Academic Journal
On the Sparsity of Optimal Linear Decision Rules for a Class of Robust Optimization Problems with Box Uncertainty Sets.
| Title: | On the Sparsity of Optimal Linear Decision Rules for a Class of Robust Optimization Problems with Box Uncertainty Sets. |
|---|---|
| Authors: | Lu, Haihao, Sturt, Bradley |
| Source: | Operations Research; Jan/Feb2026, Vol. 74 Issue 1, p500-516, 17p |
| Subject Terms: | Robust optimization, Inventory control, Linear programming, Computer simulation, Mathematical optimization, Optimization algorithms |
| Abstract: | We consider a class of production–inventory problems with box uncertainty sets from the seminal work of Ben-Tal et al. [Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math. Programming 99(2):351–376] on linear decision rules in robust optimization. We prove that there always exists an optimal linear decision rule for this class of problems in which the number of nonzero parameters in the linear decision rule grows linearly in the number of time periods. This is the first result to prove that optimal linear decision rules are sparse in a widely studied class of robust optimization problems with many time periods. Harnessing this sparsity guarantee, we introduce a reformulation technique that allows robust optimization problems such as production–inventory problems to be solved as compact linear optimization problems when most of the parameters of the linear decision rules are forced to be equal to zero. We also develop an active set method for identifying the parameters of linear decision rules that are equal to zero at optimality. In numerical experiments on production–inventory problems with hundreds of time periods, we find that our reformulation technique coupled with the active set method yields more than a 32× speedup over state-of-the-art linear optimization solvers in computing linear decision rules that are within 1% of optimal. Our proofs and algorithms are based on a principled analysis of extreme points of linear optimization formulations. [ABSTRACT FROM AUTHOR] |
| Copyright of Operations Research is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Complementary Index |
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| Items | – Name: Title Label: Title Group: Ti Data: On the Sparsity of Optimal Linear Decision Rules for a Class of Robust Optimization Problems with Box Uncertainty Sets. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lu%2C+Haihao%22">Lu, Haihao</searchLink><br /><searchLink fieldCode="AR" term="%22Sturt%2C+Bradley%22">Sturt, Bradley</searchLink> – Name: TitleSource Label: Source Group: Src Data: Operations Research; Jan/Feb2026, Vol. 74 Issue 1, p500-516, 17p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Robust+optimization%22">Robust optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Inventory+control%22">Inventory control</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+programming%22">Linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider a class of production–inventory problems with box uncertainty sets from the seminal work of Ben-Tal et al. [Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math. Programming 99(2):351–376] on linear decision rules in robust optimization. We prove that there always exists an optimal linear decision rule for this class of problems in which the number of nonzero parameters in the linear decision rule grows linearly in the number of time periods. This is the first result to prove that optimal linear decision rules are sparse in a widely studied class of robust optimization problems with many time periods. Harnessing this sparsity guarantee, we introduce a reformulation technique that allows robust optimization problems such as production–inventory problems to be solved as compact linear optimization problems when most of the parameters of the linear decision rules are forced to be equal to zero. We also develop an active set method for identifying the parameters of linear decision rules that are equal to zero at optimality. In numerical experiments on production–inventory problems with hundreds of time periods, we find that our reformulation technique coupled with the active set method yields more than a 32× speedup over state-of-the-art linear optimization solvers in computing linear decision rules that are within 1% of optimal. Our proofs and algorithms are based on a principled analysis of extreme points of linear optimization formulations. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Operations Research is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1287/opre.2023.0603 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 500 Subjects: – SubjectFull: Robust optimization Type: general – SubjectFull: Inventory control Type: general – SubjectFull: Linear programming Type: general – SubjectFull: Computer simulation Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Optimization algorithms Type: general Titles: – TitleFull: On the Sparsity of Optimal Linear Decision Rules for a Class of Robust Optimization Problems with Box Uncertainty Sets. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lu, Haihao – PersonEntity: Name: NameFull: Sturt, Bradley IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan/Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0030364X Numbering: – Type: volume Value: 74 – Type: issue Value: 1 Titles: – TitleFull: Operations Research Type: main |
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