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

European Journal of Operational Research, Vol. 255, No. 3, pp. 809-821, 2016

37 Pages Posted: 26 May 2016 Last revised: 13 Feb 2018

See all articles by Qingxia Kong

Qingxia Kong

Adolfo Ibáñez University - School of Business

Chung-Yee Lee

Hong Kong University of Science & Technology (HKUST) - Department of Industrial and Engineering and Logistics Management

Chung-Piaw Teo

NUS Business School - Department of Decision Sciences

Zhichao Zheng

Singapore Management University - Lee Kong Chian School of Business

Date Written: June 24, 2014

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 total expected 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.

Suggested Citation

Kong, Qingxia and Lee, Chung-Yee and Teo, Chung-Piaw and Zheng, Zhichao, Appointment Sequencing: Why the Smallest-Variance-First Rule May Not Be Optimal (June 24, 2014). European Journal of Operational Research, Vol. 255, No. 3, pp. 809-821, 2016. Available at SSRN: https://ssrn.com/abstract=2783648

Qingxia Kong

Adolfo Ibáñez University - School of Business ( email )

Diagonal Las Torres 2640
Santiago, 7941169
Chile

Chung-Yee Lee

Hong Kong University of Science & Technology (HKUST) - Department of Industrial and Engineering and Logistics Management ( email )

Clear Water Bay
Kowloon
Hong Kong

Chung-Piaw Teo

NUS Business School - Department of Decision Sciences ( email )

15 Kent Ridge Drive
Mochtar Riady Building, BIZ 1 8-69
119245
Singapore

Zhichao Zheng (Contact Author)

Singapore Management University - Lee Kong Chian School of Business ( email )

50 Stamford Road
Singapore, 178899
Singapore
(65) 6808 5474 (Phone)
(65) 6828 0777 (Fax)

HOME PAGE: http://www.zhengzhichao.com

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