Dynamic Pricing and Inventory Control: the Value of Demand Learning

This paper studies various approaches to demand learning in the context of a one-shot inventory replenishment problem with dynamic pricing. The customer arrival process is assumed to be piecewise deterministic and Markovian with an unknown parameter. Homogeneous customers have an iso-elastic demand function and do not behave strategically. We study full information, non-learning, passive learning and active learning pricing policies, all of which take the form of a product of a series of indices and a power function of on-hand inventory. We find that prices generated by different pricing policies can follow a super/sub/martingale, depending on an observer’s information structure. We find that without learning the optimal inventory path is deterministic, but it becomes stochastic when learning is considered. Through computational experiments, we find that passive learning pricing policies can approximate the optimal active learning pricing policy well, but that non-learning pricing policies often perform very poorly. Finally, we observe that the values of information and learning are magnified by coordination of pricing with the inventory decision.