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Appointment games with unobservable and observable schedules

Abstract

Appointment scheduling assigns start times in a session or consultation block to a set of tasks that share a common resource. For a generic repeated appointment scheduling problem, we study the trade-off between waiting for an appointment and waiting at the appointed time. Assuming that being scheduled later during a session implies that one has to wait longer for service (on average), it is often beneficial to choose a consultation block further away. We study this trade-off both when the patients have no information on how many patients are already scheduled in future consultation blocks and when they can observe the future block schedules. By some numerical examples, we find that in both cases the rational choice considerably changes between consecutive appointment blocks, patients favouring later blocks when the next appointment block starts in the near future. We also compare the rational choice with the socially optimal schedule and find that socially optimal scheduling can significantly reduce the waiting cost.

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References

  1. Cayirli, T., & Veral, E. (2003). Outpatient scheduling in health care: A review of literature. Production and Operations Management, 12(4), 519–549.

    Article  Google Scholar 

  2. Chun, Y., Mitra, M., & Mutuswami, S. (2019). Egalitarianism in the queueing problem. Journal of Mathematical Economics, 81, 48–56.

    Article  Google Scholar 

  3. Chun, Y., Park, N., & Yengin, D. (2016). Coincidence of cooperative game theoretic solutions in the appointment problem. International Journal of Game Theory, 45(3), 699–708.

    Article  Google Scholar 

  4. Curiel, I., Pederzoli, G., & Tijs, S. (1989). Sequencing games. European Journal of Operational Research, 40(3), 344–351.

    Article  Google Scholar 

  5. De Vuyst, S., Bruneel, H., & Fiems, D. (2014). Computationally efficient evaluation of appointment schedules in health care. European Journal of Operational Research, 237(3), 1142–1154.

    Article  Google Scholar 

  6. Debo, L. G., Parlour, C., & Rajan, U. (2012). Signaling quality via queues. Management Science, 58(5), 876–891.

    Article  Google Scholar 

  7. Feldman, J., Liu, N., Topaloglu, H., & Ziya, S. (2014). Appointment scheduling under patient preference and no-show behavior. Operations Research, 62(4), 794–811.

    Article  Google Scholar 

  8. Fiems, D., & Prabhu, B. (2020). Macroscopic modelling and analysis of rush-hour congestion. In Proceedings of the 13th EAI international conference on performance evaluation methodologies and tools.

  9. Fiems, D., Prabhu, B., & De Turck, K. (2019). Travel times, rational queueing and the macroscopic fundamental diagram of traffic flow. Physica A, 524, 412–421.

    Article  Google Scholar 

  10. Golitschek, M. V. (1975). Linear approximation by exponential sums on finite intervals. Bulletin of the American Mathematical Society, 81(2), 443–445.

    Article  Google Scholar 

  11. Gupta, D., & Denton, B. (2008). Appointment scheduling in health care: Challenges and opportunities. IIE Transactions, 40(9), 800–819.

    Article  Google Scholar 

  12. Gupta, D., & Wang, L. (2008). Revenue management for a primary-care clinic in the presence of patient choice. Operations Research, 56(3), 576–592.

    Article  Google Scholar 

  13. Harper, P. R., & Gamlin, H. M. (2003). Reduced outpatient waiting times with improved appointment scheduling: A simulation modelling approach. Or Spectrum, 25(2), 207–222.

    Article  Google Scholar 

  14. Hassin, R., & Haviv, M. (2009). To queue or not to queue. Amsterdam: Kluwer.

    Google Scholar 

  15. Haviv, M., & Roughgarden, T. (2007). The price of anarchy in an exponential multi-server. Operations Research Letters, 35(4), 421–426.

    Article  Google Scholar 

  16. Jain, R., Juneja, S., & Shimkin, N. (2011). The concert queueing game: To wait or to be late. Discrete Event Dynamical Systems, 21, 103–138.

    Article  Google Scholar 

  17. Kortbeek, N., Zonderland, M. E., Braaksma, A., Vliegen, I. M. H., Boucherie, R. J., Litvak, N., & Hans, E. W. (2014). Designing cyclic appointment schedules for outpatient clinics with scheduled and unscheduled patient arrivals. Performance Evaluation, 80, 5–26.

    Article  Google Scholar 

  18. Koutsoupias, E., & Papadimitriou, C. (1999). Worst-case equilibria. In: Annual symposium on theoretical aspects of computer science (pp. 404–413). Springer.

