Facility location and scale decision problem with customer preference

This paper addresses the facility location problem that aims to optimize the location and scale of a new facility in consideration of customer restrictions, including customer preference and the minimum number of customers required to open the facility. In a classic covering problem, the customer is assumed to be covered if he/she is located within the critical distance zone around the facility and is otherwise not covered. This problem is caused by customer facility selection, which differs from the classic covering problem in which services are determined only by proximity. This paper proposes a mixed integer programming formulation based on customer restrictions and also develops a heuristic solution procedure using Lagrangian relaxation. The suggested solution procedure is shown to yield acceptable results in a reasonable computation time.

► The facility’s location and scale corresponding to the service type are to be determined.
► Facility can be installed if the customers are covered at least by certain level of preferences.
► Lagrangian relaxation based heuristic is developed.
► Performances of the heuristic are evaluated through the computational experiment.
► Near optimal solutions can be found within a relatively short computational time.