananza, 1963) , as already mentioned in the P-median problem has proposed an improvement algorithm, known as neighborhood algorithm. An extension of UFLP, also is been introduced with the multi-commodity facility location problem. Klincewicz and Luss (Klincewicz & Luss, 1987) were the first that offered a model that did not set up constraints on the facilities regarding the number of products that can handle. In the most of the cases, UFLP refers to the establishment of facilities on the same level, i.e. of the same type. Although, in real life there are occasions where the allocation of facilities refers to different types, which in international literature referred as multi-level UFLP. First, Tcha and Lee (Tcha & Lee, 1984) introduce a model for the determination of an optimal set of facilities in order to minimize the total distribution costs (including fixed costs for the establishment of them). In the essence of capturing the economic impact of the interactions between facilities of different level Barros and Labbe (A.I.Barros & M.Labbé, 1994) propose an alternative version of the problem, presenting a branch-and-bound procedure, based on Lagrangian relaxation, aiming to maximize the total profit. Earlier in 1974, Soland insert the term of cost representation in the model, by examine the correlation of fixed cost for the establishment with the corresponding size of the facility (Soland, 1974).
3.1.3 Capacitated Facility Location Problem (CFLP)
In contrast with UFLP where the main characteristic is the limitless capacity of the facility, an extension of the problem has formed in order to reflect most common cases in real life, where facilities have limitations. This extension is commonly known as Capacitated Facility Location Problem (CFLP). With the term capacitated is considered a facility that has limitations on the number of customers that can handle. The formulation of the CFLP is the same as in UFLP, with the addition of an extra constraint that reflect the maximum demand that can be assigned in the facility. This constraint is provided as follows:
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∑ ℎ푖 푌푖푗 ≤ 푏푗 푥푗 (3.13) j ∊ J
The format of the variables shown in constraint (3.13) are the same as has presented in the
UFLP. The new variable 푏푗 depicts the maximum value of demand that a facility j is capable to serve. An extension of the CFLP has been provided by Melo et.al (Melo, Nickel, & Saldanha-da- Gama, 2005), who introduce a mathematical model considering simultaneously multiple commodities, with aim to support the strategic design of supply chain network. In the effort to capture the factor of cost (fixed and variable) representation in the model, Holmberg and Ling approach the cost for the capacity acquisition as arbitrary linear functions (Holmberg & JonasLing, 1997). In the same concept, other approaches used by researchers incorporating logistics costs in their facility location models (Sourirajan, Ozsen, & Uzsoy, 2007).
3.2 P–Center problem
Another wide-applied problem as it has been identified in the international literature is the P- center problem. It is basically a minimax problem; the objective of the problem is the allocation of predefined number of facilities in a that way so the demand to be satisfies, while at the same time the maximum distance that a customer need to cover in order to reach the closest to him facility will be the minimum. It can be considered as the opposite approach. The general objective under which is based P-center problem can be considered as the opposite of MiniSum problems, which analyzed in previous section. Another significant feature of this problem it is essential to be mentioned, is the existence of weights assigned on demand nodes. The type of the assigned weights may vary depending on the case study examined each time but the most common cases concern factors like cost/time/loss per unit distance. Therefore, the objective is the minimization of maximum time, cost or loss. (Biazaran & SeyediNezhad, 2009). Different approaches in the solution of the problem met regarding the location inside the network where facilities can be established. In the case where facilities can be established in any location inside the network the problem called absolute center problem, while in the case where facilities can be established only on the nodes of the network the problem called vertex center problem. In 1965, Hakimi introduce the formulation of the vertex p- center problem,
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which also takes into consideration some key assumptions. Both assumptions and formulation presented as follows (Hakimi, 1965):
Key assumptions • Facilities can be established only on the nodes of the network • There is no limitation on the capacity of the facilities • The number of facilities to be located is p • There are no weights on the demand node • Demand node are one the nodes of the network
Formulation of the problem
1, if a facility established at the candidate location 푋푗 j 0, otherwise
1, if demand on node i is satisfied from a facility on node j
푌푖푗 0, otherwise
Objective function 푚푖푛 퐷 (3.14) where D, is considered as the maximum distance among customer/demand and the closest to him facility.
Constraints
∑ 푌푖푗 = 1 ∀ i ∊ I (3.15) j ∊ J
푌푖푗 − 푋푗 ≤ 0 ∀ i ∊ I, j ∊ J (3.16)
∑ 푋푗 = 푝 (3.17) j ∊ J
퐷 ≥ ∑ 푑푖푗푌푖푗 ∀ i ∊ I (3.18) j ∊ J
푋푗 ∈ {0 , 1} ∀ j ∊ J (3.19)
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푌푖푗 ∈ {0 , 1} ∀ i ∊ I, j ∊ J (3.20)
As it can be seen, the formulation of the problem is similar to the median problem. However, in this case the objective function (3.14) aims to minimize the maximum distance between a demand node with the nearest facility to which is assigned. Constraints (3.15), 3.16) and (3.17) are similar to the constraints (3.2), (3.3) and (3.4) presented at the p-median problem. Constraint (3.18) defines the maximum distance between any demand node i with the nearest facility j and finally constraints (3.20) and (3.21) indicate that decision variables 푋푗 and 푌푖푗 are binary. In some occasions, (Daskin M. S., 1995) constraint (3.18) can take another formulation as it follows:
퐷 = ℎ푖 ∑ 퐷푖푗푌푖푗 ∀ i ∊ I (3.21) 푗 where D, is the distance under weighted demand.
The concept in Daskin’s theory is the existence of weights at each demand point which is presented under the factorℎ푖. The weights can be assigned may be time per unit distance or cost per unit distance or loss per unit distance. Furthermore, in 2003 Burkard and Dollani introduce the concept of a problem that the weights on the demand nodes can take either positive or negative values, referring to pull and push objectives respectively. Klein and Kincaid in 1994, introduce the concept of Anti P-center problem, which aims to maximize the minimum weighted distance between demand node and its nearest facility.
3.3 Coverage Problem
The concept of “coverage” is of great importance in the field of facility location. In contrast with previous methods, these types of problems the objective is to satisfy the demand, while simultaneously establish the minimum number of required facilities. A demand can be considered as “covered”, if it is satisfied in a specific threshold (travel time or distance). To get a clear view of the concept of “coverage” let’s use an example. Let’s assume that customers are been represented by the population of a municipal district, while the role of the facility takes the local fire station facilities. In this case residents are been considered as “covered” if the fire station facilities are inside a buffer zone of minutes driving distance. Covering problems
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are commonly used for the establishment of public interest facilities such as schools, police and fire stations, etc. According to the international literature review, coverage problems can be classified in two categories; location set covering problem and maximal covering location problem, which both of them are considered as NP-complete. An analysis of both categories is provided as follows.
3.3.1 Location set covering problem (SCLP)
The first category as it has mentioned above, refers the location set covering problem. The objective of this method is to minimize the number of facilities that is necessary to established in an area, so the total demand to be covered, while simultaneously the total cost is the minimum. The formulation of the problem takes into consideration the existence of two assumptions. First, facilities are considered as uncapacitated and second there is no differentiation of the fixed costs between facilities. The mathematical formulation of the SCLP is provided as follows:
Totals I: number of customers J: number of candidate locations c 푉푖: number of customer locations that cover customer i, Vi= {푗 ∈ 푉: 푑푖푗 ≤ D }
Parameters
푑푖푗: distance among demand node i and the candidate location j, ∀ i ∊ I, ∀ j ∊ J Dc: Coverage distance
Decision Variables
1, if a facility established at the candidate location j
푋푗 0, otherwise
Objective function (3.22) 푚푖푛 ∑ 푋푗 푗∈푉
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Constraints:
∑ 푋푗 ≥ 1 ∀ i ∊ V (3.23) j ∊Vi
푋푗 ∈ {0 , 1} ∀ j ∊ J (3.24)
The objective function (3.22) aims to define the minimum number of facilities are going to be established, so the total demand value to be satisfied. Concerning constraints, the first one (3.23) states that all of demand points need to be covered, while the second one (3.24) states that variable푋푗, is binary. An extension of the problem is been provided by Toregas et. Al, who introduce the establishment cost in the formulation of the problem (Toregas, Swain, ReVelle, & Bergman,
1971). The addition of the establishment cost of a facility j, depicted with a new variable, 푓푖, and the objective function takes the following form:
(3.25) min ∑ 푓푖 푋푗 푗∈퐽
The objective function (3.25) aims to identify the minimum number of facilities that serve demand points, under the minimum cost. 3.3.2 Maximal covering location problem (MCLP)
In contrast, maximal covering location problem aims to serve the maximum value of demand, with a specific number of established facilities. The main difference among two problems, is that MCLP identify the minimum number of facilities that can be established in a location, ensuring that the distance among facility and demand point will not exceed a distance threshold defined as the maximum service distance. The mathematical formulation of the MCLP is provided as follows:
Totals I: number of customers J: number of candidate locations
푁푖: Number of candidate locations covering demand on node i, 푁푖= {푗 ∈ J: 푑푖푗 ≤ S}. The demand is considered as “covered” when the distance from the nearest facility is less or equal to S, otherwise, is considered as ‘uncovered’.
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Parameters S: denotes the maximum distance beyond which a demand point is considered as ‘uncovered’
푑푖푗: the shortest distance from node i to node j p: number of facilities to be established
푎푖: population that need to be served at demand node i
Decision Variables
1, if a facility established at the candidate location 푋푗 j 0, otherwise
1, if demand node i is covered by a facility
푌푖 0, otherwise
Objective function: (3.26) 푚푖푛 ∑ 푎푖푌푖 푖∈퐼
Constraints:
∑ 푋푗 ≥ 푌푖 ∀ i ∊ I (3.27) j ∊Vi
∑ 푋푗 = 푃 (3.28) j ∊Vi
푋푗 ∈ {0 , 1} ∀ j ∊ J (3.29)
푌푖 ∈ {0 , 1} ∀ i ∊ I (3.30)
The objective function (3.26) aims to maximize the coverage of demand points. As for the constraints, constraint (3.27), ensure that every customer will be covered from an established facility. Constraint (3.28) indicates the number (p) of facilities that will be established and final constraints (3.29) and (3.30) indicate that variables 푋푗 and 푌푖 accordingly, are binary variables.
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4 Modern Facility Location Problem
4.1 Competitive Location Problem
Hotelling is considered as the “father” of competitive location problem through his research about the competition in a linear market, with the assumption that customers are uniform distributed (Hotelling, 1929). Last decades have been introduced multiple approaches concerning competitive location problem, giving decision-makers the ability to choose the appropriate for their needs, tools. A location problem can be considered as competitive if in the specified location already exist (or is planned to establish) competitive facilities affecting the market share. One of the main attributes of the competitive location problem is the calculation of the market share each facility occupies. The market share of the facilities is directly affected by three factors (Ποταμιανός, 2010): 1. Customers’ specifications, which includes elements such as, the available income of
customers, age and their education level. These elements capture customers’ life style, the
consuming habits and power.
2. Facilities’ specifications, which refers to the available variety of goods that a facility offers,
to satisfy customers’ needs.
