Tabu Search for the $(r\vert p)$-Centroid Problem Under Uncertainty*

We consider the $(r\vert p)$-centroid problem under an assumption of uncertainty in the input data. Two players, the leader and the follower, open facilities, striving to capture the largest market share. The leader opens p facilities, then the follower opens r facilities. Each customer chooses the nearest facility as his supplier and bring a particular income to the corresponding player. The aim is to choose p facilities of the leader in such a way as to maximize his market share. However, it is assumed that customers' purchasing power is not known exactly and can change after the decision made. This problem can be represented as a bilevel programming problem. In this work, we propose a local search approach based on a stochastic tabu search framework to tackle the problem. We provide the results of numerical experiments and compare the behavior of both players compared to the deterministic setting of the same problem.