Saving Seats for Strategic Customers

We consider a service provider in a market with two segments. Members of the first request a reservation ahead of service and will not patronize the firm without one. Members of the second walk in and demand service immediately. These customers have a fixed cost of reaching the firm and may behave strategically. In equilibrium, they randomize between walking in and staying home. The service provider must decide how much of a limited capacity to make available to advance customers. When the advance demand segment offers a higher per customer margin, the firm may opt to decline some reservation requests in order to bolster walk-in demand. When walk-in customers are more valuable, we have a variation of Littlewood (1972). Where Littlewood would always save some capacity for valuable late arrivals, here it is possible that the optimal policy saves no capacity for walk-ins. Thus, it may be better to ignore rather than pamper walk-in customers. This outcome is robust to changes in the model.