A Data-Driven Decision Framework for Booking Control with Customer Diversion and Capacity Constraints

This paper studies a two-period booking-control problem in which customers rejected during an initial booking period may return later with a given diversion probability and compete with new demand for the same limited service capacity. Unlike conventional booking-control models, current acceptance decisions influence future effective demand through the return of previously rejected customers. We develop an analytical model that incorporates this feedback mechanism and derive structural properties of the optimal booking policy. In particular, we show that when the service-failure cost exceeds the combined second-period revenue and avoided rejection cost, the optimal cumulative booking limit equals physical capacity. The remaining decision reduces to the first-period booking limit, for which we derive a closed-form, distribution-free diversion threshold separating capacity-protection and no-protection policies. The model is implemented using the Hotel Booking Demand Dataset, with booking-period demand estimated nonparametrically through kernel density estimation. Because historical data do not directly reveal customer diversion, we evaluate an estimator of the aggregate diversion probability and examine the performance of a plug-in booking policy based on the estimated parameter. Simulation results show that the estimator is essentially unbiased and that estimation error has negligible impact on booking decisions. The empirical analysis further shows that accounting for customer diversion can substantially change the recommended booking limits, although the corresponding profit improvements are relatively modest under the baseline calibration. Sensitivity analyses demonstrate that the economic value of modelling diversion increases as capacity becomes more restrictive. These findings provide both analytical insight into booking-control policies with returning customers and practical guidance for their implementation in reservation systems.