A Bayesian learning model for estimating unknown demand parameter in revenue management

This article proposes a series of Bayesian learning and pricing models to uncover the unknown demand parameter through a data driven process and in the meantime to achieve a good regret bound for revenue. Treating the unknown demand sensitivity as a multinomial random variable whose parameters follow a Dirichlet prior, we take an advantage of conjugate property and derive the analytical form of posterior parameters. We show that the proposed learning process ensures the asymptotic convergence of the parameters. In addition to exploration, with few restrictive assumptions we develop a heuristic algorithm for revenue exploitation and establish a regret bound that is comparable to the best bounds available in the literature. We also show that if the estimated parameter falls into the neighborhood of its true value with sufficient learning, the heuristic can switch to the dynamic programming process. The revenue gap between the optimal dynamic programming process and its approximate counterpart becomes negligible. Numerical experiments confirm the theoretical conclusion. The heuristic algorithms, including a simplified two-price policy and an approximate dynamic programming heuristic, generally lead to an expected revenue with a small gap from its optimal level.