In this research, we will focus on one variant of the problem: the capacitated facility location problem (CFLP). In many formulations of the CFLP, it is assumed that each demand point can be supplied by only one open facility, which is the simplest case of the problem. We consider the case where each demand point can be supplied by more than one open facility. We first investigate a Lagrangian relaxation approach. Then, we illustrate in the problem decomposition how to introduce tighter constraints, which solve the CFLP faster while achieving a better quality solution as well. At the same time, we apply the volume algorithm to improve both the lower and the upper bound on the optimum solution of the original problem for the large problem size.

中文翻译：

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用拉格朗日分解和体积算法求解带电容器的设施选址问题

在这项研究中，我们将重点关注该问题的一个变体：失能设施位置问题（CFLP）。在CFLP的许多公式中，假定每个需求点只能由一个开放的设施提供，这是问题的最简单情况。我们考虑一种情况，即每个需求点可以由多个开放设施提供。我们首先研究拉格朗日松弛法。然后，我们在问题分解中说明如何引入更严格的约束，从而更快地解决CFLP并同时获得更好的质量解决方案。同时，对于大问题，我们应用体积算法来改进原始问题的最优解的上下限。