Base stock policies with degraded service to larger orders

We study an inventory system controlled by a base stock policy assuming a compound renewal demand process. We extend the base stock policy by incorporating rules for degrading the service of larger orders. Two specific rules are considered, denoted Postpone(q,t) and Split(q), respectively. The aim of using these rules is to achieve a given order fill rate of the regular orders (those of size less than or equal to the parameter q) having less inventory. We develop mathematical expressions for the performance measures order fill rate (of the regular orders) and average on-hand inventory level. Based on numerical experiments, our conclusion is that Split(q) seems to perform best.