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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
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    References listed on IDEAS

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    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.
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