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Sequencing Appointments for Service Systems Using Inventory Approximations

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  • Ho-Yin Mak

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

  • Ying Rong

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

  • Jiawei Zhang

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

Abstract

Managing appointments for service systems with random job durations is a challenging task. We consider a class of appointment planning problems that involve two sets of decisions: job sequencing , i.e., determining the order in which a list of jobs should be performed by the server, and appointment scheduling , i.e., planning the starting times for jobs. These decisions are interconnected because their joint goal is to minimize the expected server idle time and job late-start penalty costs incurred because of randomness in job durations. In this paper, we design new heuristics for sequencing appointments. The idea behind the development of these heuristics is the structural connection between such appointment scheduling problems and stochastic inventory control in serial supply chains. In particular, the decision of determining time allowances as buffers against random job durations is analogous to that of selecting inventory levels as buffers to accommodate random demand in a supply chain; having excess buffers in appointment scheduling and supply chain settings incurs idle time and excess inventory holding costs, respectively, and having inadequate buffers leads to delays of subsequent jobs and backorders, respectively. Recognizing this connection, we propose tractable approximations for the job sequencing problem, obtain several insights, and further develop a very simple sequencing rule of ordering jobs by duration variance to late-start penalty cost ratio. Computational results show that our proposed heuristics produce close-to-optimal job sequences with significantly reduced computation times compared with those produced using an exact mixed-integer stochastic programming formulation based on the sample-average approximation approach.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormsom:v:16:y:2014:i:2:p:251-262
    DOI: 10.1287/msom.2013.0470
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    References listed on IDEAS

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    Cited by:

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    3. William P. Millhiser & Emre A. Veral, 2019. "A decision support system for real-time scheduling of multiple patient classes in outpatient services," Health Care Management Science, Springer, vol. 22(1), pages 180-195, March.
    4. 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.
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    6. Wu, Xueqi & Zhou, Shenghai, 2022. "Sequencing and scheduling appointments on multiple servers with stochastic service durations and customer arrivals," Omega, Elsevier, vol. 106(C).
    7. Jin Qi, 2017. "Mitigating Delays and Unfairness in Appointment Systems," Management Science, INFORMS, vol. 63(2), pages 566-583, February.
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    9. 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).
    10. Shen, Zuo-Jun Max & Xie, Jingui & Zheng, Zhichao & Zhou, Han, 2023. "Dynamic scheduling with uncertain job types," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1047-1060.
    11. Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2015. "Appointment Scheduling with Limited Distributional Information," Management Science, INFORMS, vol. 61(2), pages 316-334, February.
    12. Chang, Zhiqi & Ding, Jian-Ya & Song, Shiji, 2019. "Distributionally robust scheduling on parallel machines under moment uncertainty," European Journal of Operational Research, Elsevier, vol. 272(3), pages 832-846.
    13. Kuang, Xiaolong & Lamadrid, Alberto J. & Zuluaga, Luis F., 2019. "Pricing in non-convex markets with quadratic deliverability costs," Energy Economics, Elsevier, vol. 80(C), pages 123-131.
    14. Paola Cappanera & Filippo Visintin & Carlo Banditori & Daniele Feo, 2019. "Evaluating the long-term effects of appointment scheduling policies in a magnetic resonance imaging setting," Flexible Services and Manufacturing Journal, Springer, vol. 31(1), pages 212-254, March.
    15. Miao Bai & Robert H. Storer & Gregory L. Tonkay, 2022. "Surgery Sequencing Coordination with Recovery Resource Constraints," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1207-1223, March.
    16. Christos Zacharias & Michael Pinedo, 2017. "Managing Customer Arrivals in Service Systems with Multiple Identical Servers," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 639-656, October.
    17. 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.
    18. Christos Zacharias & Mor Armony, 2017. "Joint Panel Sizing and Appointment Scheduling in Outpatient Care," Management Science, INFORMS, vol. 63(11), pages 3978-3997, November.
    19. 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.
    20. Yuanzheng Ma & Tong Wang & Huan Zheng, 2023. "On fairness and efficiency in nonprofit operations: Dynamic resource allocations," Production and Operations Management, Production and Operations Management Society, vol. 32(6), pages 1778-1792, June.
    21. Avishai Mandelbaum & Petar Momčilović & Nikolaos Trichakis & Sarah Kadish & Ryan Leib & Craig A. Bunnell, 2020. "Data-Driven Appointment-Scheduling Under Uncertainty: The Case of an Infusion Unit in a Cancer Center," Management Science, INFORMS, vol. 66(1), pages 243-270, January.
    22. 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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