Bayesian Updating of Demand and Backorder Distributions in a Newsvendor Inventory Problem

Abstract

We consider Bayesian updating of demand and backorder distributions in a partial back‐order Newsvendor model. In inventory problems usually the demand distribution is assumed to be known and when stock‐outs occur it is commonly assumed that the excess demand is either lost or fully backordered. In this paper we consider a partial backorder setting, where the unsatisfied demand is backordered with a certain probability. Both demand and backorder probabilities are assumed to be random variables and Bayesian estimation methods are used to update the distributions of these variables as data accumulates. We develop expressions for the exact posteriors where the prior distributions are chosen from natural conjugate families. In particular, we assume that the demand within a period is Poisson and the bacorder probability has a Beta distribution.