Computing optimal (s, S) policies for inventory systems with a cut-off transaction size and the option of joint replenishment

Abstract

This paper presents a mathematical model that is developed for the synthesis of optimal replenishment policies for items exhibiting lumpy demand patterns. In order to avoid the disruption of the inventory system, a maximum issue quantity restriction is incorporated into the inventory control policy. In doing so, customer demands with a size exceeding w units will be filtered out of the inventory system, but satisfied by placing a special replenishment order. The rest of the customer demands will be met from stock. The control discipline is the continuous review (s, S) inventory policy and the nature of the demands is approximated by a discrete compound Poisson distribution. To further reduce the total annual ordering cost, specification is made such that when the current inventory position is below a critical level, A, at the time when a customer demand with a size exceeding w units arrives, a joint replenishment is placed that will not only initiate a direct shipment to the customer, but will also raise the inventory position to S. An algorithm is developed to determine the global optimal values of the control parameters, s and S for given w and A. A numerical example is used to illustrate the methodology, and the results obtained clearly show that a better cost performance can be obtained with the incorporation of both a maximum issue quantity restriction and the option of joint replenishment into the inventory control policy.