We consider a canonical revenue management problem in a network setting where the goal is to find a customer admission policy to maximize the total expected revenue over a fixed finite horizon. There is a set of resources, each of which has a fixed capacity. There are several customer classes, each with an associated arrival process, price, and resource consumption vector. If a customer is accepted, it effectively removes the resources that it consumes from the system. The exact solution cannot be obtained for reasonable-sized problems due to the curse of dimensionality. Several (approximate) solution techniques have been proposed in the literature. One way to analytically compare policies is via an asymptotic analysis where both resource sizes and arrival rates grow large. Many of the proposed policies are asymptotically optimal on the fluid scale. However, as we demonstrate in this paper, these policies may fail to be optimal on the more sensitive diffusion scale even for quite simple problem instances. We develop a new policy that achieves diffusion-scale optimality. The policy starts with a probabilistic admission rule derived from the optimization of the fluid model, embeds a trigger function that tracks the difference between the actual and expected customer acceptance, and sets threshold values for the trigger function, the violation of which invokes the reoptimization of the admission rule. We show that re-solving the fluid model, which needs to be performed at most once, is required for extending the asymptotic optimality from the fluid scale to the diffusion scale. We demonstrate the implementation of the policy by numerical examples. Key words: revenue management; asymptotic optimality; admission control; diffusion limit; fluid limit; reoptimization MSC2000 subject classification: Primary: 90B15, 90B05, 60K30; secondary: 60F05, 60F17 OR/MS subject classification: Primary: inventory and production: revenue management; secondary: probability; diffusion: limit theorems History: Received November 2, 2005; revised November 3, 2006. 1. Introduction. In this paper, we investigate a canonical revenue management problem and develop a new approach that exhibits better performance for "large" problems than previous approaches. The problem is defined as follows: There is a set of resources with fixed capacities to be used by customers who arrive randomly during a fixed finite time interval. Customers are divided into different classes based on their usage of resources and the (fixed) price they pay for the service. Depending on their classes, arriving customers are either immediately accepted for service or rejected-no waiting or backlog is allowed. If a customer is accepted, it removes the resources that it consumes from the system. Unused resources at the end of the time interval have no salvage value. The objective is to find an admission policy to maximize the total expected revenue. A classical example of this problem is airline seat inventory control, where a resource corresponds to a flight leg and capacity corresponds to the number of seats on the flight. Customer classes are defined by (itinerary, fare) combinations. The airline tries to allocate seats to different customer classes in a way that maximizes the expected revenue. Other instances of this problem can be found in various service industries such as car rental, hotel room reservation, and bandwidth provisioning in telecommunication networks. The same problem also exists in supply chain management, e.g., when an inventory manager needs to allocate some nonreplenishable stocks of components to different orders. If the exact numbers of customer arrivals of each class over the time interval were given in advance, then the optimal number of customers of each class to accept could be obtained by solving an integer program. (In the asymptotic regime that interests us, the relaxation of this integer program to a linear program (LP) introduces asymptotically negligible error, so we only consider this relaxed LP, not the exact integer program. It should be noted that the optimal objective of the LP is an upper bound on the optimal objective of the integer program.) Of course, in normal situations the actual numbers of arrivals are not known until the process is over, so we refer to the expected revenue obtained under the above procedure as the hindsight optimum. Specifically, for each sample path of arrivals, let the hindsight revenue be the revenue that the decision maker could have achieved with ex post optimization of the admission decisions. The hindsight optimum is the expected value of the hindsight revenue. In this paper, we study ex ante policies that are determined based on limited information (mean, standard deviation, or distribution) about the arrival processes. The hindsight optimum sets the upper bound for expected revenue that can be achieved and is used as the reference point for measuring the performance of a given policy. We develop our analysis under the following asymptotic framework: We introduce a sequence of problems of increasing size by scaling up customer arrivals and capacities by a factor of k k = 1 2 . We define
REF propose an admission control strategy for a reservation system with different classes of customers.
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