Branch-and-bound algorithm for a competitive facility location problem

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-andbound 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 pseudoBoolean function on subsets of solutions. We present the results of a simulation demonstrating the computational capabilities of the proposed algorithm. & 2013 Elsevier Ltd. All rights reserved.