IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v34y2022i2p729-751.html
   My bibliography  Save this article

Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics

Author

Listed:
  • Nilay Noyan

    (Industrial Engineering Program, Sabancı University, 34956 Istanbul, Turkey)

  • Gábor Rudolf

    (Department of Industrial Engineering, Koc University, 34450 Istanbul, Turkey)

  • Miguel Lejeune

    (Department of Decision Sciences, George Washington University, Washington, District of Columbia 20052)

Abstract

We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main computational challenges in solving the problems of interest and provide an overview of various settings leading to tractable formulations. Some of the arising side results, such as the mathematical programming expressions for robustified risk measures in a discrete space, are also of independent interest. Finally, we rely on state-of-the-art modeling techniques from machine scheduling and humanitarian logistics to arrive at potentially practical applications, and present a numerical study for a novel risk-averse scheduling problem with controllable processing times. Summary of Contribution: In this study, we introduce a new class of optimization problems that simultaneously address distributional and decision-dependent uncertainty. We present a unified modeling framework along with a discussion on possible ways to specify the key model components, and discuss the main computational challenges in solving the complex problems of interest. Special care has been devoted to identifying the settings and problem classes where these challenges can be mitigated. In particular, we provide model reformulation results, including mathematical programming expressions for robustified risk measures, and describe how these results can be utilized to obtain tractable formulations for specific applied problems from the fields of humanitarian logistics and machine scheduling. Toward demonstrating the value of the modeling approach and investigating the performance of the proposed mixed-integer linear programming formulations, we conduct a computational study on a novel risk-averse machine scheduling problem with controllable processing times. We derive insights regarding the decision-making impact of our modeling approach and key parameter choices.

