ABSTRACT

In this paper, we apply the minimum information theory to the uncapacitated p-median facility location problem to determine the most probable allocation solution. Indeed, we investigate the bi-level p-median model introduced by [TRANSPORT RES B-METH. 123 (2019) 1–20] in the case that facilities have unlimited capacities. At the upper level, minimizing the cost of establishing facilities and allocating demands is considered, while the most probable allocation solution in the customers’ point of view is determined through the lower level. By adding the Karush-Kuhn-Tucker optimality conditions of the lower-level problem to the upper-level constraints, the bi-level model is reduced to a one-level linear mixed integer problem. Some numerical examples are provided to verify the added value of the proposed model and its solution method.

摘要

在本文中，我们将最小信息理论应用于无能力的p中值设施位置问题，以确定最可能的分配解决方案。事实上，我们研究了由 [TRANSPORT RES B-METH.] 引入的双层p中值模型。123 (2019) 1-20] 在设施容量不受限制的情况下。在上层，考虑最小化建设设施和分配需求的成本，而在客户看来最可能的分配方案是通过下层确定的。通过将下层问题的 Karush-Kuhn-Tucker 最优性条件添加到上层约束中，bi级模型简化为一级线性混合整数问题。给出了一些数值例子来验证所提模型的附加值及其求解方法。