Close the gaps: A learning-while-doing algorithm for single-product revenue management problems

We consider a retailer selling a single product with limited on-hand inventory over a finite selling season. Customer demand arrives according to a Poisson process, the rate of which is influenced by a single action taken by the retailer (such as price adjustment, sales commission, advertisement intensity, etc.). The relationship between the action and the demand rate is not known in advance. However, the retailer is able to learn the optimal action on the fly as she maximizes her total expected revenue based on the observed demand reactions. Using the pricing problem as an example, we propose a dynamic learning-while-doing algorithm that only involves function value estimation to achieve a near-optimal performance. Our algorithm employs a series of shrinking price intervals and iteratively tests prices within that interval using a set of carefully chosen parameters. We prove that the performance of our algorithm is among the best of all possible algorithms in terms of the asymptotic regret (the relative loss compared to the full information optimal solution). Our result closes the performance gaps between parametric and nonparametric learning and between the post-price mechanism and the customer-bidding mechanism. Important managerial insight from this research is that the values of information on both the parametric form of the demand function as well as each customer's exact reservation price are less important than prior literature suggests. Our results also suggest that firms would be better off to perform dynamic learning and action concurrently rather than sequentially.