Service-oriented decisions on inventory levels in the case of incomplete demand information

Abstract

New products without historical demand information or slow-moving items with little such information cause difficulties in defining inventory management policies facing demand uncertainty. The classical approach using the Normal distribution for describing the random demand during lead time might lead to a degraded level of customer service. But the choice for other types of distributions is also no option, so it is realistic that the full functional form of the distribution is unknown, but the decision-maker has some but not incomplete information on the demand distribution during lead time. As the distribution is only partially specified, several distributions satisfy the known information. Customer service measures therefore also take values in an interval between a lower and an upper bound. In this paper, upper and lower bounds are determined for two performance measures: the number of stock-out units and the stock-out probability per replenishment cycle, given incomplete information about the demand distribution, that is only the first two moments and the range, are known. Based on these results, the optimal inventory level given the desired maximum number of stock-out units or the desired maximum stock-out probability is calculated for the case where only the first two moments are known. The results of our approach are compared to the more traditional approach where a Normal distribution of demand during lead time is assumed. Comparisons with the Gamma, Uniform and symmetric triangular distribution are made. Furthermore, the robustness of our bounds to uncertainty in the parameters is tested.