An Asymptotically Optimal Policy for a Quantity-Based Network Revenue Management Problem

Abstract

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 c...

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