A leader–follower model for discrete competitive facility location

•The leader–follower competitive location problem is investigated.•The follower׳s problem is optimally solved by a branch and bound algorithm.•An effective tabu search algorithm is designed for the solution of the leader׳s problem.•Result: the main source of extra market share is obtained by attracting new customers.

In this paper we investigate a leader–follower (Stackelberg equilibrium) competitive location model. The competitive model is based on the concept of cover. Each facility attracts consumers within a “sphere of influence” defined by a “radius of influence.” The leader and the follower, each has a budget to be spent on the expansion of their chains either by improving their existing facilities or constructing new ones. We find the best strategy for the leader assuming that the follower, knowing the action taken by the leader, will react by investing his budget to maximize his market share. The objective of the leader is to maximize his market share following the follower׳s reaction.