Censored Newsvendor Model Revisited with Unnormalized Probabilities

Abstract

This paper revisits the model of the censored newsvendor presented by Ding, Puterman and Bisi (2002). We analyze that model in an infinite-horizon context by using the interesting concept of unnormalized probabilities. The unnormalized probabilities considerably simplify the dynamic programming equation and facilitate the proof of the existence of an optimal policy. They can also be used to give a simple, alternative proof to Ding et al.'s claim that the myopic order quantity is always less than or equal to the optimal order quantity. Importantly, the concept of unnormalized probabilities can be used to treat other important operations research problems with partial observations.

Keywords: Unnormalized probabilities, Unobserved unmet demand, Newsvendor problem, dynamic programming, infinite dimensional spaces, incomplete information, partially obsereved systems, optimal control

JEL Classification: C61, M11, D8