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Appointment Scheduling with Limited Distributional Information

Author

Listed:
  • Ho-Yin Mak

    (Department of Industrial Engineering and Logistics Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Ying Rong

    (Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, China)

  • Jiawei Zhang

    (Department of Information, Operations, and Management Sciences, Stern School of Business, New York University, New York, New York 10012)

Abstract

In this paper, we develop distribution-free models that solve the appointment sequencing and scheduling problem by assuming only moments information of job durations. We show that our min--max appointment scheduling models, which minimize the worst-case expected waiting and overtime costs out of all probability distributions with the given marginal moments, can be exactly formulated as tractable conic programs. These formulations are obtained by exploiting hidden convexity of the problem. In the special case where only the first two marginal moments are given, the problem can be reformulated as a second-order cone program. Based on the structural properties of this formulation, under a mild condition, we derive the optimal time allowances in closed form and prove that it is optimal to sequence jobs in increasing order of job duration variance. We also prove similar results regarding the optimal time allowances and sequence for the case where only means and supports of job durations are known. This paper was accepted by Dimitris Bertsimas, optimization .

Suggested Citation

  • Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2015. "Appointment Scheduling with Limited Distributional Information," Management Science, INFORMS, vol. 61(2), pages 316-334, February.
    • Handle: RePEc:inm:ormnsc:v:61:y:2015:i:2:p:316-334
    DOI: 10.1287/mnsc.2013.1881
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    References listed on IDEAS

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    1. John R. Birge & Roger J.-B. Wets, 1987. "Computing Bounds for Stochastic Programming Problems by Means of a Generalized Moment Problem," Mathematics of Operations Research, INFORMS, vol. 12(1), pages 149-162, February.
    2. Qingxia Kong & Chung-Yee Lee & Chung-Piaw Teo & Zhichao Zheng, 2013. "Scheduling Arrivals to a Stochastic Service Delivery System Using Copositive Cones," Operations Research, INFORMS, vol. 61(3), pages 711-726, June.
    3. Guido Kaandorp & Ger Koole, 2007. "Optimal outpatient appointment scheduling," Health Care Management Science, Springer, vol. 10(3), pages 217-229, September.
    4. Mehmet A. Begen & Retsef Levi & Maurice Queyranne, 2012. "Technical Note---A Sampling-Based Approach to Appointment Scheduling," Operations Research, INFORMS, vol. 60(3), pages 675-681, June.
    5. Mehmet A. Begen & Maurice Queyranne, 2011. "Appointment Scheduling with Discrete Random Durations," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 240-257, May.
    6. Federico Sabria & Carlos F. Daganzo, 1989. "Approximate Expressions for Queueing Systems with Scheduled Arrivals and Established Service Order," Transportation Science, INFORMS, vol. 23(3), pages 159-165, August.
    7. Li Chen & Simai He & Shuzhong Zhang, 2011. "Tight Bounds for Some Risk Measures, with Applications to Robust Portfolio Selection," Operations Research, INFORMS, vol. 59(4), pages 847-865, August.
    8. Willard I. Zangwill, 1966. "A Deterministic Multi-Period Production Scheduling Model with Backlogging," Management Science, INFORMS, vol. 13(1), pages 105-119, September.
    9. Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2014. "Sequencing Appointments for Service Systems Using Inventory Approximations," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 251-262, May.
    10. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    11. 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.
    12. Karthik Natarajan & Chung Piaw Teo & Zhichao Zheng, 2011. "Mixed 0-1 Linear Programs Under Objective Uncertainty: A Completely Positive Representation," Operations Research, INFORMS, vol. 59(3), pages 713-728, June.
    13. Brian Denton & James Viapiano & Andrea Vogl, 2007. "Optimization of surgery sequencing and scheduling decisions under uncertainty," Health Care Management Science, Springer, vol. 10(1), pages 13-24, February.
    14. Dimitris Bertsimas & Xuan Vinh Doan & Karthik Natarajan & Chung-Piaw Teo, 2010. "Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 580-602, August.
    15. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    16. John R. Birge & Marilyn J. Maddox, 1995. "Bounds on Expected Project Tardiness," Operations Research, INFORMS, vol. 43(5), pages 838-850, October.
    17. Camilo Mancilla & Robert Storer, 2012. "A sample average approximation approach to stochastic appointment sequencing and scheduling," IISE Transactions, Taylor & Francis Journals, vol. 44(8), pages 655-670.
    18. P. Patrick Wang, 1993. "Static and dynamic scheduling of customer arrivals to a single‐server system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 345-360, April.
    19. Willard I. Zangwill, 1969. "A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System--A Network Approach," Management Science, INFORMS, vol. 15(9), pages 506-527, May.
    20. NESTEROV, Yurii, 1997. "Structure of non-negative polynomials and optimization problems," LIDAM Discussion Papers CORE 1997049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    21. Karthik Natarajan & Miao Song & Chung-Piaw Teo, 2009. "Persistency Model and Its Applications in Choice Modeling," Management Science, INFORMS, vol. 55(3), pages 453-469, March.
    22. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    23. Dongdong Ge & Guohua Wan & Zizhuo Wang & Jiawei Zhang, 2014. "A Note on Appointment Scheduling with Piecewise Linear Cost Functions," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1244-1251, November.
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