Huff-type competitive facility location model with foresight in a discrete space

Consider a chain as leader that wants to open p new facilities in a linear market, like metro. In this market, there is a competitor, called follower. The leader and the follower have established some facilities in advance. When the leader opens p new facilities, its competitor, follower, reacts the leader’s action and opens r new facilities. The optimal locations for leader and follower are chosen among predefined potential locations. Demand is considered as demand points and is assumed inelastic. Considering huff model, demand points are probabilistically absorbed by all facilities. The leader’s objective is maximization of its market share after opening follower’s new facilities. For solving leader problem, first the follower’s problem is solved for all leader’s potential locations and the best location for leader is obtained and then, a heuristic model is proposed for leader problem when the leader and the follower want to open one new facility. Computational results show that the proposed method is efficient for large scale problems.