The University of Southampton
University of Southampton Institutional Repository
 ePrints Soton is experiencing an issue with some file downloads not being available. We are working hard to fix this. Please bear with us.

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

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.

Text
r10 - Author's Original
Restricted to Repository staff only
Request a copy
Text
nrl - Author's Original
Restricted to Repository staff only
Request a copy
Text
corrected-1-March-2019-nrl - Author's Original
Restricted to Repository staff only
Request a copy
Text
submitted-OR-211018 - Accepted Manuscript
Restricted to Repository staff only
Request a copy
Text
or2 - Other
Restricted to Repository staff only
Request a copy
Text
or2 - Other
Restricted to Repository staff only
Request a copy

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.org/0000-0001-9310-8894

## Catalogue record

Date deposited: 24 Oct 2018 16:30

## Contributors

Author: Arnoud den Boer