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

Gourtani, Arash, Nguyen, Tri-Dung, Xu, Huifu (2020) A distributionally robust optimization approach for two-stage facility location problems. EURO Journal on Computational Optimization, 8 (2). pp. 141-172. ISSN 2192-4406. (doi:10.1007/s13675-020-00121-0) (KAR id:92912)

Abstract

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. © 2020, The Author(s).

Item Type: Article
DOI/Identification number: 10.1007/s13675-020-00121-0
Uncontrolled keywords: Distributionally robust optimization, Facility location problem, Semi-definite programming, Semi-infinite programming, Location, Random variables, Risk assessment, Stages, Stochastic systems, Value engineering, Conditional Value-at-Risk, Facility location problem, Incomplete information, Linear decision rules, Robust optimization, Semi infinite programming, Semi-definite programming, Stochastic mixed integer programming, Integer programming
Subjects: H Social Sciences
Divisions: Divisions > Kent Business School - Division > Department of Analytics, Operations and Systems
Depositing User: Tri-Dung Nguyen
Date Deposited: 17 Mar 2022 15:12 UTC
Last Modified: 18 Mar 2022 10:59 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/92912 (The current URI for this page, for reference purposes)

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