Integer programming formulations for three sequential discrete competitive location problems with foresight

• Published in: European journal of operational research Vol. 265; no. 3; pp. 872 - 881
• Main Authors: Gentile, José, Alves Pessoa, Artur, Poss, Michael, Costa Roboredo, Marcos
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16-03-2018; Elsevier
• Subjects: Combinatorial optimization; Competitive location; Computer Science; Integer programming; Maximal covering location problem; Operations Research; Stackelberg problem; Integer programming; Stackelberg problem; Competitive location; Combinatorial optimization; Maximal covering location problem; Maximal Covering Location Problem; Integer Programming; Competitive Location
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2017.08.041

•Exact algorithms are proposed for three competitive location problems.•Several numerical experiments are presented assessing the algorithms efficiency.•The results are compared with the methods found in the literature.
We deal with three competitive location problems based on the classical Maximal Covering Location Problem. The environment of these problems consists of an open market with two firms (leader and follower), several customers and locations where facilities can be located. In order to capture the demand of the customers, the leader enters the market by locating a set of facilities knowing the potential locations where the follower can locate her facilities after the leader’s decision. We consider here three pairs of objective functions for the leader/follower previously studied in the literature: maximizing/minimizing the demand captured by the leader, minimizing/maximizing the regret of the leader, maximizing the demand captured by each firm (also known as Stackelberg). For each model, we propose an integer linear programming formulation with a polynomial number of variables and an exponential number of constraints. The formulations are solved by branch-and-cut algorithms where the constraints are generated on demand by solving appropriate separation problems. We report extensive computational experiments realized on instances inspired by those from the literature, comparing our algorithms with the exact and heuristic algorithms previously published for these problems.