A VNS method for the conditional p-next center problem

Abstract

This paper considers the conditional $p$-next center problem (CPNCP) and proposes a metaheuristic method as a solution approach. The $p$-next center problem (PNCP) is an extension of the classical $p$-center problem that captures real-life situations when centers suddenly fail due to an accident or some other problem. When the center failure happens, the customers allocated to the closed center are redirected to the center closest to the closed one, called the backup center. On the other hand, when a service network expands, some of the existing centers are usually retained and a number of new centers are opened. The conditional $p$-next center problem involves both of these two aspects that arise in practice and, to the best of our knowledge, has not been considered in the literature so far. Since the CPNCP is NP-hard, a metaheuristic algorithm based on the Variable Neighborhood Search is developed. The proposed VNS includes an efficient implementation of the Fast Interchange heuristic which enables the VNS to tackle with real-life problem dimensions. The exhaustive computational experiments were performed on the modified PNCP test instances from the literature with up to 900 nodes. The obtained results are compared with the results of the exact solver CPLEX. It is shown that the proposed VNS reaches optimal solutions or improves the feasible ones provided by CPLEX in a significantly shorter CPU time. The VNS also quickly returns its best solutions when CPLEX failed to provide a feasible one. In order to investigate the effects of two different approaches in service network planning, the VNS solutions of the CPNCP are compared with the optimal or best-known solutions of the $p$-next center problem. In addition, the conducted computational study includes direct comparisons of the results obtained when the proposed SVNS is applied to PNCP (by setting the number of existing centers to 0) with the results of recent solution methods proposed for the PNCP.