Abstract

We consider a competitive facility location model where competing parties (Leader and Follower) make decisions considering changes of the set of customers happening during the planing horizon consisting a known number of time periods. It is assumed that the Leader makes a decision on opening their facilities at the beginning of the planning horizon, while the Follower can revise their decision in each time period. In the present paper, we study perspectives to apply a method for finding the best solution that is based on using HP-relaxation of the bilevel problem considered. The key element of this method is construction of additional inequalities strengthening the HP-relaxation and computation of upper bounds for the objective function of the problem. In the paper, we propose new families of additional constraints to strengthen the HP-relaxation that allow computing nontrivial upper bounds.

中文翻译：

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动态竞争设施选址问题的附加约束

摘要

我们考虑一种竞争性设施选址模型，其中竞争方（领导者和追随者）在做出决策时会考虑在由已知数量的时间段组成的规划范围内发生的客户群变化。假设领导者在规划范围之初就决定开放其设施，而追随者可以在每个时间段修改其决定。在本文中，我们研究了应用一种基于使用所考虑的双层问题的 HP 松弛来寻找最佳解决方案的方法的观点。该方法的关键要素是构造额外的不等式，以加强 HP 松弛和问题目标函数上限的计算。在本文中，我们提出了新的附加约束系列，以加强 HP 松弛，从而允许计算不平凡的上限。