Optimal Multiperiod Pricing with Service Guarantees

We study the multiperiod pricing problem of a service firm with capacity levels that vary over time. Customers are heterogeneous in their arrival and departure periods as well as valuations, and are fully strategic with respect to their purchasing decisions. The firm's problem is to set a sequence of prices that maximizes its revenue while guaranteeing service to all paying customers. We provide a dynamic programming based algorithm that computes the optimal sequence of prices for this problem in polynomial time. We show that due to the presence of strategic customers, available service capacity at a time period may bind the price offered at another time period. This phenomenon leads the firm to utilize the same price in multiple periods, in effect limiting the number of different prices that the service firm utilizes in optimal price policies. Also, when customers become more strategic patient for service, the firm offers higher prices. This may lead to the underutilization of capacity, lower revenues, and reduced customer welfare. We observe that the firm can combat this problem if it has an ability, beyond posted prices, to direct customers to different service periods. This paper was accepted by Dimitris Bertsimas, optimization.