IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v52y2004i1p35-53.html

The Price of Robustness

Author

Listed:
  • Dimitris Bertsimas

    (Sloan School of Management, Massachusetts Institute of Technology, E53-363, Cambridge, Massachusetts 02139)

  • Melvyn Sim

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

A robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes. A concern with such an approach is that it might be too conservative. In this paper, we propose an approach that attempts to make this trade-off more attractive; that is, we investigate ways to decrease what we call the price of robustness. In particular, we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations. An attractive aspect of our method is that the new robust formulation is also a linear optimization problem. Thus we naturally extend our methods to discrete optimization problems in a tractable way. We report numerical results for a portfolio optimization problem, a knapsack problem, and a problem from the Net Lib library.

Suggested Citation

  • Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    • Handle: RePEc:inm:oropre:v:52:y:2004:i:1:p:35-53
    DOI: 10.1287/opre.1030.0065
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1030.0065
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1030.0065?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    2. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Xingchen & Xu, Guangcheng & Wu, Jie & Xu, Chengzhen & Zhu, Qingyuan, 2024. "Evaluation of bank efficiency by considering the uncertainty of nonperforming loans," Omega, Elsevier, vol. 126(C).
    2. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    3. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    4. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    5. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    6. Güray Kara & Ayşe Özmen & Gerhard-Wilhelm Weber, 2019. "Stability advances in robust portfolio optimization under parallelepiped uncertainty," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 241-261, March.
    7. M. J. Naderi & M. S. Pishvaee, 2017. "Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2689-2711, July.
    8. Marc Goerigk, 2014. "A note on upper bounds to the robust knapsack problem with discrete scenarios," Annals of Operations Research, Springer, vol. 223(1), pages 461-469, December.
    9. Roya Soltani & Seyed J Sadjadi, 2014. "Reliability optimization through robust redundancy allocation models with choice of component type under fuzziness," Journal of Risk and Reliability, , vol. 228(5), pages 449-459, October.
    10. Xuejie Bai & Yankui Liu, 2016. "Robust optimization of supply chain network design in fuzzy decision system," Journal of Intelligent Manufacturing, Springer, vol. 27(6), pages 1131-1149, December.
    11. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    12. Jannis Kurtz, 2018. "Robust combinatorial optimization under budgeted–ellipsoidal uncertainty," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 315-337, December.
    13. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    14. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "Characterizations for Optimality Conditions of General Robust Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 835-856, June.
    15. Mehdi Ansari & Juan S. Borrero & Leonardo Lozano, 2023. "Robust Minimum-Cost Flow Problems Under Multiple Ripple Effect Disruptions," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 83-103, January.
    16. Yasmine Beck & Ivana Ljubić & Martin Schmidt, 2026. "Heuristic Methods for Γ-Robust Mixed-Integer Linear Bilevel Problems," INFORMS Journal on Computing, INFORMS, vol. 38(1), pages 165-188, January.
    17. Hassan Hijazi & Pierre Bonami & Adam Ouorou, 2013. "Robust delay-constrained routing in telecommunications," Annals of Operations Research, Springer, vol. 206(1), pages 163-181, July.
    18. Zhi Chen & Peng Xiong, 2023. "RSOME in Python: An Open-Source Package for Robust Stochastic Optimization Made Easy," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 717-724, July.
    19. Walid Ben-Ameur & Adam Ouorou & Guanglei Wang & Mateusz Żotkiewicz, 2018. "Multipolar robust optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 395-434, December.
    20. Frédéric Babonneau & Alain Haurie, 2019. "Energy technology environment model with smart grid and robust nodal electricity prices," Annals of Operations Research, Springer, vol. 274(1), pages 101-117, March.

    More about this item

    Keywords

    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:52:y:2004:i:1:p:35-53. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.