Optimizing Restaurant Reservation Scheduling

We consider a yield-management approach to determine whether a restaurant should accept or reject a pending reservation request. This approach was examined by Bossert (2009), where the decision for each request is evaluated by an approximate dynamic program (ADP) that bases its decision on a realization of future demand. This model only considers assigning requests to their desired time slot. We expand Bossert's ADP model to incorporate an element of flexibility that allows requests to be assigned to a time slot that differs from the customer's initially requested time. To estimate the future seat utilization given a particular decision, a new heuristic is presented which evaluates time-slot/table assignments based on the expected number of unused seats likely to result from a given assignment. When compared against naive seating models, the proposed model produced average gains in seat utilization of 25%.