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.

单一来源能力设施选址问题 (SSCFLP) 包括确定设施位置以满足客户需求，以便每个客户必须由单一设施提供服务。本文提出了一种用于求解大规模 SSCFLP 实例的数学算法，该算法将基于邻域的启发式程序与通过通用求解器求解两个二元线性规划子问题相结合。所提出的算法从 SSCFLP 线性松弛的最优解开始，以减小其尺寸并确定开放设施的有希望的潜在位置。在大型实例的两个基准集上进行了计算实验。对于其中之一，开发的算法获得了所有实例的最佳解决方案。对于另一组，它提供的平均相对偏差略低于文献中三种相关算法的平均相对偏差。这些结果使我们得出结论，所提出的算法生成了高质量的解决方案，并且在解决大规模 SSCFLP 实例方面具有竞争力。