3. Spatial separation among customers and facilities such as the distance that a customer needs
to cover, in order to reach the facility. In general, the longer the distance among a customer
and a facility, the less the probabilities for the customer to travel through this facility. In
literature this element is referred as transport cost, including the travel time and the actual
cost for covering the distance.
An also widespread approach on the competitive location problem has been introduced by ReVelle and is known as the maximum capture (ΜΑΧCAP) or “sphere of influence” location problem (ReVelle C. , 1986). In this problem, ReVelle examine the establishment of p facilities in an area where competitive facilities already exist. The competition between facilities is defined in terms of distance from the customers. The main objective of the new facility is to maximize as much as it gets its market-share, which will alter with the entrance of the new facility.
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The formulation as ReVelle propose is provided as follows:
Assumptions: A number of assumptions are considered in the formulation of the problem: 1. The number of competitors is considered as fixed and known
2. Customers tend to prefer facilities considered as more “attractive” to them, resulting
the most attractive facilities to dominate over the others
3. MAXCAP leads to the combinatorial optimization models such as the covering one
Totals I: number of customers (demand nodes) S: number of candidate locations
Parameters
푃푖: set of all candidate location areas s (s ∈ S), that customers i will patronize if a new facility established on.
푇푖: set of all candidate location areas, in which the establishment of a new facility would result to be considered as attractive as the existing competitive one, that has serves demand resulting from customer i.
푤푖: demand of customer i, ∀ i∊I p: number of facilities to be established
Decision Variables
1, if customer i is completely captured by the new facility
푌푖 0, otherwise
1, if customer i, whose demand is already satisfied by an existing
facility, has the option to choose of a new, equally attractive facility 푍푖 0, otherwise
1, if a facility established in the locations
푋푠 0, otherwise
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Objective function: 푤 푚푎푥 ∑ 푤 푌 + ∑ 푖 푧 (4.1) 푖 푖 2 푖 푖∈퐼 푖∈퐼
Constraints:
푌푖 ≤ ∑ 푋푠 ∀ i ∊ I (4.2) s ∊푃푖
푍푖 ≤ ∑ 푋푠 ∀ i ∊ I (4.3) s ∊푇푖
푌푖 + 푍푖 ≤ 1 ∀ i ∊ I (4.4)
∑ 푋푠 = 푃 (4.5) s ∊S
푌푖 ∈ {0 , 1} ∀ j ∊ J (4.6)
푍푖 ∈ {0 , 1} ∀ i ∊ I (4.7)
푋푠 ∈ {0 , 1} ∀ s ∊ S (4.8)
The objective function (4.1) aims to maximize customers’ demand that covered by the establishment of the new facility. As for the constraints that objective function subjects to the following ones. Constraint (4.2) indicates that the new facility has to be more attractive than the existing one in order to capture demand originated from customer i. Furthermore, constraint (4.3) indicates that even if a facility is as attractive as the existing one, additionally it has to be established in a location s ∊ 푇푖 (demand is equally distributed in both of the facilities), in order to capture demand originated from customer i. Constraint (4.4) used to highlight that a demand originated by customer i can satisfied only by one facility, either the existing one ot the new one. Both captures simultaneously cannot be achieved. Constraint (4.5) defines that p facilities will be established. It needs to be clarified that there is no mention on the existence or the number of the facilities on the area. Finally, constraints (4.6), (4.7) and (4.8) defines variables푌푖, 푍푖 and 푋푠 as binary. As it has been mentioned by ReVelle and Swain, maximum capture problem can be converted into p-Median problem by modifying the objective function (ReVelle & Swain, 1970).
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4.2 Hub location problem
The need for properly configured networks tailored to the growing needs of the consumer led to the development of a new model. Hub location problem is considered an extension of facility location problems that flourish in lately, as many researchers have dealt with. Satisfaction of demand, presupposes the coordination and movement of customers, commodities or information between an origin-destination pair. Hub location problem aims to establish a hub node in the network, which will decrease the number of transportation links, increasing simultaneously offering time- and cost-efficient connections between origin- destination nodes. By the term of hub node meaning a facility serves multiple origin-destination pairs as transformation and trade-off nodes, commonly used in transportation systems and telecommunication industry. The advantage in transportation link reduction through the transformation of a node in the system in the network as a hub node, is presented through an example. In the case of a network with N nodes and no hub node, number of links connecting each node to another is equal to 푁(푁 − 1). In contrast, in the case that one of N nodes set as a hub node and connecting it to the remaining nodes (which are introduced as spokes), then the number of links connecting all origin-destination pairs is equal to 2(푁 − 1). An illustration of both cases is presented in Figure 1.
Figure 8: A network consisted by 6 nodes and 30 origin-destination pairs (left); A hub-and-spoke network consisted by 1 hub, 5 spokes and 10 origin-destination pairs (right).
During last decades, a wide variety of algorithms offering solutions to different types of HLPs. Hub location problems can be classified into categories, depending specific elements of the problem. An indicative, not absolute, classification of hub location problems is presented as follows: • Capacity restrictions: Capacitated, Uncapacitated
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• Allocation type: Single allocation, multiple allocation • Type of HLP: Median, Center, Covering, Set covering, Maximum covering • Number of hub nodes: Single, Multiple • Cost of hub location: no cost, fixed cost, variable cost
The simplest form of hub location problem refers as single hub location problem and introduced by O’Kelly in 1897. The single hub location problem, as its name indicates, examines the allocation of a single hub node with unlimited capacity, with criterion the minimization of the total distance between hub node and the non-hub nodes connected. The formulation of the problem is presented as follows:
Key assumptions of the model: • Criterion of the model is MiniSum • The number of hub nodes is equal to one. • There is connection among each non-hub node and hub node, while connection between hub nodes is offered through hub node. • The exact number of hub nodes is known • There is no establishment cost for the hub node. • There is no limitation in capacity (Uncapacitated model) • Decision variables of the model are binary variables
Totals I: number of customers (demand nodes)
Parameters
ℎ푖푗: Amount of flow between nodes i and j
퐶푖푗: Transfer cost per unit between non-hub node i to hub j
Decision Variables
1, if a hub is located to node j
푋푗 0, otherwise
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1, if node i is connected to a hub established in node j
푌푖푗 0, otherwise
Objective Function (4.9) 푚푖푛 ∑ ∑ ∑ ℎ푖푗 (퐶푖푗 + 퐶푗푘)푌푖푗푌푘푗 푖 푗 푘
Constraints:
∑ 푋푗 = 1 (4.10) j
푌푖푗 − 푋푗 ≤ 0 ∀ i, j (4.11)
푌푖푗 ∈ {0 , 1} ∀ i, j (4.12)
푋푗 ∈ {0 , 1} ∀ j (4.13)
The aim of the objective function (4.9) is the minimization of the total cost related to transfers through hub. As for the constraints, constraint (4.10), ensures that hubs will not be more than one, while constraint (4.11), indicates that a connection is offered between demand node i and demand node j, only in the case that a hub is located in node j. Final, constraints (4.12) and
(4.13) state that 푌푖푗 and 푋푗 are binary variables.
4.3 Undesirable location problem
In the most of the occasions, literature on location analysis focus on the establishment of retail stores, emergency services. The common element of all these facilities is that they belong in the category of desirable facilities, meaning that their customers or population around desire to be located as close to them as possible. However, there are many facilities such as chemical plants, military facilities, malls, that are considered as undesirable facilities. This type of facilities, due to the activities that take place in them, having a negative impact in the areas that they are located. A distinction to noxious (pollution) and obnoxious (noise) has been introduced by Erkut and Neuman, however both of them considered as undesirable (Erkut & Neuman, 1989). In contrast with desirable facilities, in this occasion, residents of an area desire to be located as far as possible, from them.
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Despite the fact that the establishment of these facilities in proximity to residential areas is undesirable, locating them far away may lead to significant increase to the expenses. The fact that individual criteria such as minimax (center) and MiniSum (median) cannot be used for the establishment of these type of facilities, a combination of MaxiMin and MaxiSum criteria usually applied in order to maximize the minimum distance among facilities and their closest customers and, at the same time, maximize the average distance among facilities and their customers, accordingly. An extension of the Undesirable location problem is the p-dispersion problem, which aims to locate a fixed number of facilities in a way that the minimum distance between any pair of facilities will be the maximum possible. Shier is considered as a pioneer as was the first that recognize the p-dispersion problem as facility location problem (Shier, 1977). The main concept of p-dispersion problem has to deal with the allocation of obnoxious facilities in a distance capable to secure that an accident or an attack to one of them will have the minimum negative effects the neighboring ones. In addition, p-dispersion problem is usually met in the development of market systems, like franchise, in order to avoid cannibalization effects. In franchise system, ensuring an efficient distance between facilities is essential, in order the competition between the members of the same franchise company to be the minimum. Moon and Chaundry, approach dispersiveness from a different point of view. They introduce p-Defense problem which taking account the overall sum of the minimum separation distance between each facility with its neighboring one (Moon & Chaudhry, 1984). On the other hand, in 1987, Kuby present the MaxiSum problem, which aims to maximize the sum of all pairs of open facilities locations by locating p facilities (Kuby, 1987). The formulation as Kuby propose in his research is provided as follows:
Totals N: set of candidate location areas
Parameters D: minimum distance among two established facilities n: number of potential facility locations p: number of facilities to be established M: a very large number
푑푖푗: the length of the shortest path among node i and node j
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Decision Variables
1, if a facility located at node i
푋푖 0, otherwise
Objective function: max 퐷 (4.14)
Constraints:
∑ 푋푖 = 푝 ∀ i ∊ N (4.15) i ∈I
퐷 ≤ 푑푖푗 [1 + 푀(1 − 푋푖) + 푀(1 − 푋푗)] ∀ I, j ∊ N; i < 푗 (4.16)
푋푖 ∈ {0 , 1} ∀ i ∊ N (4.17)
The objective function (4.14) presented above aims to maximize the minimum distance among two established facilities. As for the constraints, constraint (4.15) indicated that p facilities are going to be established. Constraint (4.16) takes into consideration three alternative options regarding any pair of potential locations (Χατζηγιάννης, 2013):
• 푋푖 = 푋푗 = 1, if facilities established in both nodes i and j then 퐷 ≤ 푑푖푗 . In this
occasion, the length of the shortest path between two established facilities is at
maximum the shortest path between those two locations.
• 푋푖 = 0 , 푋푗 = 1 or 푋푖 = 1, 푋푗 = 0, if in each occasion a facility is established, then
퐷 ≤ 푑푖푗 (1 + 푀). In this occasion the upper bound of D is ∞.
• 푋푖 = 푋푗 = 0, if no facility established, then 퐷 ≤ 푑푖푗 (1 + 2푀) and 퐷 ≤ 푀. Equal to
the second occasion the upper bound of D is ∞.
Concluding, constraints in variable D occurs only in the first occasion, where a facility is locating in both of the nodes. Final, concerning dispersiveness, an alternative approach has been introduced by Moon and Chaundry, widely known as anti-covering problem (Moon & Chaudhry, 1984). The solution
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of this problem based on the use of distance or weighted distance as an indicator to allocate the maximum number of facilities under the minimum separation distance. As can be seen, there is a close relation between p-dispersion problem and anti-covering problem. The first one aims to maximize the minimum distance between the facilities considering the existence of p open facilities, while in the anti-covering problem the aim is to maximize the number of facilities considering a minimum distance between them.
