A distributionally robust optimization approach for two-stage facility location problems
A distributionally robust optimization approach for two-stage facility location problems
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DOI：
10.1007/s13675-020-00121-0
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发表时间：
2020-02
影响因子：
2.4
通讯作者：
Arash Gourtani;Tri-Dung Nguyen;Huifu Xu
中科院分区：
文献类型：
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作者：
Arash Gourtani;Tri-Dung Nguyen;Huifu Xu
在本文中，我们考虑了一个设施选址问题，其中客户需求构成相当大的不确定性，并且关于不确定性分布的完整信息是不可用的。我们将最优决策问题表述为一个两阶段的随机混合整数规划问题：第一阶段是设施位置的最优选择，第二阶段是每个设施运行的最优决策。提出了一个分布鲁棒优化框架，以对冲不确定性分布信息不完全所带来的风险。具体来说，通过利用力矩信息，我们构建了一个包含真实分布的分布集，其中最优决策是基于集合中的最差分布。然后，我们开发了两种解决分布鲁棒设施选址问题的数值方案：利用某些参考随机变量的矩的半无限规划方法和利用描述需求不确定性的潜在随机变量的平均值和相关性的半确定规划方法。在半无限规划方法中，我们将众所周知的线性决策规则方法应用于鲁棒对偶问题，然后通过条件风险值测度逼近半无限约束。我们提供了数值测试来证明鲁棒解的计算和性质。
In this paper, we consider a facility location problem where customer demand constitutes considerable uncertainty, and where complete information on the distribution of the uncertainty is unavailable. We formulate the optimal decision problem as a two-stage stochastic mixed integer programming problem: an optimal selection of facility locations in the first stage and an optimal decision on the operation of each facility in the second stage. A distributionally robust optimization framework is proposed to hedge risks arising from incomplete information on the distribution of the uncertainty. Specifically, by exploiting the moment information, we construct a set of distributions which contains the true distribution and where the optimal decision is based on the worst distribution from the set. We then develop two numerical schemes for solving the distributionally robust facility location problem: a semi-infinite programming approach which exploits moments of certain reference random variables and a semi-definite programming approach which utilizes the mean and correlation of the underlying random variables describing the demand uncertainty. In the semi-infinite programming approach, we apply the well-known linear decision rule approach to the robust dual problem and then approximate the semi-infinite constraints through the conditional value at risk measure. We provide numerical tests to demonstrate the computation and properties of the robust solutions.