Abstract:

We consider a joint pricing and inventory control problem where pricing can be adjusted more frequently than inventory ordering decisions. More specifically, the pricing decision is adjusted every period, while new inventories are ordered every epoch that consists of multiple periods. In this setting, the retailer determines the inventory level at the beginning of each epoch and solves a dynamic pricing problem within each epoch with no further replenishment opportunities. The optimal pricing and inventory control policy is solved by an intricate dynamic programming (DP), in which the inventory level is the state variable and the pricing policy is characterized by a function of the inventory level. We consider the situation where the demand-price function and the distribution of random demand noise are both unknown to the retailer, and the retailer needs to develop an online learning algorithm to learn those information and at the same time maximize total profit. We propose a learning algorithm by applying linear bandit techniques under the upper confidence bound (UCB) framework and prove that the algorithm converges through the DP recursions to approach the optimal pricing and inventory control policy under complete demand information. The theoretical lower bound for convergence rate of a learning algorithm is proved based on the multivariate Van Trees inequality coupled with some structural DP analyses, and we show that the upper bound of our algorithm's convergence rate matches the theoretical lower bound.

Bio:

Prof. Menglong Li is an Assistant Professor of Decision Analytics and Operations in the College of Business, City University of Hong Kong. Before joining CityU, he was a postdoctoral associate of MIT Institute for Data, Systems, and Society. He received a PhD degree in Operations Research from the University of Illinois at Urbana-Champaign, an MS degree in Mathematics from the University of Pierre and Marie Curie and a BS degree in Mathematics from Tsinghua University. His research interests include inventory management, revenue management, (discrete) convex analysis, combinatorial optimization, approximation algorithms, and data-driven decision-making.