Appointment Scheduling Under Time-Dependent Patient No-Show Behavior

58 Pages Posted: 18 Jul 2019

See all articles by Qingxia Kong

Qingxia Kong

Erasmus University Rotterdam (EUR)

Shan Li

City University of New York - Narendra Paul Loomba Department of Management

Nan Liu

Boston College - Carroll School of Management

Chung-Piaw Teo

NUS Business School - Department of Decision Sciences

Zhenzhen Yan

Nanyang Technological University

Date Written: March 2, 2019

Abstract

This paper studies how to schedule medical appointments with time-dependent patient no-show behavior and random service times. The problem is motivated by our studies of independent datasets from countries in two continents which unanimously identify a significant time-of-day effect on patient show-up probabilities. We deploy a distributionally robust model, which minimizes the worst case total expected costs of patient waiting and service provider’s idling and overtime, by optimizing the scheduled arrival times of patients. This model is challenging because evaluating the total cost for a given schedule involves a linear program with uncertainties present in both the objective function and the right-hand side of the constraints. In addition, the ambiguity set considered contains discrete uncertainties and complementary functional relationships among these uncertainties (namely, patient no-shows and service durations). We show that when patient no-shows are exogenous (i.e., time-independent), the problem can be reformulated as a co-positive program and then be approximated by semi-definite programs. When patient no-shows are endogenous on time (and hence on the schedule), the problem becomes a bilinear co-positive program. We construct a set of dual prices to guide the search for a good schedule and use the technique iteratively to obtain a near optimal solution. Our computational studies reveal a significant reduction in total expected cost by taking into account the time-of-day variation in patient show-up probabilities as opposed to ignoring it.

Keywords: Patient No-shows, Appointment Scheduling, Healthcare Management, Distributionally Robust Optimization, Co-positive Program

Suggested Citation

Kong, Qingxia and Li, Shan and Liu, Nan and Teo, Chung-Piaw and Yan, Zhenzhen, Appointment Scheduling Under Time-Dependent Patient No-Show Behavior (March 2, 2019). Management Science (Forthcoming); Baruch College Zicklin School of Business Research Paper No. 2019-04-03. Available at SSRN: https://ssrn.com/abstract=3359707

Qingxia Kong

Erasmus University Rotterdam (EUR) ( email )

Burgemeester Oudlaan 50
3000 DR Rotterdam, Zuid-Holland 3062PA
Netherlands

Shan Li (Contact Author)

City University of New York - Narendra Paul Loomba Department of Management ( email )

55 Lexington Avenue
New York, NY 10010
United States

Nan Liu

Boston College - Carroll School of Management ( email )

140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States

HOME PAGE: http://https://sites.google.com/site/nanliuacademic/

Chung-Piaw Teo

NUS Business School - Department of Decision Sciences ( email )

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

Zhenzhen Yan

Nanyang Technological University ( email )

MAS 05-19, 21 Nanyang Link
Singapore, 637371
Singapore

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