Sequential Discrete p-Facility Models for Competitive Location Planning

Two new models for duopolistic competitive discrete location planning with sequential acting and variable delivered prices are introduced. If locations and prices are assumed to be set once and for all by the players, the resulting bilevel program is nonlinear. Under the assumption that further price adjustments are possible, i.e., that a Nash equilibrium in prices is reached, the model can be simplified to a linear discrete bilevel formulation. It is shown that in either situation players should not share any locations or markets if they strive for profit-maximization.For the situation with price adjustments, a heuristic solution procedure is suggested. In addition, the bilevel models are shown to serve as a basis from which different well-known location models – as, for example, the p-median problem, the preemptive location problem and the maximum covering problem – can be derived as special cases.