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This book presents an up-to-date review of modeling and optimization approaches for location problems along with a new bi-level programming methodology which captures the effect of competition of both producers and customers on facility location decisions. While many optimization approaches simplify location problems by assuming decision making in isolation, this monograph focuses on models which take into account the competitive environment in which such decisions are made. New insights in modeling, algorithmic and theoretical possibilities are opened by this approach and new applications are possible. Competition on equal term plus competition between market leader and followers are considered in this study, consequently bi-level optimization methodology is emphasized and further developed. This book provides insights regarding modeling complexity and algorithmic approaches to discrete competitive location problems. In traditional location modeling, assignment of customer demands to supply sources are made for which the associated costs target the firm and not the customers, though in many real world situations the cost is incurred by the customers. Moreover, there may be customer competition for the provided services. Thus, a new methodological framework is needed in order to encompass such considerations into the modeling and solution process. This book offers initial directions for further research and development along these lines. Aimed toward graduate students and researchers in the field of mathematics, computer science, operational research and game theory, this title provides necessary information on which further research contributions can be based.



Chapter 1. Introduction

Facility location analysis is one of the most well-studied areas of the operations research [19, 36, 37, 77]. In the basic model, there is a predefined cost for opening a facility and also connecting a customer to a facility, the goal is to minimize the total cost. The typical facility location problem assumes that the locating facility is either a price taker or a monopolist, so that the market competition is neglected among the companies. However this simplified assumption does not fit in most real-life situation and the need arises to incorporate competition among the decision-makers. Indeed, competitive location models additionally incorporate the fact that location decisions have been or will be made by independent decision-makers who will subsequently compete with each other for market share, profit maximization, etc. [18]. In addition, the assignment of customers being served by these facilities and how these facilities are connected with each other are interesting decisions considered within the problem.
Athanasia Karakitsiou

Chapter 2. Static Competitive Facility Location Problems

In this section we review some of the most important contribution to the field of static competitive facility location problem. The main assumptions of the models presented in this section can be summarized as follows:
  • the existing competition is known and fixed,
  • the product sold is homogeneous,
  • the customers’ decision in patronizing the facility is based entirely on the distance traveled.
  • the unit costs are the same in all stores regardless of ownership
Athanasia Karakitsiou

Chapter 3. Sequential Competitive Facility Location Problems

The formalization of this class of problem and the fundamental complexity results were established by Hakimi [28]. Following the game introduced by von Stackelberg [76], Hakimi [28] presented the two basic problems in sequential location analysis, the centroid and medianoid problems. These two problems are faced by the leader and the follower, respectively. The leader attempts to locate p( ≥ 1) facilities knowing that a follower will in turn locate his r( ≥ 1) facilities based on the leader’s chosen locations; this is the (r | p)-centroid problem. The follower knows the set X p that indicates where the leader’s facilities are located, and solves an (r | X p )-medianoid problem. Customers choose among the facilities according to a function of the distance between themselves and the facilities, preferring always the closest. This is the so-called binary customer choice. The formulation of the problems is based on the assumption that co-location is not allowed and if, by any chance the distance from a customer to the closest facility of the two competitors is the same, the customer always prefers the leader’s facility. The demand of the customer is also considered to be inelastic with respect to the distance traveled.
Athanasia Karakitsiou

Chapter 4. Simultaneous Competitive Facility Location Models

The research effort of this body of literature aims at developing insights concerning the equilibrium pattern of location decisions and their stability. Another subject that is addressed by several authors is the existence or (not) of a set of locations and pricing or production quantities that will ensure a Nash equilibrium, that is, a position where neither firms have incentives to move.
Athanasia Karakitsiou

Chapter 5. Competitive Facility Location with Competition of Customers

The research work dealing with the competitive location problems is limited only to the competition among the locators, that is, it is supposed that either both the locator and the allocator are the same or the customer knows the optimality criterion of the locator and agrees passively with it. Customers preferences as well as externalities (such as road congestion, facility congestion, emissions, etc.) caused by the location decisions are either ignored or “controlled” by incorporating constraints in order to “ensure” the achievement of a predetermined target. However, this approach treats customers as irresolute beings. Thus, if, for example, the customers travel to the facilities to obtain the offered service, then there is no compulsion or incentive for them to attend the designated facility. This means that, once the facilities are open, what the locator wishes the customers to do may not coincide with their own wish and behavior.
Athanasia Karakitsiou


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