Asymptotic Behavior of an Allocation Policy for Revenue Management

Cooper, William L.

doi:10.1287/opre.50.4.720.2855

Cited by 143 publications

(134 citation statements)

References 22 publications

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“…Despite the simplicity of the model, it is shown in Cooper [3] that using the solution of the "fluid LP" (2) is asymptotically optimal on the fluid scale (see §3.1). The arrival constraints in (2) impose unnecessary restrictions on customer acceptance that may reduce total revenue.…”

Section: Previous Workmentioning

confidence: 99%

“…To motivate the development of such a policy, in this section we first present Cooper's [3] result on fluid-scale asymptotic optimality of the booking limit policy that uses the solution of the fluid LP for booking limits. We then present an example showing that the more sensitive notion of asymptotic optimality represented by (13) cannot hold for any booking limit policy in the context of that example.…”

Section: Bid Price Controlmentioning

confidence: 99%

“…Fluid scale asymptotic optimality of some existing schemes. Cooper [3] studies the asymptotic properties of the booking limit policy. Under the assumptions that customer arrivals follow some simple point processes, and scaling of the problem satisfies…”

Section: Bid Price Controlmentioning

confidence: 99%

“…Convergence property and performance advantage of T 2 policy. We demonstrate the asymptotic optimality of the T 2 policy by comparing it with the LP policy discussed in Cooper [3]. The two policies use the same information about demand (mean arrivals) and employ the same optimization technique (LP).…”

Section: Theorem 45 Given K As Defined Above Under the Scaling (5)mentioning

confidence: 99%

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

Reiman¹,

Wang²

2008

Mathematics of OR

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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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Section: Previous Workmentioning

confidence: 99%

Section: Bid Price Controlmentioning

confidence: 99%

Section: Bid Price Controlmentioning

confidence: 99%

Section: Theorem 45 Given K As Defined Above Under the Scaling (5)mentioning

confidence: 99%

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

Reiman¹,

Wang²

2008

Mathematics of OR

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“…The organizer needs to allocate the network capacity online to those bidders to maximize social welfare. A similar format also appears in online auctions [2], online keyword matching problems [9,13,16], online packing problems [5], and various other online revenue management and resource allocation problems [15,7,4].…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Near-Optimal Algorithm for Online Linear Programming

Agrawal

Wang

2014

Operations Research

225

250

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A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) where the constraint matrix is revealed column by column along with the objective function. We provide a near-optimal algorithm for this surprisingly general class of online problems under the assumption of random order of arrival and some mild conditions on the size of the LP right-hand-side input. Our learning-based algorithm works by dynamically updating a threshold price vector at geometric time intervals, where the dual prices learned from revealed columns in the previous period are used to determine the sequential decisions in the current period. Our algorithm has a feature of "learning by doing", and the prices are updated at a carefully chosen pace that is neither too fast nor too slow. In particular, our algorithm doesn't assume any distribution information on the input itself, thus is robust to data uncertainty and variations due to its dynamic learning capability. Applications of our algorithm include many online multi-resource allocation and multi-product revenue management problems such as online routing and packing, online combinatorial auctions, adwords matching, inventory control and yield management.

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Revenue Management

Gallego¹

2011

Wiley Encyclopedia of Operations Research and Management Science

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Providers of perishable capacity sold through reservation systems typically impose purchase and usage restrictions to sell the same capacity to different customers at different prices. We will assume that the fare structure (a menu of prices and restrictions) is given and that the capacity provider's goal is to allocate capacity among fare classes to maximize expected revenues. We first analyze the single resource, multiple‐fare case and then investigate the network model under the assumption of independent demands. Independent demand models are appropriate if fares are well differentiated and alternative sources of capacity are available to customers who are unable to find their preferred fare. When fares are not well differentiated, or alternative sources of capacity are not readily available, customers may buy up to the next higher fare if their preferred fare is not available. Demand dependencies can significantly erode revenues when controls are based on independent demand models. Researchers and practitioners have been actively trying to find solutions that take into account demand dependencies through the use of discrete choice models. We present a summary of these works and point out directions for future research.

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Asymptotic Behavior of an Allocation Policy for Revenue Management

Cited by 143 publications

References 22 publications

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

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

A Dynamic Near-Optimal Algorithm for Online Linear Programming

Revenue Management

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