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Goal-Driven Optimization

Author

Listed:
  • Wenqing Chen

    (NUS Business School, National University of Singapore, Singapore)

  • Melvyn Sim

    (NUS Business School, NUS Risk Management Institute, National University of Singapore and Singapore-MIT Alliance (SMA), Singapore)

Abstract

We develop a goal-driven stochastic optimization model that considers a random objective function in achieving an aspiration level, target, or goal. Our model maximizes the shortfall-aware aspiration-level criterion, which encompasses the probability of success in achieving the aspiration level and an expected level of underperformance or shortfall. The key advantage of the proposed model is its tractability. We can obtain its solution by solving a small collection of stochastic linear optimization problems with objectives evaluated under the popular conditional-value-at-risk (CVaR) measure. Using techniques in robust optimization, we propose a decision-rule-based deterministic approximation of the goal-driven optimization problem by solving subproblems whose number is a polynomial with respect to the accuracy, with each subproblem being a second-order cone optimization problem (SOCP). We compare the numerical performance of the deterministic approximation with sampling-based approximation and report the computational insights on a multiproduct newsvendor problem.

Suggested Citation

  • Wenqing Chen & Melvyn Sim, 2009. "Goal-Driven Optimization," Operations Research, INFORMS, vol. 57(2), pages 342-357, April.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:2:p:342-357
    DOI: 10.1287/opre.1080.0570
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    References listed on IDEAS

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    1. Lau, Hon-Shiang & Hing-Ling Lau, Amy, 1996. "The newsstand problem: A capacitated multiple-product single-period inventory problem," European Journal of Operational Research, Elsevier, vol. 94(1), pages 29-42, October.
    2. Enrico Diecidue & Jeroen van de Ven, 2008. "Aspiration Level, Probability Of Success And Failure, And Expected Utility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(2), pages 683-700, May.
    3. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    4. Robert Bordley & Marco LiCalzi, 2000. "Decision analysis using targets instead of utility functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 23(1), pages 53-74.
    5. 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.
    6. Mao, James C T, 1970. "Survey of Capital Budgeting: Theory and Practice," Journal of Finance, American Finance Association, vol. 25(2), pages 349-360, May.
    7. E. Sankarasubramanian & S. Kumaraswamy, 1983. "Note---Note on "Optimal Ordering Quantity to Realize a Pre-Determined Level of Profit"," Management Science, INFORMS, vol. 29(4), pages 512-514, April.
    8. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2008. "Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization," Management Science, INFORMS, vol. 54(3), pages 573-585, March.
    9. A. Charnes & W. W. Cooper & G. H. Symonds, 1958. "Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil," Management Science, INFORMS, vol. 4(3), pages 235-263, April.
    10. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    11. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    12. Xin Chen & Melvyn Sim & Peng Sun, 2007. "A Robust Optimization Perspective on Stochastic Programming," Operations Research, INFORMS, vol. 55(6), pages 1058-1071, December.
    13. John W. Payne & Dan J. Laughhunn & Roy Crum, 1981. "Note---Further Tests of Aspiration Level Effects in Risky Choice Behavior," Management Science, INFORMS, vol. 27(8), pages 953-958, August.
    14. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    15. Xin Chen & Melvyn Sim & Peng Sun & Jiawei Zhang, 2008. "A Linear Decision-Based Approximation Approach to Stochastic Programming," Operations Research, INFORMS, vol. 56(2), pages 344-357, April.
    16. John W. Payne & Dan J. Laughhunn & Roy Crum, 1980. "Translation of Gambles and Aspiration Level Effects in Risky Choice Behavior," Management Science, INFORMS, vol. 26(10), pages 1039-1060, October.
    17. Mihai Dragomirescu, 1972. "An Algorithm for the Minimum-Risk Problem of Stochastic Programming," Operations Research, INFORMS, vol. 20(1), pages 154-164, February.
    18. Erio Castagnoli & Marco LiCalzi, 2005. "Expected utility without utility," Game Theory and Information 0508004, University Library of Munich, Germany.
    19. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
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    Cited by:

    1. 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.
    2. Zhang, Yu & Tang, Jiafu, 2018. "A robust optimization approach for itinerary planning with deadline," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 113(C), pages 56-74.
    3. Huan Xu & Constantine Caramanis & Shie Mannor, 2012. "Optimization Under Probabilistic Envelope Constraints," Operations Research, INFORMS, vol. 60(3), pages 682-699, June.
    4. Shin, Youngchul & Lee, Sangyoon & Moon, Ilkyeong, 2020. "Robust multiperiod inventory model considering trade-in program and refurbishment service: Implications to emerging markets," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(C).
    5. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    6. Yun Fong Lim & Chen Wang, 2017. "Inventory Management Based on Target-Oriented Robust Optimization," Management Science, INFORMS, vol. 63(12), pages 4409-4427, December.
    7. Xin, Linwei & Goldberg, David A., 2021. "Time (in)consistency of multistage distributionally robust inventory models with moment constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1127-1141.
    8. Nicholas G. Hall & Daniel Zhuoyu Long & Jin Qi & Melvyn Sim, 2015. "Managing Underperformance Risk in Project Portfolio Selection," Operations Research, INFORMS, vol. 63(3), pages 660-675, June.
    9. Liu, Kanglin & Li, Qiaofeng & Zhang, Zhi-Hai, 2019. "Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 79-101.
    10. Dimitris Bertsimas & Melvyn Sim & Meilin Zhang, 2019. "Adaptive Distributionally Robust Optimization," Management Science, INFORMS, vol. 65(2), pages 604-618, February.
    11. Shao-Wei Lam & Tsan Sheng Ng & Melvyn Sim & Jin-Hwa Song, 2013. "Multiple Objectives Satisficing Under Uncertainty," Operations Research, INFORMS, vol. 61(1), pages 214-227, February.
    12. Baron, Opher & Berman, Oded & Fazel-Zarandi, Mohammad M. & Roshanaei, Vahid, 2019. "Almost Robust Discrete Optimization," European Journal of Operational Research, Elsevier, vol. 276(2), pages 451-465.
    13. Shin, Youngchul & Lee, Sangyoon & Moon, Ilkyeong, 2021. "Robust multiperiod inventory model with a new type of buy one get one promotion: “My Own Refrigerator”," Omega, Elsevier, vol. 99(C).
    14. Yuan Yuan & Zukui Li & Biao Huang, 2017. "Robust optimization approximation for joint chance constrained optimization problem," Journal of Global Optimization, Springer, vol. 67(4), pages 805-827, April.
    15. Rahimian, Hamed & Bayraksan, Güzin & Homem-de-Mello, Tito, 2019. "Controlling risk and demand ambiguity in newsvendor models," European Journal of Operational Research, Elsevier, vol. 279(3), pages 854-868.
    16. Jin Qi, 2017. "Mitigating Delays and Unfairness in Appointment Systems," Management Science, INFORMS, vol. 63(2), pages 566-583, February.
    17. Pavel Bazovkin & Karl Mosler, 2015. "A general solution for robust linear programs with distortion risk constraints," Annals of Operations Research, Springer, vol. 229(1), pages 103-120, June.
    18. Maximilian Zellner & Ali E. Abbas, 2023. "Experimental Assessment of Utility Functions Induced by Fixed and Uncertain Targets," Decision Analysis, INFORMS, vol. 20(3), pages 187-201, September.
    19. Zhang, Yu & Tang, Jiafu, 2018. "Itinerary planning with time budget for risk-averse travelers," European Journal of Operational Research, Elsevier, vol. 267(1), pages 288-303.

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    programming; stochastic;

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