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Static and dynamic scheduling of customer arrivals to a single‐server system

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  • P. Patrick Wang

Abstract

In this article we consider a single‐server system whose customers arrive by appointments only. Both static and dynamic scheduling problems are studied. In static scheduling problems, one considers scheduling a finite number of customer arrivals, assuming there is no scheduled customer arrival to the system. In dynamic scheduling problems, one considers scheduling one customer arrival only, assuming that there are a number of scheduled customers already. The expected delay time is recursively computed in terms of customer interarrival times for both cases. The objective is to minimize the weighted customer delay time and the server completion time. The problem is formulated as a set of nonlinear equations. Various numerical examples are illustrated. © 1993 John Wiley & Sons, Inc.

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  • 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.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:3:p:345-360
    DOI: 10.1002/1520-6750(199304)40:33.0.CO;2-N
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    1. 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.
    2. Mohan L. Chaudhry & Carl M. Harris & William G. Marchal, 1990. "Robustness of Rootfinding in Single-Server Queueing Models," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 273-286, August.
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    Cited by:

    1. Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2015. "Appointment Scheduling with Limited Distributional Information," Management Science, INFORMS, vol. 61(2), pages 316-334, February.
    2. 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.
    3. Illana Bendavid & Yariv N. Marmor & Boris Shnits, 2018. "Developing an optimal appointment scheduling for systems with rigid standby time under pre-determined quality of service," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 54-77, June.
    4. Mahes, Roshan & Mandjes, Michel & Boon, Marko & Taylor, Peter, 2024. "Adaptive scheduling in service systems: A Dynamic programming approach," European Journal of Operational Research, Elsevier, vol. 312(2), pages 605-626.
    5. Dongyang Wang & Kumar Muthuraman & Douglas Morrice, 2019. "Coordinated Patient Appointment Scheduling for a Multistation Healthcare Network," Operations Research, INFORMS, vol. 67(3), pages 599-618, May.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. S. Ayca Erdogan & Brian Denton, 2013. "Dynamic Appointment Scheduling of a Stochastic Server with Uncertain Demand," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 116-132, February.
    12. 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.
    13. Peter M. Vanden Bosch & Dennis C. Dietz & John R. Simeoni, 1999. "Scheduling customer arrivals to a stochastic service system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 549-559, August.
    14. Mehmet A. Begen & Maurice Queyranne, 2011. "Appointment Scheduling with Discrete Random Durations," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 240-257, May.
    15. Sakine Batun & Brian T. Denton & Todd R. Huschka & Andrew J. Schaefer, 2011. "Operating Room Pooling and Parallel Surgery Processing Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 220-237, May.
    16. Tugba Cayirli & Kum Khiong Yang & Ser Aik Quek, 2012. "A Universal Appointment Rule in the Presence of No‐Shows and Walk‐Ins," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 682-697, July.
    17. Shnits, Boris & Bendavid, Illana & Marmor, Yariv N., 2020. "An appointment scheduling policy for healthcare systems with parallel servers and pre-determined quality of service," Omega, Elsevier, vol. 97(C).
    18. Jin Qi, 2017. "Mitigating Delays and Unfairness in Appointment Systems," Management Science, INFORMS, vol. 63(2), pages 566-583, February.
    19. Creemers, Stefan & Lambrecht, Marc R. & Beliën, Jeroen & Van den Broeke, Maud, 2021. "Evaluation of appointment scheduling rules: A multi-performance measurement approach," Omega, Elsevier, vol. 100(C).

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