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5 Solution techniques and methods apply in Facility Location
Problems
5.1 Weighted Factor Rating Method Weighted factor rating method is one of the most widely applied methods in facility location problems, due to the wide variety of factors that takes into consideration during the evaluation process. The fact that both qualitative and quantitative factors used for the evaluation process increase the efficiency of the method. In each factor is assigned with weights to reflect the relative importance of each one based to decision maker’s point of view. However, its simplicity, it is considered as a quite effective method, as gives decision makers the ability to adjust it according their preferences and purposes. The location with the higher weighted value is considered as the more suitable location. The methodology for solving Weighted Factor Rating Method is briefly discussed as follows: 1. In the first step is necessary to compose a list with the relative factors.
2. After the identification of the factors, weights have to be assigned to each one of them. The
weights, always have to sum up to 1.00.
3. A scale for each factor has to be developed (score from 1 to 100). For each location and
factor a score has to be assigned from the scale above.
4. For each location, factor’s score has to be multiplied with its corresponding weighted value.
5. Final for each location, the sum of the weighted scores calculated. The location with the
higher value is highly preferred among the candidate ones.
5.2 Analytical Hierarchy Process (AHP) The Analytic Hierarchy Process (AHP) method is a multi-criteria decision making process, has been developed by Thomas L. Saaty (Saaty T. L., 1980). Since then, has been widely used as a decision-making process, in cases where the selection shall be made among multiple alternative options. It is suitable and wide used in facility location problems, as it is a structured method trying to support decision maker match their personal preferences with location site unique characteristics. The methodology used by the AHP applies in many objective
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programming formulations. Its main characteristic is the decomposition of complex problems into a set of components from an overall goal to criteria and alternative in successive level. More than 200 published applications have been conducted (Zahedi, 1986) . An indicative representation of the range of the fields in which AHP has been used, demonstrated in Table 1.
Table 1: Indicative fields used AHP method Fields of study AHP Published Applications Economics and Planning (Emshoff & Saaty, 1982) , (Saaty T. L., Scenarios and priorities in transport planning: Application to Sudan, 1977), (Ramanujam & Saaty, 1981), (Saaty & Vargas, a noote on estimating technological coefficients by the analytic hierarchy process, 1979) Retail (Kuo, Chi, & Kao, 1999), (Erbıyık, Özcan, & Karaboğa, 2012) Health (Saaty T. L., The analytic hierarchy process and health care problems, 1980) , (GülçinBüyüközkan, GizemÇifçi, & SezinGüleryüz, 2011), (Hussain, Malik, & Neyadi, 2016) Energy (Gholamnezhad, 1981), (Saaty & Gholamnezhad, 1982), (KonLee, Mogi, & Kim, 2008), (Amer & Daim, 2011) Education (Saaty & Rogers, Higher education in the united states (1985–2000): Scenario construction using a hierarchical framework with eigenvector weighting, 1976) , (Badri & Abdulla, 2004) Politics (Saaty & Bennett, A theory of analytical hierarchies applied to political candidacy, 1977), (Cheong, 2009) Sociology (Saaty & Wong, Projecting average family size in rural India by the analytic hierarchy process, 1983) Marketing (Wind & Saaty, 1980), (Davies, 1994) Material Handling and (Vargas & Saaty, 1981), (Rajesh & Malliga, 2013) Purchasing
The main challenge on using a multi-criteria decision is choosing the appropriate factors supporting this decision. The person who will synthesize the problem need to be familiar with
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the subject. According to Thomas L. Saaty, a well-structured hierarchy problem needs to include details such as (Saaty T. L., 1990): • A problem needs to be as representative as possible; sensitivity factors has to be selected wisely in order variation to be visualized • The Surrounding environment need to be taken under consideration in the synthetization of the problem • The identification of all features or attributes incorporated with the problem • The identification of all the participants associated tithe the problem
The appropriate selection of all these details serves two purposes. First, allows decision makers to obtain an overall view, when complex relationships among attributes occur. Secondly, provides them a tool to compare homogeneous elements accurately in each level of the analysis (Saaty T. L., 1990). More specifically, AHP as it already has been mentioned has a structured form and a number of steps need to be followed (Johnson, 1980): • Step 1: The first step is the most important phase of the process. In this phase, decision analyst has to decompose the problem into multiple interrelated decision elements in a hierarchical format according their importance. In the first level in the hierarchy objectives that reflect in more general way the best decision is contained. In the next level of the hierarchy, the objectives that usually selected also contribute in the decision-making in both qualitative and quantitative terms. An extra analysis of these objectives included in the lower level, where further details contribute in the decision of the alternatives or selection choices. The level of the complexity of the problem determines the number of the hierarchy’s level. A number of nine elements in each level has been determined as the maximum limit (Saaty T. L., 1980). However, there are no constraints for the use of more elements in each level. • Step 2: In this step, input data collection taking place by pairwise comparisons of decision elements. The contribution of achieving the objectives of the higher level indicated by the new matrices formed by the pairwise comparisons among the elements of this level. The reason why pairwise comparison took place is to provide evaluator a basis to indicate his/her preferences among two elements. The range of the values that can be assigned to the elements of the pairwise comparison varies fluctuating from 1 to
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9, where 1 indicates an equally preference between two elements and 9 absolute dominance of one activity over another as indicated in Table 2.
Table 2 : Relative importance scale matrix for AHP models Numerical Rating Verbal Judgement Explanation There is evidence of absolute dominance 9 Extremely more important of one activity over another Very Strongly to Extremely 8 Compromise among scale 8 and 9 more important There is demonstrated evidence into 7 Very Strongly more important practice that there is strongly dominance of one activity over another Strongly to Very strongly 6 Compromise among scale 7 and 6 more important Through experience, strongly preference 5 Strongly important is given to one activity over another Moderately to Strongly more 4 Compromise among scale 5 and 3 important Through experience, slightly preference 3 Moderately more important is given to one activity over another Equally to Moderately more 2 Compromise among scale 3 and 1 important 1 Equally important Equal preference among two activities
Based the numerical classification presented in Table 2, a pairwise comparison example between three indicators is presented in Table 3 following. It is useful to notice, especially in real cases where the number of indicators considered as huge, that the number of pairwise comparison can easy identified by using the equation: (푛 − 1) ∗ 푛
2 Where, n indicates the number of factors taken into consideration.
Table 3: Indicative pairwise comparison between selected criteria
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More important Verbal Pairwise Comparison Numerical Rating criterion Judgement Criterion 1 – Criterion 2 Criterion 1 Moderately 3 Indicator 1 – Criterion 3 Criterion 3 Strongly 5 Criterion 2 – Criterion 3 Criterion 3 Very Strongly 7
After the comparison of the criteria the pairwise comparison matrix is ready to be composed is it is presented in the Table 4 following.
Table 4: Pairwise comparison matrix example Criterion 1 Criterion 2 Criterion 3 Criterion 1 1 3 1/7 Criterion 2 1/3 1 1/5 Criterion 3 7 5 1
• Step 3: Next the ‘eigenvalue’ method is using for the estimation of the relative weights of decision elements, considering the pairwise comparisons matrices already have been composed. However, despite ‘eigenvalue’ a number of other estimators exists can be used. • Step 4: In this final step, an aggregation of the relative weights of decision criteria obtained from previous step, take place, in order to form a final set of ratings evaluating the decision alternative. In this way, identification and selection of the most suitable objective of the problem can be achieved.
AHP can be used as useful supportive tool for facility location selection as it is mentioned in the research of Yang and Lee. Through their publication, they present the application of AHP model through an example problem. Both quantitative and qualitative alternative factors used for evaluation (Yang & Lee, 1997). Additionally, an illustration of the process of the AHP location model used is provided and presented in Figure 9.
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Figure 9: Solution process of the AHP location model {Source: (Yang & Lee, 1997)}
AHP technique has significant benefits that contribute in the wide applications. First of all, through the hierarchic process that AHP follows, helps decision makers by simplifying the problem, while it has application in many areas as it has been identified in Table 1. That happens because AHP is a flexible method that can adjust and solve many different problems. Additionally, it has to be mentioned that is a useful tool in the hand of decision makers, because it forces them to make comparison between factors that in other occasions may be considered as insignificant. Despite the benefits, needs to be mentioned that AHP is time-consuming process. In the case there is no available software, the consistency check in every step of the process needs significant effort.
5.3 Center of gravity The center of gravity method, which is also known as Grid or Centroid method, takes into consideration the existing locations of the existing facilities and markets, the loads of goods need to be transferred and the transportation costs from one location to another. The aim of the method is to identify the location that minimize the weighted distance between the warehouse and its supply and distribution points. It is easily to assume, that center of gravity method is a suitable tool for the identification of location for the establishment of a distribution center, serving multiple destinations.
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For the identification of the location, this method assumes that the distribution cost is a function of the volumes transferred and the rectilinear distances. To calculate the distance coordinates X and Y of the existing demand points are used, weighted by their demand volumes. The solution of the problem is quite simple and its formulation is provided as follows:
∑푖 푉푖푋푖 푋푐 = (5.1) ∑푖 푉푖
∑푖 푉푖푌푖 푌푐 = (5.2) ∑푖 푉푖 where,
• 푋푐 and 푌푐 are the coordinates where the new facility will be established
• 푉푖 volumes of goods transferred to or from each of i locations
• 푋푖 and 푌푖: are the coordinates of the existing i established facilities.
5.4 Load Distance Technique The Load distance technique, as easily can be understood by its name, is a technique that aims to minimize the total weighted loads moving from one facility to another. It is a mathematical model applied for the evaluation of facilities, based on those two proximity factors. The formulation of the problem is provided as follows:
푙푑 = ∑ 푙푖푑푖 (5.3) 푖 where, • 푙푑: the Load-Distance value
• 푙푖 : the loads, which express the shipment, in units like pallets or packages, that need to be transferred from the existing set of facilities i to the new location sites are under examination.
• 푑푖: the distance needs to be covered, calculated by Euclidean or any other method. The distance travelled from an origin to a destination location can be measured through a variety of applications. Although in the framework of this master thesis three types of distances measures taken into consideration (Euclidean, Rectilinear, Highway).
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6 Case Study Presentation The aim of this chapter is the presentation of the case study examined in the framework of this master thesis. First of all an induction section where a few characteristics about nuts and their market share in Greece is presented. Following, a brief discussion about the company examined is included.
6.1 Overview of nuts industry 6.1.1 The nutritional value of nuts Nuts are parts of human diet since antiquity. Nowadays, are still consumed, in a various ways, either or snacks or as seeds. The most widely known types of nuts are: walnuts, brazil nuts, sunflower seeds, cashew nuts, macadamia nuts, hazelnuts, peanuts and pistachios. Nuts contains significant quantities of proteins, nutrients and vitamins, while researches indicate that the consumption of nuts in a regular basis, contributes to the fight against many diseases. Each type of nut contains each unique blend of vitamins and minerals, which is why nuts are now considered as essential ingredient in a healthy diet. Despite their nutritional value, nuts are extremely rich in calories, and this the reason why they were treated with reluctance by consumers. Considering this, consumers has to pay attention to the amount of nuts they consume in daily basis. That’s why consumers is recommended to advice a nutritionist as the daily recommended amount differentiate per type of nuts, as well as per consumer’s needs. There is no doubt though, that nuts in the predefined quantities, plays a key role in the daily diet.
6.1.2 Characteristics of nuts industry in Greece Greece has a significant production of nuts as well as other countries in the Mediterranean due to the soft weather conditions. The dynamic of nuts market is large, not only due to the demand occurs from households and businesses, but due to nuts characteristics. Nuts are not a sensitive product, such as fruits, so they can be stored maintained and distributed throughout the year with disturbances in supply, which would may result in fluctuations in price. In our country almond trees, walnuts and pistachios are systematically cultivated in Prefectures of Thessaly (in Larisa mainly almonds and walnuts and in Magnesia mainly almonds), Central Macedonia (in Fthiotida mainly pistachios and walnuts) and Peloponnese (in Arcadia mainly walnuts). At the same time, the quality of nuts produced in our country, are considered as high standards. In particular, the pistachios of Megara and pistachios of Aegina have been registered
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in the index of Protected Designation of Origin (PDO) of the E.U. Figure 10 shows the evolution over time of the main, in terms of quantity produced, nuts trees in Greece.
Quantity Producted per Nuts Tree
250000
200000
150000
100000
50000
0 2010 2011 2012 2013 2014 2015 2016 2017 2018
Almonds, with shell Hazelnuts, with shell Pistachios Sunflower seed Walnuts, with shell
Figure 10: Quantity produced by the main nuts trees in Greece, over time.
According to Food and Agriculture Organization of the United Nations (FAO), Greece is considered as one of the top-10 countries, in terms of production quantity, on pistachios and almonds with shell. An illustration of dominant producing countries of pistachios and almonds are presented in Figure 11 and Figure 12 accordingly.
Pistachios
Tunisia 1400000
Afghanistan 1200000 Italy 1000000 Spain Greece 800000
Syrian Arab Republic 600000 China 400000 Turkey 200000 United States of America Iran 0 2010 2011 2012 2013 2014 2015 2016 2017 2018
Figure 11: Quantity of pistachios production (in tonnes) per year by dominant producing countries
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Almonds
3000000 Greece Algeria 2500000 Syrian Arab Republic Tunisia 2000000 Turkey 1500000 Italy
Morocco 1000000 Iran Spain 500000 United States of America 0 2010 2011 2012 2013 2014 2015 2016 2017 2018
Figure 12: Quantity of almonds production (in tonnes) per year by dominant producing countries
As it can be seen above Iran and United States of America are the dominant countries in the world marketplace by producing over 50% percent of the global production of almonds and pistachios. It is about a success story that our country included in such a high ranking around the globe, as is in the 6th place in pistachios production and in the 10th place in almonds production. Despite this, there are still many prospects for further development that can be achieved through the adoption of new innovative technologies and the cooperation between both individual farmers and the state.
6.2 Presentation of Petrou Nuts Company
6.2.1 Introduction Petrou Nuts S.A. is a Greek, family-based company located in the suburbs of the city of Agia, approximately 35km away from the city of Larisa. The terrain of the wider area of Agia, considering the plentiful waters of mountain Kissavos and its shores, favors the production of silk and cotton, which were the primarily contribute to the economic development of the city. Nowadays, its inhabitants are mainly engaged in the production of apples, cherries, pears and hazelnuts.
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Picture 1: Company’s plant in the city of Agia
The history of Petrou family in the sector of agriculture last almost 100 years. Since 1930 remains loyal to the family tradition, continue on cultivating up to nowadays all its lands, exclusively with hazelnut trees, paying respect to the rich land and its products. The story behind the company starts with the establishment of the partnership, among Dimitrios Siagkas and Evangelos Petrou in 1968, with activating on peeling of hazelnuts and almonds. After, 6 years of successful partnership both of them decide to extent their activities in trading nuts and other similar agricultural products. Over the years and the retirement of its initial founders, after several succession situations and legal forms, in 2016 under the ownership of brothers Ioannis and Stavros Petrou. The company took its final legal form into a Societe Anonyme, activated in the Production, Processing and Trade of Nuts under the trade name “PETROU NUTS S.A.”. Currently, Petrou Nuts S.A. is running under the presidency of the new generation member Angeliki Petrou, continuing the family tradition.
6.2.2 Company’s structure Petrou Nuts Company currently operating through two main plants: • Production and processing plant. The plant (Picture 1) is located in the city of Agia in privately owned land where the hazelnuts are also cultivating (Picture 2). In this plant the collection, processing and production of the
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final products take place. The plant is equipped with state-of-the-art equipment, including six production lines each one adjusted to the needs of different types of nuts. Indicatively the plants equipment include X-RAY detectors, roasters, caramelizing machines, storage refrigerators and packaging equipment. Additional plant is equipped with different storage refrigerators for raw materials and final processed products for storing products until they are ready for distribution the customers. At this point, we need to mention that Petrou Nuts Company’s hasn’t in its possession the necessary fleet of vehicles to distribute the final products to their customers. Distribution is assigned to external partners (3PL) who are responsible to transfer products from the main facilities in Agia to collaborating companies.
Picture 2: Privately owned cultivation of hazelnuts
• Athens Branch. In the city of Athens is located the commercial and system management department of the company. This branch can be divided in three different departments. The sales and export department as well as the marketing department is responsible to promote company’s products, managing and concluding agreements with businesses all around Greece and abroad. Additionally in Athens branch is facilitated the Research and Development laboratory of the company. This department is responsible for the development of new innovative products enhancing company’s portfolio. Each one of the most important departments of the company, as it enables company to expand its businesses, by insert into new markets where differentiated products are needed. An illustration of company’s structure is presented in
Figure 13.
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General Manager
Processing Athens Plant Branch
Safety Supplies - Accounting Purchases Marketing Quality and Technician Production Department Sales Department RnD
Human Resources
Figure 13: Company’s chart
6.2.3 Company’s characteristics The main focus of the company is the production, trade and processing of conventional and organic nuts (hazelnuts, almonds, walnuts, cashews and pistachios in shell) only for industrial and pastry use. Through the establishment of long-term cooperation with plenty of businesses all over Greece, Petrou Nuts Company is considering as a leader in its field. Except Greek companies, lastly Petrou Nuts achieved to expand its businesses, outside Greek borders. Collaboration with businesses in Europe Balkans and the United States of America have been established following the extroversion philosophy of the company. An indicative list of the most widely known companies, Petrou Nuts collaborating with is presented in Table 5.
Table 5: Indicative list of Petrou Nuts clientele Collaboration with companies Chipita Snacks Fage Dairy products Dairy, Foods & Vivartia Refreshment Tottis Bingo Snacks Kri-Kri Dairy products
Unilever Foods & Refreshment
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Mondelēz International Snacks
The vision of Petrou family is to retain the privately owned hazelnut cultivation and expand its company’s activities into organic cultivation. After all, the approach company follows indicate that vision as since 2015 Bio Hellas has certified it, for the processing of organic nuts in all existing forms respectively with the conventional ones.
6.2.4 Company’s Portfolio Company’s moto “You want, We can”, indicates the ability of the company to easily adapt their products to the needs of each individual customer. As the time pass, new types of products added in company’s portfolio, in order to satisfy market’s needs. At present, company’s portfolio includes 7 different types of products, depending the process followed to reach to the final product. It is essential also to refer that company acquires and process five types of nuts. Nuts used are either Greek or imported. More specifically pistachios and walnuts are from cultivations around Greece, while hazelnuts collected through private-owned cultivation. As for almonds, they came from form cultivations of Greece, Spain and the U.S.A., while cashews imported from India. As mentioned above by using different techniques of processing, Petrou Nuts offers seven different types of final products. An analysis of different types of final products company offers is presented as follows: • Nut pastes. Six different types of pastes are offered depending the type of the nut. Pastes is a products addressed to businesses that use it as a component to their final product. Mostly is used as a material in croissants and candies. Depending the location of businesses different type of packages offered. For businesses located in Greece used packages of 32kg while for businesses abroad packages of 60 kg used.
Picture 3: Hazelnut paste (left), pistachios paste (right)
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• Salted Caramel Nuts. Four different types of salted caramel nuts (hazelnuts, almonds, pistachios and cashews) are offered. Respectively with pastes, they addressed to businesses that use them as a topping mostly on dairy products, such as yogurts and ice- creams. They are offered in bags of 5 kg each.
Picture 4: Salted caramelized pistachios
• Coated Nuts. Four different types of nuts (hazelnuts, almonds, pistachios and cashews) coated with dark chocolate are offered for industrial and pastry use. Coated nuts are offered in vacuum bags either of 5kg or 20kg, or in cardboard boxes of 10kg and 20kg. Commonly, the business offered to, using them as topping on dairy products such as yogurts and ice creams. • Organic Nuts. Petrou Nuts is the only plant in Greece that is certified for processing organic nuts. Organic nuts refers to three types of nuts, hazelnuts, almonds and pistachios. All of them are collected from Greek cultivations and due to the limited production they are offered only to delicatessen stores in packages of 150gr. Additional, continuous assessments by BIOHELLAS certifies the quality both of the plants operation and private hazelnuts cultivation, in order to assure good practice and products’ high quality.
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Picture 5: Organic pistachios packages for retail use (left), privately-owned bio cultivation of hazelnuts (right)
• Caramelized Nuts. Four different types of roasted nuts (hazelnuts, almonds, pistachios and cashews) are offered as final products for industrial purposes. Products offered to customers in vacuum packages of 5or 20 kg. Additionally, caramelized nuts are offered in packages of 40gr and 100gr for retail purposes. In contrast to packages for industrial use, packages offered for retail use contain only nuts originated from Greek cultivations. For this specific product category, Petrou Nuts company distinguished in international level, winning the award of superior taste quality for three consecutive years.(2016, 2017 and 2018), from the International Taste and Quality Institute(iTQi).
Picture 6: Caramelized hazelnuts packages for retail use (left), international crystal taste award (right)
• Salted Nuts. Four different types of roasted nuts (hazelnuts, almonds, pistachios and cashews) are offered as final products for industrial purposes. Products offered to customers in vacuum packages of 5or 20 kg.
Picture 7: Salted nuts
• Roasted Nuts. Four different types of roasted nuts (hazelnuts, almonds, pistachios and cashews) are offered as final products for industrial purposes. The type of the nuts and
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the package size can be customized to customers’ needs. The types of roasted nuts that Petrou Company offers to their customers are presented in Table 6.
Table 6: Types of roasted nuts Petrou Nuts Company offers Nuts Type offered 1. Whole or diced 2. Blanched whole or diced Almonds 3. Blanched diced 4. Blanched almond sticks 5. Almond powder 1. Whole Hazelnuts 2. Blanched whole or diced 3. Hazelnut powder Pistachios 1. Whole or diced pistachio kernels Cashews 1. Whole or diced
Roasted nuts after being processed, examined in terms of quality both from a third party certified laboratory and the privately owned laboratory located in the plant of Agia, to reassure products excellence.
