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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 the pricing of perishable inventory over multiple, consecutive selling seasons in the presence of demand uncertainty.There are $\nprc$ feasible prices. Each season consists of periods during which demand is a Bernoulli$(\pb_i)$ random variable whenever the $i$-th price is offered.The purchase probabilities, $\pbv=(\pb_1,\ldots,\pb_{\nprc})$, are unknown to the seller, whose objective is to maximize the expected revenue.We propose an algorithm that estimates $\pbv$ in a learning phaseand in each subsequent season applies a policy determined as the solution to a sample dynamic program, which modifies the underlying dynamic program by replacing $\pbv$ by the estimate.Revenue performance is measured by the regret: the expected revenue loss relative to the optimumachievable under knowledge of $\pbv$.For a given number of seasons $n$, we show that if the number of seasons allocated to learning is asymptotic to $(n^2\log n)^{1/3}$, then the regret is of the same order, uniformly over $\pbv$.An extensive numerical study that compares our algorithm to six benchmarks 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).

Record type: Article

Abstract

We study the pricing of perishable inventory over multiple, consecutive selling seasons in the presence of demand uncertainty.There are $\nprc$ feasible prices. Each season consists of periods during which demand is a Bernoulli$(\pb_i)$ random variable whenever the $i$-th price is offered.The purchase probabilities, $\pbv=(\pb_1,\ldots,\pb_{\nprc})$, are unknown to the seller, whose objective is to maximize the expected revenue.We propose an algorithm that estimates $\pbv$ in a learning phaseand in each subsequent season applies a policy determined as the solution to a sample dynamic program, which modifies the underlying dynamic program by replacing $\pbv$ by the estimate.Revenue performance is measured by the regret: the expected revenue loss relative to the optimumachievable under knowledge of $\pbv$.For a given number of seasons $n$, we show that if the number of seasons allocated to learning is asymptotic to $(n^2\log n)^{1/3}$, then the regret is of the same order, uniformly over $\pbv$.An extensive numerical study that compares our algorithm to six benchmarks from the literature demonstrates the effectiveness of our approach.

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More information

Submitted date: 22 October 2018
Published date: 28 June 2021
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: 26 Nov 2021 02:52

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Contributors

Author: Arnoud den Boer

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