Location Modeling in the Presence of Firm and Customer Competition

摘要

Location problems form a wide class of mathematical programming models, of great interest of both in practice and from the point of view of optimization theory. Facility location problem aims at determining the optimal sites to locate facilities such as plants, warehouses, and/or distribution centers. Competitive location models (CFL) 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. In addition decisions such as customers' allocation and pricing policies may also be incorporated to the basic model. The first paper dealing with the effect of competition in the location decisions is due Hotelling. Since then, a vast number of publications have been devoted to the subject. Sequential CFL problems are usually modeled as hierarchical or multi-level programming models. Such models are concerned with decision making problems that involve multiple decision makers ordered within a hierarchical structure. The most well-known case is the so-called Stackelberg game in which decision makers of two different levels with different, often conflicting, objectives are involved. The research work dealing with the bi-level formulation of location problems is limited only to the competition among the locators. Customers are passively assigned to the facilities according to some criteria. A first attempt to study the influence of market competition on location decisions is due to Tobin and Friesz. In this talk we formulate and study a class of location problems where the autonomous decisions of the customers regarding the facilities from which they will be served influence the locations decisions. The conditions under which customers make their choice of facilities to be served are in general complicated. We assume here that every customer will choose the facilities that minimize their own total transportation and waiting for service cost. Thus, concerning mathematical modeling we investigate facility location problems not only in the presence of firm competition but also in the presence of customer competition with respect to the quality level of the provided services. We derive bi-level programming models which are interpreted and analyzed in game theoretic terms. The issues of optimality conditions, computational complexity and solution algorithms are also discussed.