A Minimax Regret Model for Leader-follower Facility Location Problem (CEIBS Working Paper, No. 025/2020/POM/DEC, 2020)

Leader-follower facility location problem is usually consisting of a leader and a follower, in which the two competitors are going to locate new facilities sequentially. The traditional studies generally assume that the leader knows in advance the partial or full information about the follower’s response when he makes decision. This assumption, however, may be invalid or impracticable in practice. In this paper, we consider that the leader needs to locate a predetermined number of new facilities without knowing any information about the follower’s response. By separating scenarios on the follower’s response with different number of new facilities, a minimax regret model is proposed for the leader so that his maximum possible loss can be minimized. Based on the structural characteristics of the proposed model, a set of solving procedures is provided with transforming the follower’s nonlinear (fraction) programming model into a linear one. In the numerical experiments, the proposed model is compared to two other location model, deterministic model and risk model, and the efficiency of linearization in decreasing the computation