A simple and robust model for computing the service level impact of lot sizes in continuous and lumpy demand contexts

Abstract Lot sizes that cover material requirements for more than two periods' demand have a built-in service level impact. The lot sizes act as a buffer for variations in demand for every period (week) but the last. However, procedures for including the service level effect of the lot size in the lot-sizing decision have not been developed. This article develops a very simple but robust mathematical model for computing the service level guaranteed by any lot size, Q, in both continuous and lumpy demand contexts. The model turns out to be a very simple mathematical expression involving the lot size, Q, the number of periods of demand covered by the lot size, n, and the standard deviation of the demand, σ. Some purely mathematical evaluations of the model were undertaken, and were found to predict both the direction of change of the service level as a function of Q and σ and the limit of the service level very well. A simulation experiment was also designed to test how well the model predicted the service level generated by the lot size, Q. The value of Q was set at the beginning of each experiment; the parameters of demand distribution were denned a priori. The simulations involved setting the lot size, Q, randomly generating individual demands from the known distribution, and recording the impact on the inventory and service levels. The results show that the model's prediction of the service level generated by any given lot size, Q, was very precise and reliable. The performance of the model was excellent even for cases where demand variability, as measured by the standard deviation, was high. Moreover, the built-in service level of lot sizes turned out to be high, ranging from 95% to 100%. The ability to do a reasonably precise, a priori computation of the service level generated by a lot size, Q, has fundamental ramifications for production and materials management. One of these ramifications is the ability to size safety stocks to increase the service level from that generated by the lot size to the target sought by management. The article demonstrates that the safety stock will be smaller if the built-in service level of the lot size is factored in. The conclusion is that lot-sizing decisions cannot be divorced from safety stock computations, as has been done traditionally in theory and practice. Moreover, the choice of a lot-sizing approach must consider the service level objectives of the company.