Maximum issue quantity problem for inventory systems when demand is lumpy

Abstract

This paper presents a mathematical model developed for the synthesis of optimal replenishment policies for items that experience lumpy demands. In order to avoid disrupting the inventory system, a maximum issue quantity restriction is introduced such that customer demands with sizes equal to or exceeding w units will be filtered out of the inventory system and satisfied by placing a special replenishment order to a higher echelon. Customer demands with sizes less than w units will be met from stock. The control discipline is the (s, S) inventory policy with continuous review and the nature of the demands is approximated by a discrete compound Poisson distribution. The optimal values of the control parameters, s and S, are determined. The theoretical results obtained are illustrated with a numerical example.