Picture 8: Blanched diced almonds (left), blanched diced hazelnuts (right)
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7 Facility Location Analysis The objective of the analysis, took place in the framework of this master thesis, is the selection of the optimal location for the establishment of a retail store selling nuts. The models and techniques chosen to be applied, aiming to capture both subjectivity, obtained by decision maker’s point of view and preferences, as well as objectivity, obtained by the use of real data from multiple sources. In the analysis following, three techniques will presented and more specifically, the analytic hierarchy process, the weighted factor rating method and the load distance technique. In this case study, the research focuses on the identification of the optimal site for the allocation of a retail store for Petrou Nuts Company in the prefecture of Attica. Petrou Nuts S.A. has already establish its presence in Greece by collect, process and distribute nuts mainly for industrial use. The area examined for the new retail store concerns the prefecture of Attica mainly because of the size of the market and the established cooperation of the main distributor, whose facilities are located in this Prefecture. After discussion with company’s representative, as potential sites for the establishment of the retail store chosen the local centers in the municipalities of Kifissia, Peristeri and Piraeus. The selection of these sites was made in order to include in the analysis areas with different socio-economic characteristics.
7.1 Analytical Hierarchy Process (AHP)
7.1.1 Introduction The first method used for the evaluation of the candidate locations is Analytical Hierarchy Process. AHP is wide-used in complex decision problems, which allow decision maker to assess the level of importance of each criterion. The expected output is the classification of the alternative decisions based on decision maker’s preferences, aiming to identify the optimal site location. It has to be mentioned that AHP has been approached under two different scopes. In the first one, the classic AHP methodology followed; by examine all the selected criteria under qualitative scope. In the second one, a hybrid method of both qualitative and quantitative criteria have been examined for the identification of the optimal solution (Yang & Lee, 1997). 7.1.2 Classic Analytical Hierarchy Process In the first step of the analysis, with the co-operation of company’s representatives, a list of the most important criteria has been defined, in order to assess the suitability of each one of the
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potential sites. Qualitative criteria assigned with a value in a rating scale from 1 to 10 according to decision maker point of view. A presentation of the list with the criteria selected follows: • Average Rent Per Square (ARPS): The rent cost is considered as significant criterion for the operation of retail store. An extremely high cost may lead to reduction of the total profit of the company, or may deprive company of the opportunity to use some of the available budget in other business activities, such as advertising. • Accessibility to Customers (ACC): The allocation of a retail store play a key role in terms of ease of access to the customers. In urban areas, local centers that there is high concentration of businesses offer higher accessibility to customers either by using public transport, walk or other means of transport, than sites outside local centers where the access isn’t as easy for everyone. • Purchasing Power of the area (PPA): The purchasing power of an area is a quite important index that is necessary to be considered as it indicates the financial strength or weakness of the consumer audience is addressed. Data used for the calculation of this index taken by Hellenic Statistical Authority. • Consumers’ Behavior (COBE): Consumers’ Behavior is an indicative index that depicts the consuming habits of population in each city. Factors such as the categorization of the area (urban, suburban, rural, etc.), the level of income may, the cultural differentiation may into different consuming habits. • Attractiveness of the city (ATTC): Each city and each local center in the city has different level of attracted flows regarding the level of attractiveness. The level of attractiveness, in the center of the city where the most of services and shopping /leisure stores are facilitated can be characterizes as a more attractive area than a suburban of the city where land use is characterized mostly by residential use. • Number of Competitors (NCOM): Competition in a fact that any business takes into consideration when decides to start its operation or expand the existing ones. The number of competitors used as an index in the process of evaluation. • Accessibility to distributor (DIST): The index regarding accessibility to supplies refers to the distance, between the facilities of the distributor where the products stored and the potential sites for the facilitation of the retail store. Is considered as an important indicator as the distance may cause increase in transportation costs and eventually losses in the total profit of the business or even corruptions in the supply chain.
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• Touristic Attraction (TOUR): This criterion used to provide a discrete separation of the cities that have significant touristic flows. Tourism tends to enhance local economies, while additional show a preference in local products and that is the reason why this indicator was included in the analysis. • Familiarity with differentiated products (FAM): The last criterion used in the analysis, has to deal with the willingness of consumer to get familiar with differentiated products. Socioeconomic differentiation such as the available disposal income explain a differential food consumption adoption (Loizou, Michailidis, & Chatzitheodoridis, 2013) . An illustration of the decision model has been developed is presented in Figure 14. The decision model has two levels of analysis to reach into final objective, which is the identification of the optimal location. In the first level of the analysis, has been chosen nine indicators, as they presented above, while in the second level of analysis there are three potential candidate locations.
Figure 14: Hierarchy of the decision model developed
After the list of criteria and the selection of the potential sites have been defined, a pairwise comparison among the criteria has been conducted, so the importance of each one to be depicted. Decision maker asked to assign by pair of criteria a numerical rating from 1 to 9 as presented in Table 2, so the relative preference of decision maker on each pair of criteria to be
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defined. Following, after the assignment of numerical rating in each pair of criteria a pairwise comparison matrix has been composed as presented in Table 7.
Table 7: Pairwise comparison matrix ARPS ACC PPA COBE ATTC NCOM DIST TOUR FAM ARPS 1 8 3 4 7 3 7 4 4 ACC 1/8 1 1/6 1/4 1/3 1/3 3 1/5 1/4 PPA 1/3 6 1 2 2 3 6 4 2 COBE 1/4 4 1/2 1 3 1/2 5 3 1/2 ATTC 1/7 3 1/2 1/3 1 1/3 4 2 1/3 NCOM 1/3 3 1/3 2 3 1 5 3 2 DIST 1/7 1/3 1/6 1/5 1/4 1/5 1 1/5 1/4 TOUR 1/4 5 1/4 1/3 1/2 1/3 5 1 1/3 FAM 1/4 4 1/2 2 3 1/2 4 3 1
Synthetization process In the next step of the analysis, took place the calculation of the priorities that each criterion has in the accomplishment of the final objective. This step of the process is known as the synthetization process. For the calculation of the priorities data from the pairwise comparison matrix used. The steps for the calculation of the priorities are the following: 1) In the first step, the sum of each column in the pairwise comparison matrix, calculated with the results depicted in Table 8.
Table 8: Sum of the columns of pairwise comparison matrix (Table 7) ARPS ACC PPA COBE ATTC NCOM DIST TOUR FAM Sum 2.8274 34.3333 6.4167 12.1167 20.0833 9.2000 40.0000 20.4000 10.6667
2) In the second step, each value of the pairwise comparison matrix divided with the sum of the corresponding column. By the end of this step, a new matrix composed, known as normalized pairwise comparison matrix (Table 9).
Table 9: Normalized pairwise comparison matrix ARPS ACC PPA COBE ATTC NCOM DIST TOUR FAM ARPS 0.3537 0.2330 0.4675 0.3301 0.3485 0.3261 0.1750 0.1961 0.3750 ACC 0.0442 0.0291 0.0260 0.0206 0.0166 0.0362 0.0750 0.0098 0.0234 PPA 0.1179 0.1748 0.1558 0.1651 0.0996 0.3261 0.1500 0.1961 0.1875 COBE 0.0884 0.1165 0.0779 0.0825 0.1494 0.0543 0.1250 0.1471 0.0469
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ATTC 0.0505 0.0874 0.0779 0.0275 0.0498 0.0362 0.1000 0.0980 0.0313 NCOM 0.1179 0.0874 0.0519 0.1651 0.1494 0.1087 0.1250 0.1471 0.1875 DIST 0.0505 0.0097 0.0260 0.0165 0.0124 0.0217 0.0250 0.0098 0.0234 TOUR 0.0884 0.1456 0.0390 0.0275 0.0249 0.0362 0.1250 0.0490 0.0313 FAM 0.0884 0.1165 0.0779 0.1651 0.1494 0.0543 0.1000 0.1471 0.0938
3) Final, in the third step, the average value of each row of the normalized pairwise comparison matrix calculated. The value of each average value corresponds to the priority under which each criterion contributes to accomplish the objective of the analysis The results regarding the priorities of each criterion are presented in Figure 15.
PRIORITIES
FAM
TOD
DIST
NCOM
ATTC
COBE
PPA
ACC
ARPS
0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0%
ARPS ACC PPA COBE ATTC NCOM DIST TOD FAM Series1 31.2% 3.1% 17.5% 9.9% 6.2% 12.7% 2.2% 6.3% 11.0%
Figure 15: Priorities of selected criteria
As can be seen criterion ARPS seems to have the highest priority in the accomplishment of the final objective according the point of view of company’s representative, while the distance from the distributor (distributor), seems to has the lowest priority comparing to others.
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Consistency The next step of the analysis, includes the evaluation of the comparison made between criteria need to be done to check their consistency. The computation of the consistency ratio has been done as follows: 1) First, a consistency matrix composed. For the computation of the values of matrix, the values of the each column in the pairwise comparison matrix multiplied with the priority of the corresponding criterion. After the consistency matrix composed the weighted sum of each row is been calculated. Following, the weighted sum values divided with the corresponding priority, to synthesize the division values. Finally, the
average value (휆푚푎푥) of the weighted sum values calculated. The matrix finally composed under this step is presented in Table 10.
Table 10: Consistency matrix ARPS ACC PPA COBE ATTC NCOM DIST TOUR FAM Sum Division ARPS 0.3117 0.2498 0.5243 0.3947 0.4345 0.3800 0.1518 0.2520 0.4411 3.1397 10.0738 ACC 0.0390 0.0312 0.0291 0.0247 0.0207 0.0422 0.0650 0.0126 0.0276 0.2921 9.3551 PPA 0.1039 0.1873 0.1748 0.1973 0.1241 0.3800 0.1301 0.2520 0.2205 1.7701 10.1287 COBE 0.0779 0.1249 0.0874 0.0987 0.1862 0.0633 0.1084 0.1890 0.0551 0.9909 10.0428 ATTC 0.0445 0.0937 0.0874 0.0329 0.0621 0.0422 0.0867 0.1260 0.0368 0.6122 9.8631 NCOM 0.1039 0.0937 0.0583 0.1973 0.1862 0.1267 0.1084 0.1890 0.2205 1.2840 10.1373 DIST 0.0445 0.0104 0.0291 0.0197 0.0155 0.0253 0.0217 0.0126 0.0276 0.2065 9.5233 TOUR 0.0779 0.1561 0.0437 0.0329 0.0310 0.0422 0.1084 0.0630 0.0368 0.5920 9.3987 FAM 0.0779 0.1249 0.0874 0.1973 0.1862 0.0633 0.0867 0.1890 0.1103 1.1231 10.1845 흀풎풂풙 9.8564
2) In the next step, took place the calculation of the consistency Index (CI), as follows: (휆 ∗ 푁) 퐶푖 = 푚푎푥 (7.1) (푁 − 1) where,
휆푚푎푥: the average value calculated in the step 1, 푁: the number of indicators taking into consideration in the analysis. 3) Finally, the Consistency Ratio (CR) calculated as follows: 퐶푖 퐶푅 = ⁄푅푖 (7.2)
where,
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푅푖: is a known value. In the decision model developed in the framework of this master thesis, because the criteria examined is N=9, the value of the 푅푖 that corresponds to N indicators is equal to 1, 45. The results from the calculation of the consistency ratio presented in Table 11
Table 11: Consistency Ratio (CR) of the pairwise comparison between selected criteria Numerical Value Level of Acceptance CR 0,07382336 <0,10
Pairwise comparison of each criterion on candidate locations After the examination of the consistency of pairwise comparison between selected criteria, and considering that its value is acceptable (CR = 0, 07382336 < 0, 10), the analysis continued in the next step by comparing the potential sites prioritization regarding each criterion. In the comparison took place each candidate location has been compared each other regarding each one of nine selected criteria. For each one of the criteria a numerical rating from 1 to 9 (see Table 2) regarding each location, indicating the dominance of one candidate location over another. The numerical rating assigned to each one of them, based on the personal experience of the decision maker. The pairwise comparison matrices regarding to the candidate locations presented in the following tables.
