Development of a Branch and Bound Algorithm for One Competitive Facility Location Problem with Elastic Demand

Abstract

We consider a variant of the Competitive Location Problem, in which it is necessary to choose not only location, but also the design of facilities in order to maximize the share of customer demand served. It is described as an integer programming model with a nonlinear objective function. Commercial software is not suitable for finding the optimal solution to this problem in a reasonable time. Previously, Aboolian R. et al. proposed an adapted weighted greedy heuristic for this problem. In our earlier study, we developed several variants of local search algorithm. This article is devoted to development of the branch-and-bound algorithm. The scheme of branching is described, the results of a computational experiment are presented, future development possibility is discussed.