A minimax regret model for the leader–follower facility location problem

Xiang Li (First Author), Tianyu Zhang (Participant Author), Liang Wang (Participant Author), Hongguang Ma (Participant Author), Xiande Zhao (Participant Author)

Research output: Contribution to journalJournal


The leader–follower facility location problem consists of a leader and a follower who are competitors that locate new facilities sequentially. Traditional studies have generally assumed that the leader has partial or full advance information of the follower’s response when making a decision. However, this assumption might 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 anything about the follower’s response. By separating the scenarios in which the follower responds with different numbers of new facilities, a minimax regret model is proposed for the leader to minimise its maximum possible loss. Based on the structural characteristics of the proposed model, a set of solving procedures is provided that transforms the follower’s nonlinear (fraction) programming model into a linear model. In the numerical experiments, the proposed model is compared with two other location models, a deterministic model and a risk model, and the efficiency of the linearisation in decreasing the computation time is verified. The results show that the proposed model is more applicable to the leader when there is no information about the number or probability distribution of the follower’s new facilities.
Original languageEnglish
Pages (from-to)861-882
Number of pages22
JournalAnnals of Operations Research
Issue number2
Publication statusPublished - 2022

Corresponding author email



  • Competition
  • Leader–follower facility location
  • Linearisation
  • Minimax regret model

Indexed by

  • ABDC-A
  • SCIE


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