Table 12: Location pairwise comparison regarding accessibility to consumers ACC Kifissia Peristeri Piraeus Kifissia 1.00 0.14 0.20 Peristeri 7.00 1.00 3.00 Piraeus 5.00 0.33 1.00 SUM 13.00 1.48 4.20
Table 13: Location pairwise comparison regarding consumers’ behavior COBE Kifissia Peristeri Piraeus Kifissia 1.00 5.00 4.00 Peristeri 0.20 1.00 0.33 Piraeus 0.25 3.00 1.00 SUM 1.45 9.00 5.33
Table 14: Location pairwise comparison regarding attractiveness of the city ATTC Kifissia Peristeri Piraeus
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Kifissia 1.00 7.00 3.00 Peristeri 0.13 1.00 0.20 Piraeus 0.33 5.00 1.00 SUM 1.46 13.00 4.20
Table 15: Location pairwise comparison regarding the touristic character of the city TOUR Kifissia Peristeri Piraeus Kifissia 1.00 7.00 0.14 Peristeri 0.14 1.00 0.11 Piraeus 4.00 8.00 1.00 SUM 5.14 16.00 1.25
Table 16: Location pairwise comparison regarding familiarity with differentiated products FAM Kifissia Peristeri Piraeus Kifissia 1.00 8.00 4.00 Peristeri 0.13 1.00 0.25 Piraeus 0.25 4.00 1.00 SUM 1.38 13.00 5.25
Table 17: Location pairwise comparison regarding average rent per square ARPS Kifissia Peristeri Piraeus Kifissia 1.00 0.13 0.14 Peristeri 8.00 1.00 2.00 Piraeus 7.00 0.50 1.00 SUM 16.00 1.63 3.14
Table 18: Location pairwise comparison regarding purchasing power of the area PPA Kifissia Peristeri Piraeus Kifissia 1.00 4.00 3.00 Peristeri 0.25 1.00 0.33 Piraeus 0.33 3.00 1.00 SUM 1.58 8.00 4.33
Table 19: Location pairwise comparison regarding number of competitors NCOM Kifissia Peristeri Piraeus Kifissia 1.00 2.00 3.00 Peristeri 0.50 1.00 2.00 Piraeus 0.33 0.50 1.00 SUM 1.83 3.50 6.00
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Table 20: Location pairwise comparison regarding the accessibility to the distributor DIST Kifissia Peristeri Piraeus Kifissia 1.00 0.20 0.33 Peristeri 5.00 1.00 2.00 Piraeus 3.00 0.50 1.00 SUM 9.00 1.70 3.33
After the definition of the location pairwise comparison regarding each criterion the calculation of the priorities that each criterion has in each candidate location, took place. The methodology used for the definition of the priorities was the same three-step procedure presented previously for the prioritization of the criteria in the pairwise comparison matrix. The results regarding qualitative prioritization of each potential site is presented Figure 16.
Priorities per candidate location
DIST
NCOM
PPA
ARPS
FAM
TOUR
ATTC
COBE
ACC
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Kifissia Peristeri Piraeus
Figure 16: Priorities of each potential site regarding each criterion
As Figure 16 indicates, there is no absolute dominance of one candidate location over another. However, Kifissia seems to be more preferable candidate location regarding five out of nine criteria. As it can be seen Kifissia seems as more preferable candidate based on NCOM, PPA, FAM, ATTC and COBE. Peristeri seems to be more preferable as location regarding ACC, DIST and ARPS, while Piraeus seems to dominate over others only regarding criterion TOUR.
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Following, the consistency of the pairwise comparison need to be examined. The methodology used for the calculation of the consistency ratio, is the same as described previously in the analysis. Totally nine consistency matrices has been composed, one for each criterion, the average value (휆푚푎푥) of the weighted sum values calculated. The matrices composed for the consistency process are presented as follows.
Table 21: Consistency matrix regarding accessibility to customers’ criterion ACC Kifissia Peristeri Piraeus Sum Division Kifissia 0.0738 0.0919 0.0566 0.2223 3.0127 Peristeri 0.5164 0.6434 0.8485 2.0083 3.1215 Piraeus 0.3689 0.2145 0.2828 0.8662 3.0624
흀풎풂풙 3.0655
Table 22: Consistency matrix regarding consumers’ behavior criterion COBE Kifissia Peristeri Piraeus Sum Division Kifissia 0.6651 0.5192 0.9243 2.1086 3.1705 Peristeri 0.1330 0.1038 0.0770 0.3139 3.0226 0.1663 0.3115 0.2311 0.7089 3.0677 Piraeus
흀풎풂풙 3.0869
Table 23: Consistency matrix regarding attractiveness of the city criterion ATTC Kifissia Peristeri Piraeus Sum Division Kifissia 0.6893 0.5355 0.9750 2.1998 3.1913 Peristeri 0.0862 0.0669 0.0488 0.2018 3.0157 0.1723 0.3347 0.2438 0.7507 3.0799 Piraeus
흀풎풂풙 3.0956
Table 24: Consistency matrix regarding touristic destination criterion TOUR Kifissia Peristeri Piraeus Sum Division Kifissia 0.2486 0.4174 0.0988 0.7648 3.0763 Peristeri 0.0355 0.0596 0.0769 0.1720 2.8846 0.9945 0.4770 0.6917 2.1633 3.1272 Piraeus 흀풎풂풙 3.0294
Table 25: Consistency matrix regarding familiarity with differentiated products criterion FAM Kifissia Peristeri Piraeus Sum Division Kifissia 0.7015 0.5745 0.9066 2.1827 3.1114 Peristeri 0.0877 0.0718 0.0567 0.2162 3.0100 0.1754 0.2873 0.2267 0.6893 3.0411 Piraeus 흀풎풂풙 3.0542
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Table 26: Consistency matrix regarding average rent per square criterion ARPS Kifissia Peristeri Piraeus Sum Division Kifissia 0.0616 0.0730 0.0506 0.1853 3.0061 Peristeri 0.4930 0.5839 0.7089 1.7858 3.0584 0.4314 0.2920 0.3545 1.0778 3.0407 Piraeus 흀풎풂풙 3.0351
Table 27: Consistency matrix regarding purchasing power of the area criterion PPA Kifissia Peristeri Piraeus Sum Division Kifissia 0.6080 0.4798 0.8163 1.9040 3.1318 Peristeri 0.1520 0.1199 0.0907 0.3626 3.0234 0.2027 0.3598 0.2721 0.8346 3.0672 Piraeus 흀풎풂풙 3.0741
Table 28: Consistency matrix regarding number of customers’ criterion NCOM Kifissia Peristeri Piraeus Sum Division Kifissia 0.5390 0.5945 0.4913 1.6248 3.0147 Peristeri 0.2695 0.2973 0.3276 0.8943 3.0085 0.1797 0.1486 0.1638 0.4921 3.0044 Piraeus 흀풎풂풙 3.0092
Table 29: Consistency matrix regarding accessibility to distributor criterion DIST Kifissia Peristeri Piraeus Sum Division Kifissia 0.1096 0.1163 0.1031 0.3289 3.0012 Peristeri 0.5479 0.5813 0.6183 1.7475 3.0064 0.3288 0.2906 0.3092 0.9285 3.0035 Piraeus 흀풎풂풙 3.0037
Following, and taking into consideration that the value of N has modified as in this occasion represents the number of the candidate locations (N = 3) the consistency index calculated for
each criterion. The consistency Index calculated by divided the average value (휆푚푎푥) of the weighted sum values of each criterion with the number of the candidate locations (N) The consistency index as calculated for each one of the consistency matrices is presented in Table 30.
Table 30: Consistency Index per criterion Consistency Index ACC COBE ATTC TOUR FAM ARPS PPA NCOM DIST per criterion CI 0.0328 0.0435 0.0478 0.0147 0.0271 0.0175 0.0371 0.0046 0.0018
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After the calculation of the consistency index for each criterion, the calculation of the consistency ratio for each one calculated too. The consistency ratio for each criterion calculated by dividing the value of the consistency Index of each criterion with a fixed value, which is
defined by the number of N value. The fixed value (푅푖) that corresponds to N = 3 is equal to 0.58. The results of the regarding the consistency ratio calculated for each criterion is presented in Table 31
Table 31: Consistency ratio per criterion Consistency Ratio ACC COBE ATTC TOUR FAM ARPS PPA NCOM DIST per criterion CR 0.0565 0.0750 0.0824 0.0253 0.0467 0.0302 0.0639 0.0079 0.0032
As it can be seen the consistency ration for each criterion can be considered as acceptable as it under the maximum value (<0,10). The last step of the process refers to the final composition of the priorities managed to reach to the final objective, which is the selection of the optimal site for the establishment of the retail store. To achieve an overall prioritization ranking between potential sites calculated. The calculation of the overall priority for each location, made by multiply the general priority of each criterion by the corresponding criterion’s priority on each location. The final overall ranking matrix presented in Table 32.
Table 32: Overall priority ranking per candidate location Criterion (j) Priority (Wj) Kifissia (ri,1) Peristeri (ri,2) Piraeus (ri,3)
ACC 0.031224 0.073772 0.643389 0.282839
COBE 0.098671 0.665070 0.103847 0.231082
ATTC 0.062072 0.689311 0.066933 0.243756
TOUR 0.062991 0.248623 0.059628 0.691749
FAM 0.110272 0.701521 0.071817 0.226662
ARPS 0.311674 0.061626 0.583916 0.354458
PPA 0.174757 0.607962 0.119939 0.272099
NCOM 0.126657 0.538961 0.297258 0.163781
DIST 0.021683 0.109586 0.581264 0.309150
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Overall Rating 0.399824 0.299371 0.300805 (풘풋 ∗ 풓풊풋) =
As indicating the results presented in Table 32, Kifissia is the optimal location for the establishment of the retail store, when compared to the other locations. Piraeus seems to be the second most preferable location, having though a small difference from the third candidate location.
