IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v311y2023i3p1023-1039.html
   My bibliography  Save this article

Robust optimization with order statistic uncertainty set

Author

Listed:
  • Zhang, Pengfei
  • Gupta, Diwakar

Abstract

In this paper, we propose a new uncertainty set for robust models of linear optimization problems. We first study data-free and distribution-free statistical properties of continuous and independent random variables using the Probability Integral Transform. Based on these properties, we construct a new uncertainty set by placing constraints on the order statistics of random variables. We utilize the quantiles of random variables to depict the uncertainties and then adopt the formulation of the assignment problem to develop a tractable formulation for the order statistic uncertainty set. We show that the robust optimization models with the interval uncertainty set, the budget uncertainty set, and the demand uncertainty set can be obtained as special cases of the robust optimization model with the order statistic uncertainty set. Finally, using a robust portfolio construction problem as an example, we show via numerical experiments that the order statistic uncertainty set has better performance than other uncertainty sets when the sample size is small and the correlation between random variables is low.

Suggested Citation

  • Zhang, Pengfei & Gupta, Diwakar, 2023. "Robust optimization with order statistic uncertainty set," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1023-1039.
    • Handle: RePEc:eee:ejores:v:311:y:2023:i:3:p:1023-1039
    DOI: 10.1016/j.ejor.2023.05.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723003892
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.05.024?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Chaithanya Bandi & Dimitris Bertsimas & Nataly Youssef, 2015. "Robust Queueing Theory," Operations Research, INFORMS, vol. 63(3), pages 676-700, June.
    3. Chaithanya Bandi & Diwakar Gupta, 2020. "Operating Room Staffing and Scheduling," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 958-974, September.
    4. Chassein, André & Dokka, Trivikram & Goerigk, Marc, 2019. "Algorithms and uncertainty sets for data-driven robust shortest path problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 671-686.
    5. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    6. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
    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. Hamed Mamani & Shima Nassiri & Michael R. Wagner, 2017. "Closed-Form Solutions for Robust Inventory Management," Management Science, INFORMS, vol. 63(5), pages 1625-1643, May.
    2. Namakshenas, Mohammad & Mazdeh, Mohammad Mahdavi & Braaksma, Aleida & Heydari, Mehdi, 2023. "Appointment scheduling for medical diagnostic centers considering time-sensitive pharmaceuticals: A dynamic robust optimization approach," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1018-1031.
    3. Shaojian Qu & Can Feng & Shan Jiang & Jinpeng Wei & Yuting Xu, 2022. "Data-Driven Robust DEA Models for Measuring Operational Efficiency of Endowment Insurance System of Different Provinces in China," Sustainability, MDPI, vol. 14(16), pages 1-21, August.
    4. Marla, Lavanya & Rikun, Alexander & Stauffer, Gautier & Pratsini, Eleni, 2020. "Robust modeling and planning: Insights from three industrial applications," Operations Research Perspectives, Elsevier, vol. 7(C).
    5. 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.
    6. 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.
    7. Chassein, André & Dokka, Trivikram & Goerigk, Marc, 2019. "Algorithms and uncertainty sets for data-driven robust shortest path problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 671-686.
    8. 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.
    9. 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.
    10. Steve Zymler & Daniel Kuhn & Berç Rustem, 2013. "Worst-Case Value at Risk of Nonlinear Portfolios," Management Science, INFORMS, vol. 59(1), pages 172-188, July.
    11. Shunichi Ohmori, 2021. "A Predictive Prescription Using Minimum Volume k -Nearest Neighbor Enclosing Ellipsoid and Robust Optimization," Mathematics, MDPI, vol. 9(2), pages 1-16, January.
    12. Roberto Gomes de Mattos & Fabricio Oliveira & Adriana Leiras & Abdon Baptista de Paula Filho & Paulo Gonçalves, 2019. "Robust optimization of the insecticide-treated bed nets procurement and distribution planning under uncertainty for malaria prevention and control," Annals of Operations Research, Springer, vol. 283(1), pages 1045-1078, December.
    13. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    14. Soyster, A.L. & Murphy, F.H., 2013. "A unifying framework for duality and modeling in robust linear programs," Omega, Elsevier, vol. 41(6), pages 984-997.
    15. F. Davarian & J. Behnamian, 2022. "Robust finite-horizon scheduling/rescheduling of operating rooms with elective and emergency surgeries under resource constraints," Journal of Scheduling, Springer, vol. 25(6), pages 625-641, December.
    16. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.
    17. Fanwen Meng & Jin Qi & Meilin Zhang & James Ang & Singfat Chu & Melvyn Sim, 2015. "A Robust Optimization Model for Managing Elective Admission in a Public Hospital," Operations Research, INFORMS, vol. 63(6), pages 1452-1467, December.
    18. Viktoryia Buhayenko & Dick den Hertog, 2017. "Adjustable Robust Optimisation approach to optimise discounts for multi-period supply chain coordination under demand uncertainty," International Journal of Production Research, Taylor & Francis Journals, vol. 55(22), pages 6801-6823, November.
    19. Gilani, H. & Sahebi, H. & Oliveira, Fabricio, 2020. "Sustainable sugarcane-to-bioethanol supply chain network design: A robust possibilistic programming model," Applied Energy, Elsevier, vol. 278(C).
    20. Wenqing Chen & Melvyn Sim, 2009. "Goal-Driven Optimization," Operations Research, INFORMS, vol. 57(2), pages 342-357, April.

    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:eee:ejores:v:311:y:2023:i:3:p:1023-1039. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.