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.