Learning in revenue management: Exploiting estimation of arrival rate and price response

Abstract

The paper first studies dynamic pricing to maximize expected revenue
of a fixed inventory of a single product under Poisson arrivals of random rate, given a Bayesian prior,
and known distribution of reservation prices.
For a single unit having a salvage value, we show
there exists a unique revenue-maximizing price, which increases in the salvage value,
provided the reservation-price hazard function is increasing.
For multiple units, a discrete-time dynamic program is studied.
\rr{Empirically, the optimal} price increases in uncertainty, and is sensitive to the prior choice.
The paper then considers a seller that knows no parameter values; all he knows is
that sales arise from Poisson arrivals,
where a Bernoulli random variable, independent of everything else, converts any arrival into a sale.
This can represent any demand function as in \citet{ymGAL94a} and \citet{ymBES09a}, but
additional independence conditions are present here.
Observing arrivals and sales at each price during part of the sale horizon,
we construct estimators of the arrival rate and purchase probabilities; \rr{we refer to this process as learning}.
We derive the bias and mean squared error of the resulting demand-function estimator.
Relative to the sale-count-only estimator of \citet{ymBES12a},
the summed mean squared error (across all prices) is consistently reduced, empirically.
Exploitation methods based on \rr{these estimators} are proposed, where the time spent learning is as \citet{ymBES12a} prescribe.
Empirically, the methods' loss against the full-information optimum is competitive to the benchmark of \citet{ymBES12a}.

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Identifiers

ORCID for Athanassios.N. Avramidis: orcid.org/0000-0001-9310-8894

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