Continuous review (s, S) policies for inventory systems incorporating a cutoff transaction size

In this paper, a mathematical model is developed for the analysis of optimal replenishment policies for items which experience lumpy demands. In order to avoid disrupting the inventory system, a cutoff transaction size of w units is specified such that customer demands with sizes exceeding w units will be filtered out of the inventory system and treated as special orders to be satisfied by special deliveries. Customer demands with sizes > 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 stuttering Poisson distribution. Recursive formulae are developed for the determination of the probabilities of the lead time demand and the available inventory position. The optimal values of the control parameters, s and S, are determined. The theoretical results obtained are illustrated with a numerical example.