Dynamic Appointment Scheduling

TL;DR

This paper develops a dynamic scheduling model for appointments that adapts to real-time information, using phase-type distributions and dynamic programming, demonstrating significant improvements over static schedules through numerical experiments.

Contribution

It introduces a phase-type-based dynamic scheduling approach that accounts for general service time variability, extending beyond exponential assumptions.

Findings

Dynamic schedules outperform static ones in numerical tests.

Assuming exponential service times can lead to suboptimal scheduling.

Rescheduling yields significant efficiency gains.

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.