A new alternating heuristic for the (r | p)–centroid problem on the plane

Abstract

In the (r | p)-centroid problem, two players, called leader and follower, open facilities to service clients. We assume that clients are identified with their lo- cation on the Euclidian plane, and facilities can be opened anywhere in the plane. The leader opens p facilities. Later on, the follower opens r facilities. Each client pa- tronizes the closest facility. Our goal is to find p facilities for the leader to maximize his market share. For this Stackelberg game we develop a new alternating heuristic, based on the exact approach for the follower problem. At each iteration ofthe heuris- tic, we consider the solution ofone player and calculate the best answer for the other player. At the final stage, the clients are clustered, and an exact polynomial-time algorithm for the (1 | 1)-centroid problem is applied. Computational experiments show that this heuristic dominates the previous alternating heuristic of Bhadury, Eiselt, and Jaramillo.