Motivated by the increasing use of online appointment booking platforms, we study how to offer appointment slots to customers to maximize the total number of slots booked. We develop two models, nonsequential 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 nonsequential 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 two 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 nonsequential 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 with nonsequential 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.
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Management Science
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Liu, N, van de Ven, P.M, & Zhang, B. (2019). Managing appointment booking under customer choices. Management Science, 65(9), 4280–4298. doi:10.1287/mnsc.2018.3150