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Robust Appointment Scheduling with Waiting Time Guarantees

Author

Listed:
  • Carolin Bauerhenne
  • Rainer Kolisch
  • Andreas S. Schulz

Abstract

Appointment scheduling problems under uncertainty encounter a fundamental trade-off between cost minimization and customer waiting times. Most existing studies address this trade-off using a weighted sum approach, which puts little emphasis on individual waiting times and, thus, customer satisfaction. In contrast, we study how to minimize total cost while providing waiting time guarantees to all customers. Given box uncertainty sets for service times and no-shows, we introduce the Robust Appointment Scheduling Problem with Waiting Time Guarantees. We show that the problem is NP-hard in general and introduce a mixed-integer linear program that can be solved in reasonable computation time. For special cases, we prove that polynomial-time variants of the well-known Smallest-Variance-First sequencing rule and the Bailey-Welch scheduling rule are optimal. Furthermore, a case study with data from the radiology department of a large university hospital demonstrates that the approach not only guarantees acceptable waiting times but, compared to existing robust approaches, may simultaneously reduce costs incurred by idle time and overtime. This work suggests that limiting instead of minimizing customer waiting times is a win-win solution in the trade-off between customer satisfaction and cost minimization. Additionally, it provides an easy-to-implement and customizable appointment scheduling framework with waiting time guarantees.

Suggested Citation

  • Carolin Bauerhenne & Rainer Kolisch & Andreas S. Schulz, 2024. "Robust Appointment Scheduling with Waiting Time Guarantees," Papers 2402.12561, arXiv.org.
  • Handle: RePEc:arx:papers:2402.12561
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    References listed on IDEAS

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    1. Jin Qi, 2017. "Mitigating Delays and Unfairness in Appointment Systems," Management Science, INFORMS, vol. 63(2), pages 566-583, February.
    2. 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.
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    4. 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.
    5. 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.
    6. 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.
    7. F. Biélen & N. Demoulin, 2007. "Waiting time influence on the satisfaction-loyalty relationship in services," Post-Print hal-00254951, HAL.
    8. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2011. "The Price of Fairness," Operations Research, INFORMS, vol. 59(1), pages 17-31, February.
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    11. Mona Issabakhsh & Seokgi Lee & Hyojung Kang, 2021. "Scheduling patient appointment in an infusion center: a mixed integer robust optimization approach," Health Care Management Science, Springer, vol. 24(1), pages 117-139, March.
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