Fast metaheuristics for the discrete $(r|p)$-centroid problem

Two players, the leader and his competitor, open facilities, striving to capture the largest market share. The leader opens $p$ facilities, then the follower opens $r$ facilities. Each client chooses the nearest facility as his supplier. We need to choose $p$ facilities of the leader in such a way as to maximize his market share. This problem can be represented as a bilevel programming problem. Based on this representation, in this work we propose two numerical approaches: local search with variable neighborhoods and stochastic tabu search. We pay the most attention to improving the methods' efficiency at no loss to the quality of the resulting solutions. Results of numerical experiments support the possibility to quickly find an exact solution for the problem and solutions with small error.