Exact algorithms for solving a bi-level location–allocation problem considering customer preferences

The issue discussed in this paper is a bi-level problem in which two rivals compete in attracting customers and maximizing their profits which means that competitors competing for market share must compete in the centers that are going to be located in the near future. In this paper, a nonlinear model presented in the literature considering customer preferences is linearized. Customer behavior means that the customer patronizes the most attractive (most comfort) location that he/she wants to be served among the locations of the first-level decision maker (Leader) and the second-level decision maker (Follower). Four types of exact algorithms have been introduced in this paper which include three types of full enumeration procedures and a developed branch-and-bound procedure. Moreover, a clustering-based algorithm has been presented that can provide a good approximation (a good lower bound) to the mentioned binary problem. For this purpose, the numerical results obtained are compared with the results of the full enumeration, heuristic and the branch-and-bound procedure.