Real-Time Dynamic Pricing for Revenue Management with Reusable Resources and Deterministic Service Time Requirements

Abstract

We consider the setting of a firm that sells a finite amount of resources to price-sensitive customers who arrive randomly over time according to a specified non-stationary rate. Each customer requires a service that consumes one unit of resource for a deterministic amount of time, and the resource is reusable in the sense that it can be immediately used to serve a new customer upon the completion of the previous service. The firm’s objective is to set the price dynamically to maximize its expected total revenues. This is a fundamental problem faced by many firms in many industries. We formulate this as an optimal stochastic control problem and develop two heuristic controls based on the solution of the deterministic relaxation of the original stochastic problem. The first heuristic control is static since the corresponding price sequence is determined before the selling horizon starts; the second heuristic control is dynamic, it uses the first heuristic control as its baseline control and adaptively adjusts the price based on previous demand realizations. We show that both heuristic controls are asymptotically optimal in the regime with large demand and large number of resources. Finally, we consider two important generalizations of the basic model to the setting with multiple service types requiring different service times and the setting with advance service bookings.