Competitive Location: New Models and Methods and Future Trends

Abstract

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.