Abstract
This study investigates appointment systems (AS), as combinations of access rules and appointment-scheduling rules, explicitly designed for dealing with walk-in seasonality. In terms of ‘access rules’, strategies are tested for adjusting capacity through intra-week, or monthly seasonality of walk-ins, or their combined effects. In terms of ‘appointment rules’, strategies are tested to determine which particular slots to double-book or leave open in cases where seasonal walk-in rates exceed or fall short of the overall yearly rate. In that regard, this study integrates capacity and appointment decisions, which are usually addressed in an isolated manner in previous studies. Simulation optimization is used to derive heuristic solutions to the appointment-scheduling problem, and the findings are compared in terms of in-clinic measures of patient wait time, physician idle time and overtime. The goal is to provide practical guidelines for healthcare practitioners on how to best design their AS when seasonal walk-ins exist.
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Acknowledgements
This research is funded by the Scientific and Technological Research Council of Turkey (TUBITAK) grant 109K451. We thank our research assistants Ronay Ak and Pinar Dursun for their valuable contributions in simulation modeling.
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Appendices
Appendix A
Appendix B
Appendix C
C.1. Sensitivity to trade-offs between waiting costs for scheduled and walk-in patients
We test our results to the sensitivity of the choice of β-parameter, given that some trade-offs may be expected in the waiting times of walk-in and scheduled patients. The analysis is done using the proposed heuristics in Section 5.2 against the benchmark case of No_Adj. In Figure C1, for the ‘high’ environment with probability of walk-ins P=40%, and high levels on monthly, intra-weekly, and intraday seasonality, different β-values (ie, β=1, 2, 5, 10, 15) are used in deriving the efficient frontiers. Note that β=1 corresponds to the efficient frontier derived for the same environment in Figure 6 (Section 5.2).
Efficient frontiers for different relative wait costs for walk-ins and scheduled patients (β).
As observed in Figure C1, No_Adj policy becomes one of the best policies beyond β⩾10, replacing Heuristic1 on the efficient frontier when α is 1. In a similar analysis conducted on the other extreme ‘low’ environment with P=20% and low/none levels on all types of seasonality, the shift to No_Adj occurs when α=1 and β⩾20, approximately. Therefore, when the patient's time is highly valuable and when scheduled patient's time is relatively much higher compared with walk-ins, it may be best not to use any seasonal adjustments. For moderate/high cost ratios tested at α=5, 20, best appointment rules remain the same regardless of β-value.
On the one hand, these findings suggest that further details on the cost trade-offs between walk-ins and scheduled patients may be important in determining the best policy, that includes ‘no adjustment’. On the other hand, clinics that accept walk-ins are less likely to value their walk-in patients’ time at such extreme trade-offs (for example, β=10 means a scheduled patient's 5-min wait is equivalent to a walk-in's 50-min wait). For that reason, our conclusions in Sections 5.1 and 5.2 remain valid for most clinics that target smaller β-values with the goal of serving all patients within a fairly reasonable amount of time.
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Cayirli, T., Gunes, E. Outpatient appointment scheduling in presence of seasonal walk-ins. J Oper Res Soc 65, 512–531 (2014). https://doi.org/10.1057/jors.2013.56
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DOI: https://doi.org/10.1057/jors.2013.56