Some probability distributions related to the arrival of demands in a two-echelon inventory system

Abstract

This paper is concerned with a generalization of the two-echelon (base-depot) inventory system considered by Shanker in which the demands occurring at bases depend now on the total number of demands that have arrived before. Simple probabilistic arguments are used to derive the probability distribution of the number of demands. It is also shown that the results of Shanker on some conditional distributions related to the arrival of demands remain valid for this more general model.