7.1.3 Hybrid Analytical Hierarchy Process Additionally to the classical approach of the analytical hierarchy process where the criteria are managed under a qualitative approach, an alternative method applied. In this decision model the criteria chosen to be examined under a mixed qualitative-quantitative approach. It has to be mentioned that the nine criteria remain the same as in the classic analytical hierarchy process examined previously. The first part of the process where the composition of the pairwise comparison matrix of the criteria based on decision maker’s preferences remains the same as used previously. As modifications in the pairwise comparison of the selected criteria did not occurred, the priority of each criterion remains the same. Finally, as nothing changed in the first part of the analysis the consistency of the pairwise comparison is solid as described previously. The difference of this approach refers to the second phase of the analysis where the priorities of each candidate location regarding each criterion defined. Finally, it is essential to mention that the candidate locations remains the same as in the classic hierarchy process (Kifissia, Peristeri, and Piraeus). The difference with classic approach is that four out of nine criteria examined as quantitative criteria, while the remaining five still examined as qualitative criteria. In Table 33 there is a brief presentation of the criteria used in the analysis and the way they approached (qualitative- quantitative).
Table 33:Location criteria Criterion Quantifiable Data provided Average rent per Yes Real estate agent square Accessibility to Estimation of the decision No consumers maker
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Purchasing power of Yes Hellenic Statistical Authority the area Estimation of the decision Consumers' behavior No maker Attractiveness of the Estimation of the decision No city maker Number of competitors Yes Greek yellow pages Accessibility to Distance in km, obtained by Yes distributor google maps Estimation of the decision Touristic attraction No maker Familiarity with Estimation of the decision No differentiated products maker In the first occasion, quantitative criteria assigned with their corresponding values (i.e. average rent per square), while qualitative criteria retain their values assigned in the previous analysis. In the second category, comparison has been made concerning quantitative criteria, where actual values assigned to each location (i.e. distance in kilometers), regarding each criterion (i.e. distributor’s accessibility). The matrix composed regarding quantitative criteria, is presented in Table 34.
Table 34: Location comparison regarding quantitative criteria Potential Sites Real Data Kifissia Peristeri Piraeus 30 9 10,5 ARPS (€/풎ퟐ) PPA (€) 15.036 5.580 9.706 NCOM (number) 6 13 15 DIST (km) 20,0 4,2 9,2
Priorities of each location regarding each criterion The priorities of the qualitative criteria (ACC, COBE, ATTC, TOUR, and FAM) for each candidate location remains the same as in the classic analytical hierarchy process presented in the previous section. The priorities of the qualitative criteria used in the analysis are presented in Table 35.
Table 35: Priorities of each potential site regarding qualitative criteria Kifissia Peristeri Piraeus ACC 0.073772 0.643389 0.282839 COBE 0.665070 0.103847 0.231082 ATTC 0.689311 0.066933 0.243756 TOUR 0.248623 0.059628 0.691749 FAM 0.701521 0.071817 0.226662
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|For the calculation of the priorities for each location regarding quantitative criteria, different approach than the classic one has been followed. More specifically, the methodology used is the following (Yang & Lee, 1997): 1. First of all the weights of the value assigned to each potential site per criterion, in order
to normalize 푇푖푗 values (see Table 34), calculated as follows: 100 (7.3) 푊 = 푖푗 푇푖푗 where,
• 푊푖푗: the weighted value for criterion i and potential site i
• 푇푖: the actual data assigned for criterion i to potential site j
After that, the sum of 푊푖푗 values calculated for each criterion and candidate location, with the results been presented in Table 36.
Table 36: Weighted values for each criterion and candidate location Wi=(100/Ti) Kifissia Peristeri Piraeus Sum ARPS 3.333333 11.111111 9.523810 23.968254 PPA 0.006651 0.017924 0.010303 0.034878 NCOM 16.666667 7.692308 6.666667 31.025641 DIST 5 23.809524 10.869570 39.679089
2. Final the priorities for each potential site per criterion calculated by dividing each 푊푖푗 value by each corresponding sum. The results regarding quantitative prioritization of each potential site is presented in Table 37.
Table 37 Priorities of each candidate location regarding quantitative criteria Priorities per Kifissia Peristeri Piraeus criterion ARPS 0.139073 0.463576 0.397351 PPA 0.190685 0.513916 0.295399 NCOM 0.537190 0.247934 0.214876 DIST 0.126011 0.600052 0.273937
Final, the last step, the final composition of the priorities managed to reach to the final objective, which is the selection of the optimal site for the establishment of the retail store. To achieve an overall prioritization ranking between potential sites calculated. The calculation of
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the overall priority for each location, made by multiply the general priority of each criterion by the corresponding criterion’s priority on each location. The final overall ranking matrix presented in Table 38.
Table 38: Overall rating of candidate locations Peristeri Piraeus Criterion (j) Priority (Wj) Kifissia (ri,1) (ri,2) (ri,3) ARPS 0.311674 0.139073 0.463576 0.397351 ACC 0.031224 0.073772 0.643389 0.282839 PPA 0.174757 0.190685 0.513916 0.295399 COBE 0.098671 0.665070 0.103847 0.231082 ATTC 0.062072 0.689311 0.066933 0.243756 NCOM 0.126657 0.537190 0.247934 0.214876 DIST 0.021683 0.126011 0.600052 0.273937 TOUR 0.062991 0.248623 0.059628 0.691749 FAM 0.110272 0.701521 0.071817 0.226662 Overall Rating 0.351173 0.324874 0.323953 (풘풋 ∗ 풓풊풋)
As the results indicate, Kifissia is the optimal location for the establishment of the retail store. The results obtained by the application of this mixed quantitative-qualitative AHP provides the same result as the classic analytical hierarchy process. It has to be mentioned though, that there is a convergence of the final score between candidate locations in comparison with the previous method.
7.1.4 Sensitivity Analysis In order to check the solidness of the results obtained from the analysis, a sensitivity analysis of the AHP was performed. Because analytic hierarchy encompass subjectivity in the process is crucial to observe how the results will differentiate if the values of the criteria variate. The sensitivity analysis include both the classic and the alternative approach of the analytical hierarchy process methods, examined previously.
7.1.4.1 Sensitivity analysis in classic Analytical Hierarchy Process In order to identify the solidness of the result occurred by the application of the classic Analytical Hierarchy, two scenarios has been selected. An analysis of the methodology used, the kind of factors modifies as well as the results occurred in each scenario is presented as follows.
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Scenario 1 In the analysis already made, the criterion of average rent per square identified as the highest priority according decision’s maker point of view. The first scenario decided to examine what would happened in the occasion where all of the criteria having the same level of priority. The new priorities of the indicators presented in Table 39
Table 39: Priorities of criteria in the initial analysis for scenario 1. Criteria Initial Priorities Scenario 1 ARPS 0,3117 0,1111 ACC 0,0312 0,1111 PPA 0,1748 0,1111 COBE 0,0987 0,1111 ATTC 0,0621 0,1111 NCOM 0,1267 0,1111 DIST 0,0217 0,1111 TOUR 0,0630 0,1111 FAM 0,1103 0,1111
By applying the new priorities of the criteria in the analysis, the result does not seem to variate. In contrast, the location of Kifissia seems to strengthen its candidacy as the optimal site. The results, related to the overall ranking over the analysis made in scenario 1 is presented in Table 40.
Table 40: Overall ratings for scenario 1 Kifissia Peristeri Piraeus Criterion (j) Priority (Wj) (ri,1) (ri,2) (ri,3) ACC 0.1111 0.073772 0.643389 0.282839 COBE 0.1111 0.665070 0.103847 0.231082 ATTC 0.1111 0.689311 0.066933 0.243756 TOUR 0.1111 0.248623 0.059628 0.691749 FAM 0.1111 0.701521 0.071817 0.226662 ARPS 0.1111 0.061626 0.583916 0.354458 PPA 0.1111 0.607962 0.119939 0.272099 NCOM 0.1111 0.538961 0.297258 0.163781 DIST 0.1111 0.109586 0.581264 0.309150 Overall Ratings 0.410715 0.280888 0.308397 (풘풋 ∗ 풓풊풋)=
As it can be clearly seen, Kifissia not only remains the optimal location for the establishment of the new retail store, but also improves its rating. Piraeus remains as the second in the
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hierarchy place by retaining its priority in the same level as in the initial analysis, while Peristeri is in the third place with decreased overall rating compared to the initial analysis.
Scenario 2 In the second scenario, a different approach used in order to evaluate the solidness of the results by the initial analysis. Three specific criteria has been chosen for modifications regarding the values assigned in the pairwise comparison, in order to identify whom the final decision will differentiate. More specifically, the first criterion chosen refers to the accessibility to distributor (DIST), which ranked with the lowest priority compared with the others criteria. Additionally, the criterion regarding the purchasing power of the area (PPA) modified. Finally, the criterion regarding the consumers’ behavior (COBE), which has a middle-ranked priority modified too. The selection of the criteria made in such a way so criteria of high, medium and low ranking priority included. The modification of those criteria occurred in the pairwise comparison matrix. More specifically the values regarding the criterion of accessibility to distributor has been increased by 2 (scenario 2a), while the values regarding the purchasing power of the area have been decreased by 1(scenario 2b). Finally the values of the criterion referring to the consumers’ behavior have been decreased by 1 (Scenario 2c) and increased by 1 (Scenario 2d). By applying the modifications in each scenario, a new pairwise comparison matrix obtained. Following the synthetization process, as is presented in previous section new priorities assigned to each criterion for all 4 scenarios. The new priorities of the criteria in each scenario are presented in Table 41.
Table 41: New priorities obtained by the modifications in scenario 2 Priorities per scenario Scenario 2a Scenario 2b Scenario 2c Scenario 2d ARPS 31.0% 32.4% 31.6% 30.5% ACC 2.7% 3.1% 3.2% 3.1% PPA 17.3% 13.0% 18.1% 16.4% COBE 9.7% 10.6% 7.3% 13.8% ATTC 5.9% 6.8% 6.4% 6.0% NCOM 12.4% 13.4% 13.2% 11.8% DIST 3.4% 2.2% 2.2% 2.1% TOUR 6.1% 6.4% 6.5% 6.1% FAM 11.5% 11.9% 11.5% 10.2%
After the synthetization process the consistency of the model in each sub-scenario examined. In all four sub-scenarios the consistency ratio was under the appropriate threshold (CR<0.10).
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The results regarding the consistency ratios occurred by the corresponding modifications in the criteria are presented in Table 42.
Table 42: Consistency Ratio (CR) for examined scenarios Scenario 2a Scenario 2b Scenario 2c Scenario 2d CR 0.062145 0.076783 0.073744 0.068319
The next step of the process refers the pairwise comparison of each criterion between the candidate locations. As no modifications occurred in the values of the pairwise comparison matrices the priorities of the each criterion as well as the consistency check of them is taken as granted from the initial analysis. The overall ranking of the candidate locations obtained by the modifications has been made in each sub-scenario are presented in Table 43.
Table 43: Overall ranking of the candidate locations for scenario 2 Kifissia Peristeri Piraeus Scenario 2a 0.397956 0.301520 0.300524 Scenario 2b 0.393157 0.306073 0.300770 Scenario 2c 0.394826 0.302899 0.302275 Scenario 2d 0.406635 0.294102 0.299264
As the results indicate, the modifications in the selected criteria do not affect the selection of Kifissia as the optimal location for the establishment of the retail store. The fact that the location remains the same in all of the scenarios indicates that the solution obtained by the initial model is consistent and reliable, as large and unjustified modifications should be occurred to change the result.
