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

A distributionally robust optimization approach for two-stage facility location problems
A distributionally robust optimization approach for two-stage facility location problems
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 (CVaR) measure. We provide numerical tests to demonstrate the computation and properties of the robust solutions.
2192-4406
Gourtani, Arash
4bbb8f40-64d0-44db-bdd8-c6c2d1ca6923
Nguyen, Tri-Dung
a6aa7081-6bf7-488a-b72f-510328958a8e
Xu, Huifu
67f2baf6-df5b-476a-95cd-3e7580635d39
Gourtani, Arash
4bbb8f40-64d0-44db-bdd8-c6c2d1ca6923
Nguyen, Tri-Dung
a6aa7081-6bf7-488a-b72f-510328958a8e
Xu, Huifu
67f2baf6-df5b-476a-95cd-3e7580635d39

Gourtani, Arash, Nguyen, Tri-Dung and Xu, Huifu (2020) A distributionally robust optimization approach for two-stage facility location problems. EURO Journal on Computational Optimization. (doi:10.1007/s13675-020-00121-0).

Record type: Article

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 (CVaR) measure. We provide numerical tests to demonstrate the computation and properties of the robust solutions.

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EJCO Robust Facility Location - Accepted Manuscript
Restricted to Repository staff only until 8 January 2021.
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More information

Submitted date: 2018
Accepted/In Press date: 9 January 2020
e-pub ahead of print date: 4 February 2020
Organisations: Centre of Excellence for International Banking, Finance & Accounting, Operational Research

Identifiers

Local EPrints ID: 369871
URI: http://eprints.soton.ac.uk/id/eprint/369871
ISSN: 2192-4406
PURE UUID: ca091e50-7753-4b69-8488-462a84839a8d
ORCID for Tri-Dung Nguyen: ORCID iD orcid.org/0000-0002-4158-9099

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Date deposited: 08 Oct 2014 14:38
Last modified: 20 Feb 2020 01:31

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Contributors

Author: Arash Gourtani
Author: Tri-Dung Nguyen ORCID iD
Author: Huifu Xu

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