Abstract
This paper considers appointment scheduling in a setting in which at every client arrival the schedule of all future clients can be adapted. Starting our analysis with an explicit treatment of the case of exponentially distributed service times, we then develop a phase-type-based approach to also cover cases in which the service times’ squared coefficient of variation differs from 1. The approach relies on dynamic programming, with the state information being the number of clients waiting, the elapsed service time of the client in service, and the number of clients still to be scheduled. The use of dynamic schedules is illustrated through a set of numerical experiments, showing (i) the effect of wrongly assuming exponentially distributed service times, and (ii) the gains (over static schedules, that is) achieved by rescheduling.
| Original language | English |
|---|---|
| Pages (from-to) | 605-626 |
| Number of pages | 22 |
| Journal | European Journal of Operational Research |
| Volume | 312 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 16 Jan 2024 |
Bibliographical note
Publisher Copyright:© 2023 The Author(s)
Funding
The authors would like to thank John Gilbertson (for discussions on the homogeneous exponential case and making Gilbertson (2016) available), Alex Kuiper (for providing Fig. 1) and Ruben Brokkelkamp (for numerical support). In addition we thank the anonymous reviewers and associate editor for helpful and constructive comments.
Keywords
- Appointment scheduling
- Dynamic programming
- Queueing
- Service systems