Linear programming models to support inventory decision-making in the case of incomplete information on demand during lead-time

Abstract

Most logistics managers face uncertainty in demand which forces them to hold safety stock to provide high levels of service to their customers. The level of safety stock depends on what the company’s targets are on some performance characteristics of an inventory management decision problem like the expected number of units short or the stock-out probability. In the case only incomplete information is available on the demand distribution during the lead-time, which is relevant in inventory decision-making, preset service levels do not lead to a unique value of the safety stock to be hold, but rather to a range of values. Incomplete information refers to the fact that the full functional form of the distribution is not known, but some knowledge is available like the range or the mode or a few moments of the demand size distribution. In this way, upper and lower bounds may be determined for the safety stock in the inventory management problem. It is shown how the bounds of both performance measures can be obtained through a numerical approximation using linear programming. Results are obtained for demand distributions for which the range, and first and second moments are known.