Managing Appointment Booking Under Customer Choices

Management Science, Forthcoming

62 Pages Posted: 24 Apr 2018 Last revised: 23 Jun 2018

See all articles by Nan Liu

Nan Liu

Boston College - Carroll School of Management

Peter van de Ven

Center for Mathematics and Computer Science (CWI)

Bo Zhang

IBM Corporation - Thomas J. Watson Research Center

Date Written: June 16, 2018


Motivated by the increasing use of online appointment booking platforms, we study how to offer appointment slots to customers in order to maximize the total number of slots booked. We develop two models, non-sequential offering and sequential offering, to capture different types of interactions between customers and the scheduling system. In these two models, the scheduler offers either a single set of appointment slots for the arriving customer to choose from, or multiple sets in sequence, respectively. For the non-sequential model, we identify a static randomized policy which is asymptotically optimal when the system demand and capacity increase simultaneously, and we further show that offering all available slots at all times has a constant factor of 2 performance guarantee. For the sequential model, we derive a closed-form optimal policy for a large class of instances and develop a simple, effective heuristic for those instances without an explicit optimal policy. By comparing these two models, our study generates useful operational insights for improving the current appointment booking processes. In particular, our analysis reveals an interesting equivalence between the sequential offering model and the non-sequential offering model with perfect customer preference information. This equivalence allows us to apply sequential offering in a wide range of interactive scheduling contexts. Our extensive numerical study shows that sequential offering can significantly improve the slot fill rate (6-8% on average and up to 18% in our testing cases) compared to non-sequential offering. Given the recent and ongoing growth of online and mobile appointment booking platforms, our research findings can be particularly useful to inform user interface design of these booking platforms.

Keywords: Service Operations Management, Customer Choice, Appointment Scheduling, Markov Decision Process, Asymptotically Optimal Policy

JEL Classification: C44, C61, M10, I10

Suggested Citation

Liu, Nan and van de Ven, Peter and Zhang, Bo, Managing Appointment Booking Under Customer Choices (June 16, 2018). Management Science, Forthcoming, Available at SSRN: or

Nan Liu (Contact Author)

Boston College - Carroll School of Management ( email )

140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States


Peter Van de Ven

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB

Bo Zhang

IBM Corporation - Thomas J. Watson Research Center ( email )

1101 Kitchawan Road, Route 134
Yorktown Heights, NY 10598
United States

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