Bio: Boxiao (Beryl) Chen’s research applies data-driven techniques from statistical machine learning and stochastic optimization to solve business related problems. She develops online and offline machine learning algorithms for inventory and supply chain management, and pricing and revenue management. Prof. Chen’s research has appeared in top tier journals, such as Management Science, Operations Research, Manufacturing & Service Operations Management, Production and Operations Management, and Mathematics of Operations Research. She serves as Senior Editor for Production and Operations Management and as Associate Editor for Operations Research Letters.
Abstract: We consider a joint pricing and inventory control problem in which pricing can be adjusted more frequently than inventory ordering decisions. More specifically, the pricing decision is adjusted every period, while new inventory is ordered every epoch, with each epoch consisting of multiple periods. This setting is motivated by many examples, especially among online retailers, in which prices are much easier to change than inventory levels, because changing the latter is subject to prior arrangements or logistical constraints. In this setting, the retailer determines the inventory level at the beginning of each epoch and solves a dynamic pricing problem within that epoch, with no further replenishment opportunities. The optimal pricing and inventory control policy is obtained from an intricate dynamic program (DP), in which the inventory level is the state variable and the pricing policy is characterized as a function of the inventory level. We consider the situation in which the demand–price function and the distribution of random demand noise are both unknown to the retailer, who must develop an online learning algorithm to learn this information while simultaneously maximizing total profit. We propose a learning algorithm that applies linear bandit techniques under the upper confidence bound (UCB) framework, and we prove that it converges through the DP recursions to the optimal pricing and inventory control policy that would be obtained under complete demand information. The theoretical lower bound for the convergence rate of the 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. Numerical results show that our learning algorithm performs very well.
