A new customer choice rule, which may model in some cases the actual patronising behaviour of customers towards the facilities closer to reality than other existing rules, is proposed. According to the new rule, customers split their demand among the firms in the market by patronising only one facility from each firm, the one with the highest utility, and the demand is split among those facilities proportionally to their attraction. The influence of the choice rule in the location of facilities is investigated. In particular, a new continuous competitive single-facility location and design problem using this new rule is proposed. Both exact and heuristic methods are proposed to solve it. A comparison with the classical proportional (or Huff) choice rule when solving the location model reveals that both the location and the
Two new models for sitting a new facility in a competitive environment are introduced. Both the location and the quality of the new facility are to be found, so as to maximize the profit obtained by the locating firm. The patronizing behavior of customers is assumed to be probabilistic, i.e., they split their demand among all the existing facilities in the area, proportionally to the attraction they feel for them. The attraction is determined both by the distance between the demand point and the facility and by the quality of the facility. Contrarily to what is commonly done in literature, the demand is not fixed, but varies depending on the location of the facilities. The first model assumes a static scenario, whereas in the second one a competing chain reacts by location a single new facility too, leading to a Stackelberg (or leader-follower) problem. The new continuous location models lead to hard-to-solve global optimization problems. A new evolutionary algorithm called UEGO was used to deal with those problems. The computational results showed its usefulness and robustness. Parallel implementations of UEGO are also presented to cope with large instances. The efficiency and scalability of the parallel algorithms were shown through a computational study. Future trends which will allow the construction of an expert system for facility location are also discussed.
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