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Integer Programming Approaches for Appointment Scheduling with Random No-Shows and Service Durations

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  • Ruiwei Jiang

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

  • Siqian Shen

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

  • Yiling Zhang

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

Abstract

We consider a single-server scheduling problem given a fixed sequence of appointment arrivals with random no-shows and service durations. The probability distribution of the uncertain parameters is assumed to be ambiguous, and only the support and first moments are known. We formulate a class of distributionally robust (DR) optimization models that incorporate the worst-case expectation/conditional value-at-risk penalty cost of appointment waiting, server idleness, and overtime into the objective or constraints. Our models flexibly adapt to different prior beliefs of no-show uncertainty. We obtain exact mixed-integer nonlinear programming reformulations and derive valid inequalities to strengthen the reformulations that are solved by decomposition algorithms. In particular, we derive convex hulls for special cases of no-show beliefs, yielding polynomial-sized linear programming models for the least and the most conservative supports of no-shows. We test various instances to demonstrate the computational efficacy of our approaches and to compare the results of various DR models given perfect or ambiguous distributional information.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:6:p:1638-1656
    DOI: 10.1287/opre.2017.1656
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    6. 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.
    7. Kuiper, Alex & de Mast, Jeroen & Mandjes, Michel, 2021. "The problem of appointment scheduling in outpatient clinics: A multiple case study of clinical practice," Omega, Elsevier, vol. 98(C).
    8. Qingxia Kong & Shan Li & Nan Liu & Chung-Piaw Teo & Zhenzhen Yan, 2020. "Appointment Scheduling Under Time-Dependent Patient No-Show Behavior," Management Science, INFORMS, vol. 66(8), pages 3480-3500, August.
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    10. Yu Fu & Amarnath Banerjee, 2021. "A Stochastic Programming Model for Service Scheduling with Uncertain Demand: an Application in Open-Access Clinic Scheduling," SN Operations Research Forum, Springer, vol. 2(3), pages 1-32, September.
    11. Shan Wang & Nan Liu & Guohua Wan, 2020. "Managing Appointment-Based Services in the Presence of Walk-in Customers," Management Science, INFORMS, vol. 66(2), pages 667-686, February.
    12. Shehadeh, Karmel S. & Cohn, Amy E.M. & Jiang, Ruiwei, 2020. "A distributionally robust optimization approach for outpatient colonoscopy scheduling," European Journal of Operational Research, Elsevier, vol. 283(2), pages 549-561.
    13. Tito Homem-de-Mello & Qingxia Kong & Rodrigo Godoy-Barba, 2022. "A Simulation Optimization Approach for the Appointment Scheduling Problem with Decision-Dependent Uncertainties," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2845-2865, September.
    14. Arlen Dean & Amirhossein Meisami & Henry Lam & Mark P. Van Oyen & Christopher Stromblad & Nick Kastango, 2022. "Quantile regression forests for individualized surgery scheduling," Health Care Management Science, Springer, vol. 25(4), pages 682-709, December.
    15. Yu Zhang & Zhenzhen Zhang & Andrew Lim & Melvyn Sim, 2021. "Robust Data-Driven Vehicle Routing with Time Windows," Operations Research, INFORMS, vol. 69(2), pages 469-485, March.
    16. Liping Zhou & Na Geng & Zhibin Jiang & Shan Jiang, 2022. "Integrated Multiresource Capacity Planning and Multitype Patient Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 129-149, January.
    17. Tsang, Man Yiu & Shehadeh, Karmel S., 2023. "Stochastic optimization models for a home service routing and appointment scheduling problem with random travel and service times," European Journal of Operational Research, Elsevier, vol. 307(1), pages 48-63.
    18. 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.
    19. Shehadeh, Karmel S. & Cohn, Amy E.M. & Epelman, Marina A., 2019. "Analysis of models for the Stochastic Outpatient Procedure Scheduling Problem," European Journal of Operational Research, Elsevier, vol. 279(3), pages 721-731.
    20. Lu, Haimin & Pei, Zhi, 2023. "Single machine scheduling with release dates: A distributionally robust approach," European Journal of Operational Research, Elsevier, vol. 308(1), pages 19-37.
    21. Wu, Xueqi & Zhou, Shenghai, 2022. "Sequencing and scheduling appointments on multiple servers with stochastic service durations and customer arrivals," Omega, Elsevier, vol. 106(C).
    22. Carolin Bauerhenne & Rainer Kolisch & Andreas S. Schulz, 2024. "Robust Appointment Scheduling with Waiting Time Guarantees," Papers 2402.12561, arXiv.org.
    23. Oualid Jouini & Saif Benjaafar & Bingnan Lu & Siqiao Li & Benjamin Legros, 2022. "Appointment-driven queueing systems with non-punctual customers," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 1-56, June.

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