IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v255y2016i3p809-821.html
   My bibliography  Save this article

Appointment sequencing: Why the Smallest-Variance-First rule may not be optimal

Author

Listed:
  • Kong, Qingxia
  • Lee, Chung-Yee
  • Teo, Chung-Piaw
  • Zheng, Zhichao

Abstract

We study the design of a healthcare appointment system with a single physician and a group of patients whose service durations are stochastic. The challenge is to find the optimal arrival sequence for a group of mixed patients such that the expected total cost of patient waiting time and physician overtime is minimized. While numerous simulation studies report that sequencing patients by increasing order of variance of service duration (Smallest-Variance-First or SVF rule) performs extremely well in many environments, analytical results on optimal sequencing are known only for two patients. In this paper, we shed light on why it is so difficult to prove the optimality of the SVF rule in general. We first assume that the appointment intervals are fixed according to a given template and analytically investigate the optimality of the SVF rule. In particular, we show that the optimality of the SVF rule depends on two important factors: the number of patients in the system and the shape of service time distributions. The SVF rule is more likely to be optimal if the service time distributions are more positively skewed, but this advantage gradually disappears as the number of patients increases. These results partly explain why the optimality of the SVF rule can only be proved for a small number of patients, and why in practice, the SVF rule is usually observed to be superior, since most empirical distributions of the service durations are positively skewed, like log-normal distributions. The insights obtained from our analytical model apply to more general settings, including the cases where the service durations follow log-normal distributions and the appointment intervals are optimized.

Suggested Citation

  • Kong, Qingxia & Lee, Chung-Yee & Teo, Chung-Piaw & Zheng, Zhichao, 2016. "Appointment sequencing: Why the Smallest-Variance-First rule may not be optimal," European Journal of Operational Research, Elsevier, vol. 255(3), pages 809-821.
  • Handle: RePEc:eee:ejores:v:255:y:2016:i:3:p:809-821
    DOI: 10.1016/j.ejor.2016.06.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716304246
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2016.06.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Turkcan, Ayten & Zeng, Bo & Muthuraman, Kumar & Lawley, Mark, 2011. "Sequential clinical scheduling with service criteria," European Journal of Operational Research, Elsevier, vol. 214(3), pages 780-795, November.
    2. Wang, P. Patrick, 1999. "Sequencing and scheduling N customers for a stochastic server," European Journal of Operational Research, Elsevier, vol. 119(3), pages 729-738, December.
    3. 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.
    4. Mehmet A. Begen & Maurice Queyranne, 2011. "Appointment Scheduling with Discrete Random Durations," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 240-257, May.
    5. Lawrence W. Robinson & Rachel R. Chen, 2011. "Estimating the Implied Value of the Customer's Waiting Time," Manufacturing & Service Operations Management, INFORMS, vol. 13(1), pages 53-57, February.
    6. 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.
    7. Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2015. "Appointment Scheduling with Limited Distributional Information," Management Science, INFORMS, vol. 61(2), pages 316-334, February.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Yuan Gao & Qian Zhang & Chun Kit Lau & Bhagwat Ram, 2022. "Robust Appointment Scheduling in Healthcare," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    3. Matthias Grot & Simon Kugai & Lukas Degen & Isabel Wiemer & Brigitte Werners & Birgitta M. Weltermann, 2023. "Small Changes in Patient Arrival and Consultation Times Have Large Effects on Patients’ Waiting Times: Simulation Analyses for Primary Care," IJERPH, MDPI, vol. 20(3), pages 1-11, January.
    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. Weiwei Fan & L. Jeff Hong & Xiaowei Zhang, 2020. "Distributionally Robust Selection of the Best," Management Science, INFORMS, vol. 66(1), pages 190-208, January.
    6. 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.
    7. 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.
    8. Wu, Xueqi & Zhou, Shenghai, 2022. "Sequencing and scheduling appointments on multiple servers with stochastic service durations and customer arrivals," Omega, Elsevier, vol. 106(C).
    9. Carolin Bauerhenne & Rainer Kolisch & Andreas S. Schulz, 2024. "Robust Appointment Scheduling with Waiting Time Guarantees," Papers 2402.12561, arXiv.org.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2015. "Appointment Scheduling with Limited Distributional Information," Management Science, INFORMS, vol. 61(2), pages 316-334, February.
    7. Jin Qi, 2017. "Mitigating Delays and Unfairness in Appointment Systems," Management Science, INFORMS, vol. 63(2), pages 566-583, February.
    8. Alex Kuiper & Robert H. Lee, 2022. "Appointment Scheduling for Multiple Servers," Management Science, INFORMS, vol. 68(10), pages 7422-7440, October.
    9. 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.
    10. 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.
    11. 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.
    12. Wu, Xueqi & Zhou, Shenghai, 2022. "Sequencing and scheduling appointments on multiple servers with stochastic service durations and customer arrivals," Omega, Elsevier, vol. 106(C).
    13. 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.
    14. 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.
    15. Weiwei Fan & L. Jeff Hong & Xiaowei Zhang, 2020. "Distributionally Robust Selection of the Best," Management Science, INFORMS, vol. 66(1), pages 190-208, January.
    16. Wen-Ya Wang & Diwakar Gupta, 2011. "Adaptive Appointment Systems with Patient Preferences," Manufacturing & Service Operations Management, INFORMS, vol. 13(3), pages 373-389, July.
    17. Yong Liang & Mengshi Lu & Zuo‐Jun Max Shen & Runyu Tang, 2021. "Data Center Network Design for Internet‐Related Services and Cloud Computing," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2077-2101, July.
    18. 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.
    19. Zhan, Yang & Wang, Zizhuo & Wan, Guohua, 2021. "Home service routing and appointment scheduling with stochastic service times," European Journal of Operational Research, Elsevier, vol. 288(1), pages 98-110.
    20. Yuan Gao & Qian Zhang & Chun Kit Lau & Bhagwat Ram, 2022. "Robust Appointment Scheduling in Healthcare," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:255:y:2016:i:3:p:809-821. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.