Suggested Citation

  • Nilay Noyan & Gábor Rudolf & Miguel Lejeune, 2022. "Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 729-751, March.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:2:p:729-751
    DOI: 10.1287/ijoc.2021.1096
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2021.1096
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2021.1096?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. Nilay Noyan & Gábor Rudolf, 2013. "Optimization with Multivariate Conditional Value-at-Risk Constraints," Operations Research, INFORMS, vol. 61(4), pages 990-1013, August.
    2. Nilay Noyan & Gábor Rudolf, 2015. "Kusuoka representations of coherent risk measures in general probability spaces," Annals of Operations Research, Springer, vol. 229(1), pages 591-605, June.
    3. Kelly J. Cormican & David P. Morton & R. Kevin Wood, 1998. "Stochastic Network Interdiction," Operations Research, INFORMS, vol. 46(2), pages 184-197, April.
    4. F. Hooshmand Khaligh & S.A. MirHassani, 2016. "A mathematical model for vehicle routing problem under endogenous uncertainty," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 579-590, January.
    5. Chang, Zhiqi & Song, Shiji & Zhang, Yuli & Ding, Jian-Ya & Zhang, Rui & Chiong, Raymond, 2017. "Distributionally robust single machine scheduling with risk aversion," European Journal of Operational Research, Elsevier, vol. 256(1), pages 261-274.
    6. Lejeune, Miguel A. & Shen, Siqian, 2016. "Multi-objective probabilistically constrained programs with variable risk: Models for multi-portfolio financial optimization," European Journal of Operational Research, Elsevier, vol. 252(2), pages 522-539.
    7. Pflug, Georg Ch. & Pichler, Alois & Wozabal, David, 2012. "The 1/N investment strategy is optimal under high model ambiguity," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 410-417.
    8. Georg Ch. Pflug & Alois Pichler, 2011. "Approximations for Probability Distributions and Stochastic Optimization Problems," International Series in Operations Research & Management Science, in: Marida Bertocchi & Giorgio Consigli & Michael A. H. Dempster (ed.), Stochastic Optimization Methods in Finance and Energy, edition 1, chapter 0, pages 343-387, Springer.
    9. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    10. Semih Atakan & Kerem Bülbül & Nilay Noyan, 2017. "Minimizing value-at-risk in single-machine scheduling," Annals of Operations Research, Springer, vol. 248(1), pages 25-73, January.
    11. Tore Jonsbråten & Roger Wets & David Woodruff, 1998. "A class of stochastic programs withdecision dependent random elements," Annals of Operations Research, Springer, vol. 82(0), pages 83-106, August.
    12. David Wozabal, 2014. "Robustifying Convex Risk Measures for Linear Portfolios: A Nonparametric Approach," Operations Research, INFORMS, vol. 62(6), pages 1302-1315, December.
    13. Hanif D. Sherali & Warren P. Adams & Patrick J. Driscoll, 1998. "Exploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problems," Operations Research, INFORMS, vol. 46(3), pages 396-405, June.
    14. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    15. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    16. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    17. Georg Pflug & David Wozabal, 2007. "Ambiguity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 435-442.
    18. Ran Ji & Miguel A. Lejeune, 2021. "Data-driven distributionally robust chance-constrained optimization with Wasserstein metric," Journal of Global Optimization, Springer, vol. 79(4), pages 779-811, April.
    19. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    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. Viet Anh Nguyen & Soroosh Shafiee & Damir Filipovi'c & Daniel Kuhn, 2021. "Mean-Covariance Robust Risk Measurement," Papers 2112.09959, arXiv.org, revised Nov 2023.
    2. Viet Anh Nguyen & Fan Zhang & Shanshan Wang & Jose Blanchet & Erick Delage & Yinyu Ye, 2021. "Robustifying Conditional Portfolio Decisions via Optimal Transport," Papers 2103.16451, arXiv.org, revised Apr 2024.
    3. Antonio J. Conejo & Nicholas G. Hall & Daniel Zhuoyu Long & Runhao Zhang, 2021. "Robust Capacity Planning for Project Management," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1533-1550, October.
    4. Wang, Fan & Zhang, Chao & Zhang, Hui & Xu, Liang, 2021. "Short-term physician rescheduling model with feature-driven demand for mental disorders outpatients," Omega, Elsevier, vol. 105(C).
    5. 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).
    6. Yannan Chen & Hailin Sun & Huifu Xu, 2021. "Decomposition and discrete approximation methods for solving two-stage distributionally robust optimization problems," Computational Optimization and Applications, Springer, vol. 78(1), pages 205-238, January.
    7. David Wozabal, 2014. "Robustifying Convex Risk Measures for Linear Portfolios: A Nonparametric Approach," Operations Research, INFORMS, vol. 62(6), pages 1302-1315, December.
    8. Wei Liu & Li Yang & Bo Yu, 2022. "Kernel density estimation based distributionally robust mean-CVaR portfolio optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 1053-1077, December.
    9. Wei Liu & Li Yang & Bo Yu, 2021. "KDE distributionally robust portfolio optimization with higher moment coherent risk," Annals of Operations Research, Springer, vol. 307(1), pages 363-397, December.
    10. 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.
    11. Pengyu Qian & Zizhuo Wang & Zaiwen Wen, 2015. "A Composite Risk Measure Framework for Decision Making under Uncertainty," Papers 1501.01126, arXiv.org.
    12. Ran Ji & Miguel A. Lejeune, 2021. "Data-Driven Optimization of Reward-Risk Ratio Measures," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1120-1137, July.
    13. Steffen Rebennack, 2022. "Data-driven stochastic optimization for distributional ambiguity with integrated confidence region," Journal of Global Optimization, Springer, vol. 84(2), pages 255-293, October.
    14. Liu, Jia & Chen, Zhiping, 2018. "Time consistent multi-period robust risk measures and portfolio selection models with regime-switching," European Journal of Operational Research, Elsevier, vol. 268(1), pages 373-385.
    15. Ran Ji & Miguel A. Lejeune, 2021. "Data-driven distributionally robust chance-constrained optimization with Wasserstein metric," Journal of Global Optimization, Springer, vol. 79(4), pages 779-811, April.
    16. Postek, K.S. & den Hertog, D. & Melenberg, B., 2015. "Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures (revision of CentER DP 2014-031)," Discussion Paper 2015-047, Tilburg University, Center for Economic Research.
    17. Luo, Fengqiao & Mehrotra, Sanjay, 2019. "Decomposition algorithm for distributionally robust optimization using Wasserstein metric with an application to a class of regression models," European Journal of Operational Research, Elsevier, vol. 278(1), pages 20-35.
    18. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    19. Ch. Pflug, Georg & Timonina-Farkas, Anna & Hochrainer-Stigler, Stefan, 2017. "Incorporating model uncertainty into optimal insurance contract design," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 68-74.
    20. Napat Rujeerapaiboon & Daniel Kuhn & Wolfram Wiesemann, 2016. "Robust Growth-Optimal Portfolios," Management Science, INFORMS, vol. 62(7), pages 2090-2109, July.

    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:orijoc:v:34:y:2022:i:2:p:729-751. 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.