The Censored Newsvendor Problem with Newsvendor Demand Distributions

We study the dynamic newsvendor problem with censored demand for both perishable and storable inventory models. We focus on the cases when demand is represented by a member of the newsvendor family of distributions. We show that the Weibull density is the only member of newsvendor distributions for which the optimal solution can be expressed in scalable form. Consequently, scalability yields sufficient dimensionality reduction so that when inventory is perishable, we can derive the optimal solution and cost in easily computable simple recursions for the Weibull demand and in explicit closed form for the exponential demand. Moreover, for the storable inventory problem with exponential demand, scalability is shown to lead to convexity and recursion for the cost function, thereby yielding efficient computation of the unique optimal solution.