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Dynamic pricing with finite price sets and unknown price sensitivity

Dynamic pricing with finite price sets and unknown price sensitivity
Dynamic pricing with finite price sets and unknown price sensitivity
We study the pricing of perishable inventory over multiple selling seasons in the presence of demand uncertainty. There are k feasible prices.Each season consists of periods during which demand is a Bernoulli(λi) random variable whenever the i-th price is offered.The purchase probabilities, λ = (λ1,...,λκ), are unknown to the seller, whose objective is to maximize the expected revenue.We propose an algorithm that estimates λ 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 λ by the estimate.Revenue performance is measured by the regret: the expected revenue loss relative to the optimum achievable under knowledge of λ.For a given number of seasons n, we show that if the number of seasons allocated to learning is asymptotic to (n2 log n)1/3, then the regret is of the same order, uniformly over λ. We also develop a multi-armed bandit alternative whose regret is O(log n),but is (asymptotically) at least δ times the number of δ-suboptimal arms, for any δ>0. Numerical results demonstrate the effectiveness of our approach.
Avramidis, Athanasios
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
Avramidis, Athanasios
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001

Avramidis, Athanasios (2018) Dynamic pricing with finite price sets and unknown price sensitivity. Author's Original. (Submitted)

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Abstract

We study the pricing of perishable inventory over multiple selling seasons in the presence of demand uncertainty. There are k feasible prices.Each season consists of periods during which demand is a Bernoulli(λi) random variable whenever the i-th price is offered.The purchase probabilities, λ = (λ1,...,λκ), are unknown to the seller, whose objective is to maximize the expected revenue.We propose an algorithm that estimates λ 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 λ by the estimate.Revenue performance is measured by the regret: the expected revenue loss relative to the optimum achievable under knowledge of λ.For a given number of seasons n, we show that if the number of seasons allocated to learning is asymptotic to (n2 log n)1/3, then the regret is of the same order, uniformly over λ. We also develop a multi-armed bandit alternative whose regret is O(log n),but is (asymptotically) at least δ times the number of δ-suboptimal arms, for any δ>0. Numerical results demonstrate the effectiveness of our approach.

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Submitted date: 22 October 2018

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Local EPrints ID: 425539
URI: http://eprints.soton.ac.uk/id/eprint/425539
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: 24 Jul 2019 00:34

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