  19. Liu, N., Finkelstein, S. R., Kruk, M. E., & Rosenthal, D. (2017). When waiting to see a doctor is less irritating: Understanding patient preferences and choice behavior in appointment scheduling. Management Science, 64(5), 1975–1996.

    Article  Google Scholar 

  20. Luo, J., Kulkarni, V. G., & Ziya, S. (2015). A tandem queueing model for an appointment-based service system. Queueing Systems, 79(1), 53–85.

    Article  Google Scholar 

  21. Maniquet, F. (2003). A characterization of the Shapley value in queueing problems. Journal of Economic Theory, 109, 90–103.

    Article  Google Scholar 

  22. Mehrotra, A., Keehl-Markowitz, L., & Ayanian, J. Z. (2008). Implementing open-access scheduling of visits in primary care practices: A cautionary tale. Annals of Internal Medicine, 148(12), 915–922.

    Article  Google Scholar 

  23. Murray, M., & Berwick, D. M. (2003). Advanced access: Reducing waiting and delays in primary care. JAMA, 289(8), 1035–1040.

    Article  Google Scholar 

  24. Naor, P. (1969). The regulation of queue size by levying tolls. Econometrica, 37(1), 15–24.

    Article  Google Scholar 

  25. Osadchiy, N., & KC, D. (2017). Are patients patient? The role of time to appointment in patient flow. Production and Operations Management, 26(3), 469–490.

    Article  Google Scholar 

  26. Patrick, J., Puterman, M. L., & Queyranne, M. (2008). Dynamic multipriority patient scheduling for a diagnostic resource. Operations Research, 56(6), 1507–1525.

    Article  Google Scholar 

  27. Polsky, D., Richards, M., Basseyn, S., Wissoker, D., Kenney, G. M., Zuckerman, S., & Rhodes, K. V. (2015). Appointment availability after increases in medicaid payments for primary care. New England Journal of Medicine, 372(6), 537–545.

    Article  Google Scholar 

  28. Robinson, L. W., & Chen, R. R. (2010). A comparison of traditional and open-access policies for appointment scheduling. Manufacturing & Service Operations Management, 12(2), 330–346.

    Article  Google Scholar 

  29. Rose, K. D., Ross, J. S., & Horwitz, L. I. (2011). Advanced access scheduling outcomes: A systematic review. Archives of Internal Medicine, 171(13), 1150–1159.

    Article  Google Scholar 

  30. Sampson, F., Pickin, M., O’Cathain, A., Goodall, S., & Salisbury, C. (2008). Impact of same-day appointments on patient satisfaction with general practice appointment systems. British Journal of General Practice, 58(554), 641–643.

    Article  Google Scholar 

  31. Sundar, D. K., & Ravikumar, K. (2014). An actor-critic algorithm for multi-agent learning in queue-based stochastic games. Neurocomputing, 127, 258–265.

    Article  Google Scholar 

  32. Wales, D. J., & Doye, J. P. K. (1997). Global optimization by basin-hopping and the lowest energy structures of Lennard–Jones clusters containing up to 110 atoms. Journal of Physical Chemistry A, 101, 5111–5116.

    Article  Google Scholar 

  33. Wang, J., & Fung, R. Y. K. (2015). Dynamic appointment scheduling with patient preferences and choices. Industrial Management & Data Systems, 115(4), 700–717.

    Article  Google Scholar 

  34. Wang, J., & Zhang, F. (2018). Equilibrium analysis of the observable queues with balking and delayed repairs. Applied Mathematics and Computation, 2716–2729, 2011.

    Google Scholar 

  35. Wang, W.-Y., & Gupta, D. (2011). Adaptive appointment systems with patient preferences. Manufacturing & Service Operations Management, 13(3), 373–389.

    Article  Google Scholar 

  36. Zacharias, C., & Armony, M. (2016). Joint panel sizing and appointment scheduling in outpatient care. Management Science, 63(11), 3978–3997.

    Article  Google Scholar 

  37. Zander, A. (2016). Modeling indirect waiting times with an M/D/1/K/N queue. In Proceedings of the second KSS research workshop, Karlsruhe, Germany.

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Correspondence to Dieter Fiems.

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Deceuninck, M., De Vuyst, S., Claeys, D. et al. Appointment games with unobservable and observable schedules. Ann Oper Res (2021). https://doi.org/10.1007/s10479-021-04168-z

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Keywords

  • Appointment scheduling
  • Game theory
  • Wardrop equilibrium