A Restaurateur's Dilemma: A Two-Period Capacity Decision Problem with Uncertain Demand and Repeat Customers

We consider a profit maximizing restaurateur who operates in a two-period environment in which she faces uncertain demand in each period. We further assume that all customers served in the first period return for service in the second period. The restaurateur's decision is to set her two-period price and capacity at the start of the first period in order to maximize her expected discounted profits over both periods. Using a simple demand function we derive an expression for the expected discounted profits, the first order condition for maximizing profits. We show that the primary effect of the uncertainty is on the restaurant's capacity rather than the price of its meals.