Revenue Management of Reusable Resources with Advanced Reservations

We consider a revenue management problem wherein the seller is endowed with a single type resource with a finite capacity and the resource can be repeatedly used to serve customers. There are multiple classes of customers arriving according to a multi‐class Poisson process. Each customer, upon arrival, submits a service request that specifies his service start time and end time. Our model allows customer advanced reservation times and services times in each class to be arbitrarily distributed and correlated. Upon arrival of each customer, the seller must instantaneously decide whether to accept this customer's service request. A customer whose request is denied leaves the system. A customer whose request is accepted is allocated with a specific item of the resource at his service start time. The resource unit occupied by a customer becomes available to other customers after serving this customer. The seller aims to design an admission control policy that maximizes her expected long‐run average revenue. We propose a policy called the ε ‐ perturbation class selection policy ( ε ‐CSP), based on the optimal solution in the fluid setting wherein customers are infinitesimal and customer arrival processes are deterministic, under the restriction that the seller can utilize at most (1 −  ε ) of her capacity for any ε  ∈ (0, 1). We prove that the ε ‐CSP is near‐optimal. More precisely, we develop an upper bound of the performance loss of the ε ‐CSP relative to the seller's optimal revenue, and show that it converges to zero with a square‐root convergence rate in the asymptotic regime wherein the arrival rates and the capacity grow up proportionally and the capacity buffer level ε decays to zero.