Revenue Management with Heterogeneous Resources: Unit Resource Capacities, Advance Bookings, and Itineraries over Time Intervals

We study revenue management problems with heterogeneous resources, each with unit capacity. An arriving customer makes a booking request for a particular interval of days in the future. We offer an assortment of resources in response to each booking request. The customer makes a choice within the assortment to use the chosen resource for her desired interval of days. The goal is to find a policy that determines an assortment of resources to offer to each customer to maximize the total expected revenue over a finite selling horizon. The problem has two useful features. First, each resource is unique with unit capacity. Second, each customer uses the chosen resource for a number of consecutive days. We consider static policies that offer each assortment of resources with a fixed probability. We show that we can efficiently perform rollout on any static policy, allowing us to build on any static policy and construct an even better policy. Next, we develop two static policies, each of which is derived from linear and polynomial approximations of the value functions. We give performance guarantees for both policies, so the rollout policies based on these static policies inherit the same guarantee. Last, we develop an approach for computing an upper bound on the optimal total expected revenue. Our results for efficient rollout, static policies, and upper bounds all exploit the aforementioned two useful features of our problem. We use our model to manage hotel bookings based on a data set from a real-world boutique hotel, demonstrating that our rollout approach can provide remarkably good policies and our upper bounds can significantly improve those provided by existing techniques.