Optimal Learning Policies for the Newsvendor Problem with Censored Demand and Unobservable Lost Sales

In this paper, we consider a version of the newsvendor problem in which the demand for newspapers is unknown and the lost sales are unobservable. This problem serves as a surrogate for more complex supply chain problems in which learning plays a role. We propose the knowledge gradient (KG) policy, which considers how much is learned about the demand distribution from each order. This policy combines computability with good performance. We analyze the behavior of this policy under two demand distributions: an exponential distribution with a gamma prior, under which the optimal policy is computable, and a general demand distribution with finite support and Dirichlet prior under which the optimal policy is very hard to compute. In the exponential demand case we contrast the KG policy with two naive policies and the optimal policy, and in the general demand case we contrast the KG policy with a naive policy. Our simulations show similar behavior to the optimal policy in the exponential demand case, and good performance in the general case.