7.1.4.2 Sensitivity analysis in hybrid Analytical Hierarchy Process Following the same methodology applied previously a sensitivity analysis occurred in the alternative analytical hierarchy process to identify if the level of sensitivity variates from the classic process. Scenario 3 As in the classic process, in the scenario 1 examines the effect that the priorities of the criteria have in the final outcome. So an equal value assigned to the selected criteria as presented in
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Table 39. By applying, the new priorities in the analysis process the following overall ranking per candidate location obtained as presented in Table 44.
Table 44: Overall ratings per candidate location for scenario 3 Criterion (j) Priority (Wj) Kifissia (ri,1) Peristeri (ri,2) Piraeus (ri,3) ARPS 0.111111 0.139073 0.463576 0.397351 ACC 0.111111 0.073772 0.643389 0.282839 PPA 0.111111 0.190685 0.513916 0.295399 COBE 0.111111 0.665070 0.103847 0.231082 ATTC 0.111111 0.689311 0.066933 0.243756 NCOM 0.111111 0.537190 0.247934 0.214876 DIST 0.111111 0.126011 0.600052 0.273937 TOUR 0.111111 0.248623 0.059628 0.691749 FAM 0.111111 0.701521 0.071817 0.226662 Overall Ratings 0.374584 0.307899 0.317517 (풘풋 ∗ 풓풊풋)=
As it can be clearly seen Kifissia remains the optimal location for the establishment of the new retail store, will additionally improves its rating. Furthermore small variation obtained in the overall rating for the location of Piraeus and Peristeri. After the examination of the results of scenario 1, a similar behavior with the classic analytical hierarchy process observed.
Scenario 4 As in scenario 2 examined previously, in this scenario, three criteria selected, with high, medium and low priority ranking, so modifications to their values in the pairwise comparison matrix to be done. As the priority ranking of the criteria is the same in both classic and alternative analytical hierarchy process, the same three criteria selected (PPA, COBE and DIST). Additionally the modifications in their values in the pairwise comparison matrix was the same as in the scenario 2 of the classic analytic hierarchy process. More specifically, values of DIST increased by one (scenario 4a), values of criterion PPA decreased by two (scenario 4b), while values of the criterion COBE decreased by one (scenario 4c) and increased by one (scenario 4d). By applying the modifications in each scenario, a new pairwise comparison matrix obtained. Following the synthetization process, as is presented in previous section new priorities assigned to each criterion for all four scenarios. The new priorities of the criteria in each scenario are the same as they presented in Table 41
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Following the consistency of the model examined regarding each sub-scenario. In all four sub- scenarios the consistency ratio was under the appropriate threshold (CR<0.10). The results regarding the consistency ratios occurred by the corresponding modifications in the criteria are presented in Table 45.
Table 45: Consistency Ratio (CR) for scenario 4 Scenario 4a Scenario 4b Scenario 4c Scenario 4d CR 0.062145 0.076783 0.073744 0.068319
The next step of the process refers the pairwise comparison of each criterion between the candidate locations. As no modifications occurred in the values of the pairwise comparison matrices the priorities of the each criterion as well as the consistency check of them is taken as granted from the initial analysis of the hybrid method. The overall ranking of the candidate locations obtained by the modifications in each sub- scenario are presented in Table 46.
Table 46: Overall rating per candidate location for scenario 4 Overall Kifissia Peristeri Piraeus ratings Initial score 0.351173 0.324874 0.323953 Scenario 4a 0.349975 0.326986 0.323039 Scenario 4b 0.364120 0.312086 0.323794 Scenario 4c 0.343958 0.330028 0.326014 Scenario 4d 0.362102 0.316480 0.321418
As the results indicate, the modifications in the selected criteria do not affect the selection of Kifissia as the optimal location for the establishment of the retail store. The fact that the location remains the same in all of the sub-scenarios indicates that the solution obtained by the initial model is consistent and reliable.
7.2 Weighted Factor Rating Method The next method used for the assessment of the optimal location of the retail stores refers to the weighted factor rating method. For the assessment of the optimal location five criteria has been selected. The priority of each criterion is presented as weighs in order to depict company’s representative preferences. It has to mention that the sum of the weights assigned to each
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criterion has to be equal to 100. The criteria used for the needs of the analysis under its weighted factor is presented in Table 47.
Table 47: Indicators and their corresponding weighted factor Criteria Weighted factor (%) Rent Cost 35% Position 25% Income per capita 12%
Willingness to try differentiated products 20% Competition 8% SUM 100%
Following in the analysis an evaluation of each candidate location based the selected criteria, occurred. The ratings assigned to each one has to be in a scale of 1 to 100. The ratings assigned in each location reflect company’s representative point of view and is presented in Table 48.
Table 48: Location comparison based on each criterion Criteria Kifissia Peristeri Piraeus Rent Cost 55 20 30 Position 30 70 50 Income per capita 70 30 45 Competition 30 70 80 Willingness in try differentiated 60 40 45 products
After the weighted factors of each criterion as well as the rating of each candidate location per criterion completed, the final rate for each location calculated. More specifically, each weighted factor multiplied with the corresponding rating on each location. Following this procedure for every criterion and candidate location Table 49 results. As results indicated Kifissia is considering as the optimal location for the establishment of Petrou Nuts retail store.
Table 49: Weighted Factor Rating Method results Willingness in Final Income per try Rent Cost Position Competition weighted capita differentiated score products Kifissia 19,25 7,5 8,4 2,4 12 49,55 Peristeri 5 17,5 3,6 5,6 8 39,7 Piraeus 3,6 12,5 5,4 6,4 9 36,9
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7.3 Load Distance Technique As already mentioned in previous chapter, the objective of load distance technique is the minimization of the total transport cost. The analysis took place refers to the same three candidate locations examined as previous. After discussion, with company’s representative, decided the location of the retail store to be in the center of each one of the candidate locations. Additionally, it was selected the retail store to facilitate in pedestrian area, where multiple business activities are deployed, while ease of customers accessibility achieved. More specifically certain pedestrian areas selected in each candidate location· in Kifissia the street of Georgiou Drosini, in Peristeri the street of Ethnikis Amynis and in Piraeus the street of Sotiros Dios are selected as the candidate locations. For computation reasons, the exact coordinates it was necessary to be defined. The coordinates of the selected candidate locations as well as the coordinates of distributor’s facility are presented in Table 50
Table 50: Coordinates of both candidate locations and distributor’s facility Candidate locations X Y Kifissia 483370,140 4213626,408 Peristeri 472863,500 4206970,226 Piraeus 468793,127 4199133,749 Distributor's Facilities 472207,170 4203872,823
In the analysis, a very important factor is the calculation of the distance between distributor’s facility and candidate locations. In the framework of this master thesis, four different types of distance measurement chose to apply. More specifically, used Euclidean distance, Rectilinear or Manhattan distance, highway distance and driving time. As distance unit used for the first three distance metrics, used kilometers, while driving time is calculated in minutes. The distance calculated among each candidate location and the distributor is presented in Table 51.
Table 51: Different types of distance measures used in the analysis Distance from Euclidean (km) Highway (km) Rectilinear (km) Driving time (min) distributor Kifissia 14,82 20 20,92 26 Peristeri 3,17 4,20 3,75 12 Piraeus 5,84 9,20 8,15 14
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After the calculation of the distance, the calculation of the load value followed. For the calculation of the load value used the transport cost per unit of product, as well as an estimation of the annual demand that each store will need. For both of them, data provided by company’s representative. The value of the transport cost per unit do not have significant fluctuations, as there is no significance difference between the candidate locations. Concerning the annual demand a moderate approach followed, based company’s representative experience. An annual demand of 300 packages per nut type (5 types of nuts) has been indicated, regardless the location of the store. Therefore, annual demand excluded from the calculation.
Table 52: Transportation cost per unit of product Transport cost per unit (€) Kifissia 2,5 Peristeri 2 Piraeus 2
After implementing the formula (5.3) presented in previous chapter, the final load-distance values has been calculated for each candidate location and distance measure type. The results presented in Table 53, and is clearly, that in all cases Peristeri is the optimal location for the establishment of the new retail store, as the transportation costs are the minimum, comparing to other candidate locations.
Table 53: Load – Distance technique values per distance type Load - Distance Euclidean (km) Highway(km) Rectilinear(km) Driving time(min) Kifissia 55589,16 75000,00 78437,08 97500,00 Peristeri 8865,29 11760,00 10510,45 33600,00 Piraeus 16354,14 25760,00 22828,73 39200,00
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8 Conclusions In the framework of this master thesis, a wide variety of facility location models has been presented, based on the international literature. Despite the fact the identification of the optimal facility location is a problem concerns humans from the ancient years, only the last decades has been approached with a consistent systematically. By the examination of the international literature has been concluded that the decision for the relocation or the establishment of a new facility is crucial for a business due to the high costs occurred by this decision, as well as to the long-term commitment. For this reason, this decision needs to be approached under a methodological framework, with meticulousness, in order to take into consideration all the possible opportunities and threats that may occur in the future. The aim of this master thesis was to explore techniques and methods used to support a facility location decision. The case study refers to the identification of the optimal location for the establishment of retail store. The company for whom the analysis occurred is a traditional Greek company focused in the production, trade and processing of conventional and organic nuts. Until now the operations of the company’s products referring mostly to industries. In the framework of this master thesis, and considering that the company is interested on expanding into the retail market, the identification of the optimal location is examined. Three different approaches followed to accomplish this objective AHP, Weighted factor rating method and Load distance technique. Additionally AHP examined under two approaches, the first refers to the classic analytical hierarchy process where the criteria examined under the subjective point of view of the decision maker and a second hybrid where encompasses objectivity in the process using actual data. Different results obtained regarding each approach.
The application of AHP indicates Kifissia as the optimal location for the establishment of the retail store in both approaches. In the classic approach though observed that the selection of Kifissia as the optimal location is clearer choice, as there is greater deviation of the values, compared to the mixed quantitative-qualitative approach of the AHP. This is probably due to the subjectivity that contained in the classic AHP, as a decision maker is not possible to fully attribute the gravity of the criteria to their true dimension. Final the sensitivity analysis conducted for both of the approaches indicate that there is solidness on the outcomes, as well as that both of the approaches shows the same behavior in the modifications occurred. Weighted factor rating method just as AHP is a subjective method, whom results depend primary to the preferences and the of the decision maker. Respectively to AHP, the weighted
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factor rating method indicates Kifissia as the optimal location for the establishment of the retail store. Last, the Load distance technique applied mainly because of its simplicity, as well as, because of the level of the objectivity that encompass in its process. This was the only one that indicates the city of Peristeri as the optimal location. However, the result is direct affected by the factor of distance, as the transportation cost per unit presents small variations per candidate location. Each method takes into consideration different criteria and examine the facility location problem under different scope. At the end, the decision maker is the responsible to choose the appropriate one, which will lead him to the optimal solution based to its needs.
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