Fluid Approximations for Revenue Management under High-Variance Demand

26 Pages Posted: 23 Jun 2022 Last revised: 4 Jan 2023

See all articles by Yicheng Bai

Yicheng Bai

Cornell University - School of Operations Research and Information Engineering

Omar El Housni

Cornell University - School of Operations Research and Information Engineering

Billy Jin

Cornell University

Paat Rusmevichientong

University of Southern California - Marshall School of Business

Huseyin Topaloglu

Cornell University - School of Operations Research and Information Engineering

David Williamson

Cornell University - School of Operations Research and Information Engineering

Date Written: June 14, 2022

Abstract

One of the most prevalent demand models in the revenue management literature is based on dividing the selling horizon into a number of time periods such that there is at most one customer arrival at each time period. This demand model is equivalent to using a discrete-time approximation to a Poisson process, but it has an important shortcoming. If the mean number of customer arrivals is large, then the coefficient of variation of the number of customer arrivals has to be small. In other words, large demand volume and large demand variability cannot co-exist in this demand model. In this paper, we start with a revenue management model that incorporates general mean and variance for the number of customer arrivals. This revenue management model has a random selling horizon length, capturing the distribution of the number of customer arrivals. The question we seek to answer is the form of the fluid approximation that corresponds to this revenue management model. It is tempting to construct the fluid approximation by computing the expected consumption of the resource capacities in the constraints and the total expected revenue in the objective function through the distribution of the number of customer arrivals. We demonstrate that this answer is wrong in the sense that it yields a fluid approximation that is not asymptotically tight as the resource capacities get large. We give an alternative fluid approximation, where, perhaps surprisingly, the distribution of the number of customer arrivals does not play any role in the constraints. We show that this fluid approximation is asymptotically tight as the resource capacities get large. A numerical study also demonstrates that the policies driven by the latter fluid approximation perform substantially better, so there is practical value in getting the fluid approximation right under high-variance demand.

Keywords: Revenue Management, Fluid Approximations, High-Variance, Dynamic Programming

Suggested Citation

Bai, Yicheng and El Housni, Omar and Jin, Billy and Rusmevichientong, Paat and Topaloglu, Huseyin and Williamson, David, Fluid Approximations for Revenue Management under High-Variance Demand (June 14, 2022). Available at SSRN: https://ssrn.com/abstract=4136445 or http://dx.doi.org/10.2139/ssrn.4136445

Yicheng Bai

Cornell University - School of Operations Research and Information Engineering ( email )

Ithaca, NY 14853
United States

Omar El Housni (Contact Author)

Cornell University - School of Operations Research and Information Engineering ( email )

2 E Loop Rd
New York, NY 10044
United States

HOME PAGE: http://https://people.orie.cornell.edu/oe46/

Billy Jin

Cornell University ( email )

Ithaca, NY
United States

Paat Rusmevichientong

University of Southern California - Marshall School of Business ( email )

701 Exposition Blvd
Los Angeles, CA California 90089
United States

Huseyin Topaloglu

Cornell University - School of Operations Research and Information Engineering ( email )

Ithaca, NY
United States

David Williamson

Cornell University - School of Operations Research and Information Engineering

Ithaca, NY 14853
United States

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