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 probl...

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Autores principales:	Arash Gourtani, Tri-Dung Nguyen, Huifu Xu
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2020
Materias:	90B80 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/35aa5129c63d4c06bcf8298ae16c7dcc
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spelling	oai:doaj.org-article:35aa5129c63d4c06bcf8298ae16c7dcc2021-12-02T05:01:14ZA distributionally robust optimization approach for two-stage facility location problems2192-440610.1007/s13675-020-00121-0https://doaj.org/article/35aa5129c63d4c06bcf8298ae16c7dcc2020-06-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621001258https://doaj.org/toc/2192-4406In 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.Arash GourtaniTri-Dung NguyenHuifu XuElsevierarticle90B80Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 8, Iss 2, Pp 141-172 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	90B80 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90B80 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Arash Gourtani Tri-Dung Nguyen Huifu Xu A distributionally robust optimization approach for two-stage facility location problems
description	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.
format	article
author	Arash Gourtani Tri-Dung Nguyen Huifu Xu
author_facet	Arash Gourtani Tri-Dung Nguyen Huifu Xu
author_sort	Arash Gourtani
title	A distributionally robust optimization approach for two-stage facility location problems
title_short	A distributionally robust optimization approach for two-stage facility location problems
title_full	A distributionally robust optimization approach for two-stage facility location problems
title_fullStr	A distributionally robust optimization approach for two-stage facility location problems
title_full_unstemmed	A distributionally robust optimization approach for two-stage facility location problems
title_sort	distributionally robust optimization approach for two-stage facility location problems
publisher	Elsevier
publishDate	2020
url	https://doaj.org/article/35aa5129c63d4c06bcf8298ae16c7dcc
work_keys_str_mv	AT arashgourtani adistributionallyrobustoptimizationapproachfortwostagefacilitylocationproblems AT tridungnguyen adistributionallyrobustoptimizationapproachfortwostagefacilitylocationproblems AT huifuxu adistributionallyrobustoptimizationapproachfortwostagefacilitylocationproblems AT arashgourtani distributionallyrobustoptimizationapproachfortwostagefacilitylocationproblems AT tridungnguyen distributionallyrobustoptimizationapproachfortwostagefacilitylocationproblems AT huifuxu distributionallyrobustoptimizationapproachfortwostagefacilitylocationproblems
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A distributionally robust optimization approach for two-stage facility location problems

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