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 as Postpone(q,t) and Split(q), respectively. The parameter q distinguishes between regular orders (of size less than or equal to q) and larger orders. We develop mathematical expressions for the performance measures: order fill rate of the regular orders and average on-hand inventory level. We make numerical experiments where the postpone parameter t and the base stock levels of each rule are such that all customers (of both order types) are indifferent between the two rules. When comparing the difference in the average on-hand inventory levels, we can then make an assessment of the threshold value of the cost of splitting an order (which may otherwise be hard to quantify) in the rule Split(q). Our numerical results indicate that this threshold value is increasing in the variance of the order sizes. Based on the numerical experiment our conclusion is therefore that when the variance of the order sizes is low, then Postpone(q,t) seems to be a good option, while when the variance is high, then Split(q) is more competitive.