Competitive location on a network
Operations Research
Heuristic and exact methods for the discrete (r|p)-centroid problem
EvoCOP'10 Proceedings of the 10th European conference on Evolutionary Computation in Combinatorial Optimization
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We study a mathematical model generalizing the well-known facility location problem. In this model we consider two competing sides successively placing their facilities and aiming to ''capture'' consumers, in order to make maximal profit. We state the problem as a bilevel integer programming problem, regarding optimal noncooperative solutions as optimal solutions. We propose a branch-and-bound algorithm for finding the optimal noncooperative solution. While constructing the algorithm, we represent our problem as the problem of maximizing a pseudo-Boolean function. An important ingredient of the algorithm is a method for calculating an upper bound for the values of the pseudo-Boolean function on subsets of solutions. We present the results of a simulation demonstrating the computational capabilities of the proposed algorithm.