Revenue Management of Reusable Resources with Advanced Reservations

Abstract

W e 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 e-perturbation class selection policy (e-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 À e) of her capacity for any e 2 (0, 1). We prove that the e-CSP is near-optimal. More precisely, we develop an upper bound of the performance loss of the e-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 e decays to zero.Our main results about the performance of the e-CSP are as follows:1. Finite upper bound. The expected long-run average revenue loss of the e-CSP has a finite upper bound. (This result is formally stated later in Theorem 1.) 2. Asymptotic optimality. In the asymptotic regime wherein the customer arrival rates and the Chen, Levi, and Shi: Revenue Management with Advanced Reservations Production and Operations Management 26(5), pp. 836-859,

The Online Reservation Problem

“…Several studies that analyze online scheduling problems that are similar to the ORP assume that some distributional information on job arrivals and/or durations is available [12][13][14]. Because the focus in these studies is on exploiting the distributional information, we do not review them.…”

Innovative Approach in Modeling Business Processes with a Focus on Improving the Allocation of Human Resources

“…In [6], authors solved class of revenue management problems in systems with reusable resources. The authors suggested 2approximation algorithm for revenue management models in which resources can be reused, and [7] was expanded so advance reservations are possible. Some authors use approximation algorithms for solving this problem.…”

An overview of revenue management and dynamic pricing models in hotel business

“…The revenue management problems through the prism of dynamic pricing were also studied by Ladany and Arbel [72], Gallego and Van Ryzin [47,113], Feng and Gallego [39] and You [128]. Levi and Shi [77] and Chen et al [28] suggested efficient and simple heuristic approaches to revenue management of reusable resources with advanced reservations within the scope of queuing theory. The results in [28] are applicable for fixed prices as well as for variable prices.…”

“…Levi and Shi [77] and Chen et al [28] suggested efficient and simple heuristic approaches to revenue management of reusable resources with advanced reservations within the scope of queuing theory. The results in [28] are applicable for fixed prices as well as for variable prices.…”