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Data-Driven Percentile Optimization for Multi-Class Queueing Systems with Model Ambiguity: Theory and Application

Author

Listed:
  • Bren, Austin

    (Arizona State University)

  • Saghafian, Soroush

    (Harvard University)

Abstract

Multi-class queueing systems widely used in operations research and management typically experience ambiguity in real world settings in the form of unknown parameters. For such systems, we incorporate robustness in the control policies by applying a data-driven percentile optimization technique that allows for (1) expressing a controller’s optimism level toward ambiguity, and (2) utilizing incoming data in order to learn the true system parameters. We show that the optimal policy under the percentile optimization objective is related to a closed-form priority-based policy. We also identify connections between the optimal percentile optimization and cµ-like policies, which in turn enables us to establish effective but easy-to-use heuristics for implementation in complex systems. Using real-world data collected from a leading U.S. hospital, we also apply our approach to a hospital Emergency Department (ED) setting, and demonstrate the benefits of using our framework for improving current patient flow policies.

Suggested Citation

  • Bren, Austin & Saghafian, Soroush, 2018. "Data-Driven Percentile Optimization for Multi-Class Queueing Systems with Model Ambiguity: Theory and Application," Working Paper Series rwp18-008, Harvard University, John F. Kennedy School of Government.
    • Handle: RePEc:ecl:harjfk:rwp18-008
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    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. Erick Delage & Shie Mannor, 2010. "Percentile Optimization for Markov Decision Processes with Parameter Uncertainty," Operations Research, INFORMS, vol. 58(1), pages 203-213, February.
    4. Yiwei Chen & Vivek F. Farias, 2013. "Simple Policies for Dynamic Pricing with Imperfect Forecasts," Operations Research, INFORMS, vol. 61(3), pages 612-624, June.
    5. Soroush Saghafian & Wallace J. Hopp & Mark P. Van Oyen & Jeffrey S. Desmond & Steven L. Kronick, 2014. "Complexity-Augmented Triage: A Tool for Improving Patient Safety and Operational Efficiency," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 329-345, July.
    6. Hao Zhang, 2010. "Partially Observable Markov Decision Processes: A Geometric Technique and Analysis," Operations Research, INFORMS, vol. 58(1), pages 214-228, February.
    7. Dimitris Bertsimas & David Gamarnik & Alexander Anatoliy Rikun, 2011. "Performance Analysis of Queueing Networks via Robust Optimization," Operations Research, INFORMS, vol. 59(2), pages 455-466, April.
    8. Christos H. Papadimitriou & John N. Tsitsiklis, 1987. "The Complexity of Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 441-450, August.
    9. Richard D. Smallwood & Edward J. Sondik, 1973. "The Optimal Control of Partially Observable Markov Processes over a Finite Horizon," Operations Research, INFORMS, vol. 21(5), pages 1071-1088, October.
    10. Soroush Saghafian & Wallace J. Hopp & Mark P. Van Oyen & Jeffrey S. Desmond & Steven L. Kronick, 2012. "Patient Streaming as a Mechanism for Improving Responsiveness in Emergency Departments," Operations Research, INFORMS, vol. 60(5), pages 1080-1097, October.
    11. Arnab Nilim & Laurent El Ghaoui, 2005. "Robust Control of Markov Decision Processes with Uncertain Transition Matrices," Operations Research, INFORMS, vol. 53(5), pages 780-798, October.
    12. Hansen, Lars Peter & Sargent, Thomas J., 2007. "Recursive robust estimation and control without commitment," Journal of Economic Theory, Elsevier, vol. 136(1), pages 1-27, September.
    13. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    14. Shie Mannor & Duncan Simester & Peng Sun & John N. Tsitsiklis, 2007. "Bias and Variance Approximation in Value Function Estimates," Management Science, INFORMS, vol. 53(2), pages 308-322, February.
    15. Wolfram Wiesemann & Daniel Kuhn & Berç Rustem, 2013. "Robust Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 153-183, February.
    16. Nilay Tan{i}k Argon & Serhan Ziya, 2009. "Priority Assignment Under Imperfect Information on Customer Type Identities," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 674-693, June.
    17. Andrew E. B. Lim & J. George Shanthikumar & Gah-Yi Vahn, 2012. "Robust Portfolio Choice with Learning in the Framework of Regret: Single-Period Case," Management Science, INFORMS, vol. 58(9), pages 1732-1746, September.
    18. Garud N. Iyengar, 2005. "Robust Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 257-280, May.
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