A partial fill problem in inventory control

This paper presents a mathematical model developed for the synthesis of optimal replenishment policies for items which experience lumpy demands. In order to avoid disrupting the inventory system, a cutoff point of w units is introduced such that the system would only satisfy routinely customer orders with transaction sizes less than or equal to w units. For customer orders with transaction sizes larger than w units, the system would only supply the cutoff amount (w units). The excess units would be refused. 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, w, s and S, are determined. The theoretical results obtained are illustrated with a numerical example.