A Multi-Objective Approach to the Competitive Facility Location Problem

In this paper, a new modeling approach is introduced for a competitive facility location problem in which multiple competitors aim to maximize their market shares. The problem is called the Competitive Maximal Covering Location Problem (CMCLP) based on the classical Maximal Covering Location Problem. Typically, the CMCLP is modeled as a Stackelberg game in which the first player and then the other one locate a fixed number of facilities. On the other hand, the present work considers multiple competitors, and the objective is on discovering a set of the competitors' decision tuples that are not dominated by any other decision tuples in the solution space. Thereby, the proposed modeling approach aims to help competing firms understand tradeoffs when they engage in negotiations. A mathematical formulation for the CMCLP with two competitors is presented. A multi-objective genetic algorithm is used to solve the problems with multiple competitors. Computational experiments demonstrate that the genetic algorithm is able to approximate the true Pareto front.