Publication Type

Journal Article

Publication Date

12-2016

Abstract

We study the design of a healthcare appointment system with a single physician and a group of patients whose service durations are stochastic. The challenge is to find the optimal arrival sequence for a group of mixed patients such that the expected total cost of patient waiting time and physician overtime is minimized. While numerous simulation studies report that sequencing patients by increasing order of variance of service duration (Smallest-Variance-First or SVF rule) performs extremely well in many environments, analytical results on optimal sequencing are known only for two patients. In this paper, we shed light on why it is so difficult to prove the optimality of the SVF rule in general. We first assume that the appointment intervals are fixed according to a given template and analytically investigate the optimality of the SVF rule. In particular, we show that the optimality of the SVF rule depends on two important factors: the number of patients in the system and the shape of service time distributions. The SVF rule is more likely to be optimal if the service time distributions are more positively skewed, but this advantage gradually disappears as the number of patients increases. These results partly explain why the optimality of the SVF rule can only be proved for a small number of patients, and why in practice, the SVF rule is usually observed to be superior, since most empirical distributions of the service durations are positively skewed, like log-normal distributions. The insights obtained from our analytical model apply to more general settings, including the cases where the service durations follow log-normal distributions and the appointment intervals are optimized.

Keywords

OR in health services; Appointment Sequencing; Smallest-Variance-First Rule; Stochastic Ordering

Discipline

Medicine and Health Sciences | Operations and Supply Chain Management

Research Areas

Operations Management

Publication

European Journal of Operational Research

Volume

255

Issue

3

First Page

809

Last Page

821

ISSN

0377-2217

Identifier

10.1016/j.ejor.2016.06.004

Publisher

Elsevier

Additional URL

http://dx.doi.org/10.1016/j.ejor.2016.06.004

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