Restructuring hierarchical capacitated facility location problem with extended coverage radius under uncertainty

The Restructuring Facility Location Problem (RFLP) seeks to locate facilities by resizing, closing, or opening new facilities, to provide the service required by the customers, at minimum total cost. All of the previous researches on RFLP had only single-level facilities. In the present study, we addressed a new problem of restructuring hierarchical facilities, named Extended Radius bi-levels Restructuring Capacitated Facility Location Problem (ER-RCFLP), comprising main and auxiliary facilities in the first and second levels, respectively. In ER-RCFLP, there is an extended coverage radius for the main facility which customers in the coverage radius of auxiliary facilities of the main facility can get service from the main facility. A mixed-integer linear program (MILP) has been projected to minimize the restructuring cost for the introduced problem. The proposed model, not only considers both closing down and opening new facilities, and addresses the problem of resizing open facilities, but also defines the auxiliary facilities in order to minimize the total cost. The auxiliary facility increases the coverage radius of the existing and new main facilities. Also, a robust MILP model has been developed for the ER-RCFLP problem under uncertainty of demand. The impact of auxiliary facilities in the network, impact of various decisions resizing, closing or opening main facilities, and impact of demand uncertainty have been studied through six experiments and 555 sample problems. Computational results related to deterministic problems indicate that opening auxiliary facilities in a single level network enjoys 24% reduction in total cost in average. Furthermore, in an existing hierarchical network of main and auxiliary facilities, resizing of auxiliary facilities has more effect on cost reduction in comparison with closing main facilities. Moreover for the networks under uncertainty, opening new auxiliary facilities has great effect on total cost reduction of network. In addition, establishing auxiliary facilities along with resizing main facilities have more impact on network cost reduction.