Scheduling Arrivals to a Stochastic Service Delivery System Using Copositive Cones

Operations Research, Vol. 61, No. 3, pp. 711-726, 2013

55 Pages Posted: 25 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: August 5, 2010

Abstract

In this paper, we investigate a stochastic appointment scheduling problem in an outpatient clinic with a single doctor. The number of patients and their sequence of arrivals are fixed, and the scheduling problem is to determine an appointment time for each patient. The service durations of the patients are stochastic, and only the mean and covariance estimates are known. We do not assume any exact distributional form of the service durations, and solve for distributionally robust schedules that minimize the expectation of the weighted sum of patients' waiting time and doctor's overtime. We formulate this scheduling problem as a convex conic optimization problem with a tractable semidefinite relaxation. Our model can be extended to handle additional support constraints of the service durations. Using the primal-dual optimality conditions, we prove several interesting structural properties of the optimal schedules. We develop an efficient semidefinite relaxation of the conic program, and show that we can still obtain near optimal solutions on benchmark instances in the existing literature. We apply our approach to develop a practical appointment schedule at an eye clinic that can significantly improve the efficiency of the appointment system in the clinic, compared to an existing schedule.

Keywords: Appointment Scheduling; Copositive Programming; Semidefinite Programming; Network Flow

Suggested Citation

Kong, Qingxia and Lee, Chung-Yee and Teo, Chung-Piaw and Zheng, Zhichao, Scheduling Arrivals to a Stochastic Service Delivery System Using Copositive Cones (August 5, 2010). Operations Research, Vol. 61, No. 3, pp. 711-726, 2013, Available at SSRN: https://ssrn.com/abstract=2783626

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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