A variable neighbourhood search method for solving the long-term care facility location problem

Abstract

This article deals with a problem of determining locations for installing long-term care facilities in the given network, in order to minimize the maximum number of patients that are assigned to a single installed facility. The problem is known as the Long-Term Care Facility Location Problem (LTCFLP). We propose an improved mathematical formulation for the LTCFLP and evaluate its efficiency through a set of computational experiments on test instances with up to 80 potential facility locations. To solve instances of larger problem dimensions, we develop a metaheuristic method based on a Variable Neighbourhood Search (VNS). A reduced VNS algorithm is employed to provide a good-quality initial solution, which is then used as a starting point of the basic VNS method. A local search procedure with efficient fast interchange method is implemented in the proposed VNS-based approach. The algorithm is benchmarked on a large-scale dataset involving up to 400 potential facility locations. Presented computational results show that the proposed VNS quickly reaches all optimal solutions from the literature, and in most cases outperforms existing heuristic methods for solving the LTCFLP.