Learning and Pricing with Inventory Constraints

Chen, Q (George), Wang, H and Wang, Z (2022) Learning and Pricing with Inventory Constraints. In: The Elements of Joint Learning and Optimization in Operations Management. Springer Series in Supply Chain Management . Springer, pp. 103-135. ISBN 9783031019258 (In Press)

Abstract

The presence of inventory constraints is prevalent in revenue management applications and affects how pricing should be managed. This chapter reviews recent developments for the joint learning and pricing problem with inventory constraints using both frequentist and Bayesian approaches. As the total demand and supply in the system scales proportionally, information-theoretical lower bounds indicate that any algorithm must have a regret (i.e., the cumulative expected revenue loss comparing to the full-information optimal solution) that is at least in the square root order of the scaling factor. We introduce effective heuristics that match the square root regret up to multiplicative logarithmic terms. For the frequentist approach, if there is a single product, a shrinking price interval heuristic achieves square root regret. When there are multiple products, a self-adjusting heuristic achieves square root regret when the demand comes from a known class of parametric functions; if the class of functions is unknown but the demand function is sufficiently smooth, then such heuristic can attain a regret which is arbitrarily close to square root. For the Bayesian approach, a Thompson sampling-based heuristic can achieve square root regret.