Constant Job-Allowance Policies for Appointment Scheduling: Performance Bounds and Numerical Analysis

47 Pages Posted: 7 Mar 2018 Last revised: 5 Nov 2019

See all articles by Shenghai Zhou

Shenghai Zhou

Central South University; Shanghai Jiao Tong University (SJTU) - Antai College of Economics and Management; Jiangxi University of Finance and Economics

Yichuan Ding

Desautels Faculty of Management, McGill University

Woonghee Tim Huh

University of British Columbia

Guohua Wan

Shanghai Jiao Tong University (SJTU) - Antai College of Economics and Management

Date Written: March 2, 2018

Abstract

We consider the appointment scheduling problem, which determines the job allowance over the planning horizon. In particular, we study a simple but effective scheduling policy -- the so-called plateau policy, which allocates a constant job allowance for each appointment. Prior studies on appointment scheduling suggests a "dome" shape structure for the optimal job allowance over the planning horizon. This implies that job allowance does not vary significantly in the middle of the schedule sequence, but varies at the beginning and also at the end of the optimal schedule. Using a dynamic programming formulation, we derive an explicit performance gap between the plateau policy and the optimal schedule, and examine how this gap behaves as the number of appointments increases. We show that a plateau policy is asymptotically optimal when the number of appointments increases. We extend this result to a more general setting with multiple service types. Numerical experiments show that the plateau policy is near optimal even for a small number of appointments, which complements the theoretical results that we derived. Our result provides a justification and strong support for the plateau policy, which is commonly used in practice. Moreover, with minor modifications, the plateau policy can be adapted to more general scenarios with patient no-shows or heterogeneous appointment types.

Keywords: appointment scheduling, dome shape, asymptotic optimality, D/G/1 queue

Suggested Citation

Zhou, Shenghai and Ding, Yichuan and Huh, Woonghee Tim and Wan, Guohua, Constant Job-Allowance Policies for Appointment Scheduling: Performance Bounds and Numerical Analysis (March 2, 2018). Available at SSRN: https://ssrn.com/abstract=3133508 or http://dx.doi.org/10.2139/ssrn.3133508

Shenghai Zhou

Central South University ( email )

Changsha, Hunan 410083
China

Shanghai Jiao Tong University (SJTU) - Antai College of Economics and Management ( email )

No.535 Fahuazhen Road
Shanghai Jiao Tong University
Shanghai, Shanghai 200052
China

Jiangxi University of Finance and Economics ( email )

South Lushan Road
Nanchang, Jiangxi 330013
China

Yichuan Ding (Contact Author)

Desautels Faculty of Management, McGill University ( email )

1001 Sherbrook St W
Montreal, Quebec H3A 1G5
Canada
5143982482 (Phone)

HOME PAGE: http://https://www.mcgill.ca/desautels/yichuan-daniel-ding

Woonghee Tim Huh

University of British Columbia ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada

Guohua Wan

Shanghai Jiao Tong University (SJTU) - Antai College of Economics and Management ( email )

No.535 Fahuazhen Road
Shanghai Jiao Tong University
Shanghai, Shanghai 200052
China

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