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Dynamic pricing with finite price sets: a non-parametric approach

Dynamic pricing with finite price sets: a non-parametric approach
Dynamic pricing with finite price sets: a non-parametric approach

We study price optimization of perishable inventory over multiple, consecutive selling seasons in the presence of demand uncertainty. Each selling season consists of a finite number of discrete time periods, and demand per time period is Bernoulli distributed with price-dependent parameter. The set of feasible prices is finite, and the expected demand corresponding to each price is unknown to the seller, whose objective is to maximize cumulative expected revenue. We propose an algorithm that estimates the unknown parameters in a learning phase, and in each subsequent season applies a policy determined as the solution to a sample dynamic program, which modifies the underlying dynamic program by replacing the unknown parameters by the estimate. Revenue performance is measured by the regret: the expected revenue loss relative to the optimal attainable revenue under full information. For a given number of seasons n, we show that if the number of seasons allocated to learning is asymptotic to (n2logn)1/3, then the regret is of the same order, uniformly over all unknown demand parameters. An extensive numerical study that compares our algorithm to six benchmarks adapted from the literature demonstrates the effectiveness of our approach.

Asymptotic analysis, Dynamic pricing, Dynamic programming, Markov decision process, Regret
1432-2994
Avramidis, Athanasios
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
den Boer, Arnoud
ec761202-becc-4c7e-aac4-abdc6da9caf3
Avramidis, Athanasios
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
den Boer, Arnoud
ec761202-becc-4c7e-aac4-abdc6da9caf3

Avramidis, Athanasios and den Boer, Arnoud (2021) Dynamic pricing with finite price sets: a non-parametric approach. Mathematical Methods of Operations Research, 94 (1). (doi:10.1007/s00186-021-00744-y).

Record type: Article

Abstract

We study price optimization of perishable inventory over multiple, consecutive selling seasons in the presence of demand uncertainty. Each selling season consists of a finite number of discrete time periods, and demand per time period is Bernoulli distributed with price-dependent parameter. The set of feasible prices is finite, and the expected demand corresponding to each price is unknown to the seller, whose objective is to maximize cumulative expected revenue. We propose an algorithm that estimates the unknown parameters in a learning phase, and in each subsequent season applies a policy determined as the solution to a sample dynamic program, which modifies the underlying dynamic program by replacing the unknown parameters by the estimate. Revenue performance is measured by the regret: the expected revenue loss relative to the optimal attainable revenue under full information. For a given number of seasons n, we show that if the number of seasons allocated to learning is asymptotic to (n2logn)1/3, then the regret is of the same order, uniformly over all unknown demand parameters. An extensive numerical study that compares our algorithm to six benchmarks adapted from the literature demonstrates the effectiveness of our approach.

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Submitted date: 22 October 2018
Published date: 28 June 2021
Additional Information: Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
Keywords: Asymptotic analysis, Dynamic pricing, Dynamic programming, Markov decision process, Regret

Identifiers

Local EPrints ID: 425539
URI: http://eprints.soton.ac.uk/id/eprint/425539
ISSN: 1432-2994
PURE UUID: 86a551d5-9256-4908-a90a-e7558e286ef7
ORCID for Athanasios Avramidis: ORCID iD orcid.org/0000-0001-9310-8894

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Date deposited: 24 Oct 2018 16:30
Last modified: 29 Oct 2022 01:42

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Author: Arnoud den Boer

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