A distributionally robust optimization approach for two-stage facility location problems

被引:12
作者
Gourtani, Arash [1 ]
Nguyen Tri-Dung [1 ,2 ]
Xu, Huifu [3 ]
机构
[1] Univ Southampton, Sch Math, Southampton SO17 1BJ, Hants, England
[2] Univ Southampton, Sch Management, Southampton SO17 1BJ, Hants, England
[3] Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Hong Kong, Peoples R China
基金
英国工程与自然科学研究理事会;
关键词
Distributionally robust optimization; Facility location problem; Semi-definite programming; Semi-infinite programming; QUADRATIC-PROGRAMMING PROBLEMS; JOINT CHANCE CONSTRAINTS; UNCERTAINTY; NETWORK;
D O I
10.1007/s13675-020-00121-0
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
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.
引用
收藏
页码:141 / 172
页数:32
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