TY - JOUR

T1 - Appointment Sequencing: Why the Smallest-Variance-First Rule may Not Be Optimal

AU - Kong, Cynthia

AU - Lee, CY

AU - Teo, CP (Chung-Piaw)

AU - Zheng, ZC

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

U2 - 10.1016/j.ejor.2016.06.004

DO - 10.1016/j.ejor.2016.06.004

M3 - Article

VL - 255

SP - 809

EP - 821

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -