A hybrid iterated local search matheuristic for large-scale single source capacitated facility location problems

The Single Source Capacitated Facility Location Problem (SSCFLP) consists of determining locations for facilities to meet customer demands so that each customer must be served by a single facility. This paper proposes a matheuristic algorithm for solving large-scale SSCFLP instances that combines neighborhood-based heuristic procedures with the solution of two binary linear programming sub-problems through a general-purpose solver. The proposed algorithm starts from the optimal solution of the linear relaxation of the SSCFLP to reduce its size and identify promising potential locations for opening facilities. Computational experiments were performed on two benchmark sets of large instances. For one of them, the developed algorithm obtained optimal solutions for all instances. For the other set, it provided average relative deviations slightly lower than those of three relevant algorithms from the literature. These results allow us to conclude that the proposed algorithm generates good-quality solutions and is competitive in solving large-scale SSCFLP instances.