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Technical Note---A Sampling-Based Approach to Appointment Scheduling

Author

Listed:
  • Mehmet A. Begen

    (Ivey School of Business, University of Western Ontario, London, Ontario N6A 3K7, Canada)

  • Retsef Levi

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139)

  • Maurice Queyranne

    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada)

Abstract

We consider the problem of appointment scheduling with discrete random durations but under the more realistic assumption that the duration probability distributions are not known and only a set of independent samples is available, e.g., historical data. For a given sequence of appointments (jobs, tasks), the goal is to determine the planned starting time of each appointment such that the expected total underage and overage costs due to the mismatch between allocated and realized durations is minimized. We use the convexity and subdifferential of the objective function of the appointment scheduling problem to determine bounds on the number of independent samples required to obtain a provably near-optimal solution with high probability.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:3:p:675-681
    DOI: 10.1287/opre.1120.1053
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    References listed on IDEAS

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    1. Mehmet A. Begen & Maurice Queyranne, 2011. "Appointment Scheduling with Discrete Random Durations," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 240-257, May.
    2. 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.
    3. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2007. "Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 821-839, November.
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    Citations

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    Cited by:

    1. 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.
    2. Christos Zacharias & Tallys Yunes, 2020. "Multimodularity in the Stochastic Appointment Scheduling Problem with Discrete Arrival Epochs," Management Science, INFORMS, vol. 66(2), pages 744-763, February.
    3. Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2015. "Appointment Scheduling with Limited Distributional Information," Management Science, INFORMS, vol. 61(2), pages 316-334, February.
    4. 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.
    5. Wang Chi Cheung & David Simchi-Levi, 2019. "Sampling-Based Approximation Schemes for Capacitated Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 668-692, May.
    6. Khaniyev, Taghi & Kayış, Enis & Güllü, Refik, 2020. "Next-day operating room scheduling with uncertain surgery durations: Exact analysis and heuristics," European Journal of Operational Research, Elsevier, vol. 286(1), pages 49-62.
    7. Ruiwei Jiang & Siqian Shen & Yiling Zhang, 2017. "Integer Programming Approaches for Appointment Scheduling with Random No-Shows and Service Durations," Operations Research, INFORMS, vol. 65(6), pages 1638-1656, December.
    8. Mohammad Heydari & Kin Keung Lai & Yanan Fan & Xiaoyang Li, 2022. "A Review of Emergency and Disaster Management in the Process of Healthcare Operation Management for Improving Hospital Surgical Intake Capacity," Mathematics, MDPI, vol. 10(15), pages 1-34, August.
    9. van Eekelen, Wouter, 2023. "Distributionally robust views on queues and related stochastic models," Other publications TiSEM 9b99fc05-9d68-48eb-ae8c-9, Tilburg University, School of Economics and Management.
    10. Yifei Sun & Usha Nandini Raghavan & Vikrant Vaze & Christopher S Hall & Patricia Doyle & Stacey Sullivan Richard & Christoph Wald, 2021. "Stochastic programming for outpatient scheduling with flexible inpatient exam accommodation," Health Care Management Science, Springer, vol. 24(3), pages 460-481, September.
    11. Arden Baxter & Pinar Keskinocak & Mohit Singh, 2023. "Heterogeneous Multi-resource Planning and Allocation Under Stochastic Demand," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 929-951, September.
    12. 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.
    13. Ahmadi-Javid, Amir & Jalali, Zahra & Klassen, Kenneth J, 2017. "Outpatient appointment systems in healthcare: A review of optimization studies," European Journal of Operational Research, Elsevier, vol. 258(1), pages 3-34.
    14. Dogru, Ali K. & Melouk, Sharif H., 2019. "Adaptive appointment scheduling for patient-centered medical homes," Omega, Elsevier, vol. 85(C), pages 166-181.
    15. Xi Chen & Liu Zhao & Haiming Liang & Kin Keung Lai, 2019. "Matching patients and healthcare service providers: a novel two-stage method based on knowledge rules and OWA-NSGA-II algorithm," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 221-247, January.
    16. Shenghai Zhou & Yichuan Ding & Woonghee Tim Huh & Guohua Wan, 2021. "Constant Job‐Allowance Policies for Appointment Scheduling: Performance Bounds and Numerical Analysis," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2211-2231, July.
    17. Zhou, Shenghai & Li, Debiao & Yin, Yong, 2021. "Coordinated appointment scheduling with multiple providers and patient-and-physician matching cost in specialty care," Omega, Elsevier, vol. 101(C).
    18. Pinar Keskinocak & Nicos Savva, 2020. "A Review of the Healthcare-Management (Modeling) Literature Published in Manufacturing & Service Operations Management," Manufacturing & Service Operations Management, INFORMS, vol. 22(1), pages 59-72, January.

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