An analytical determination of lead time with normal demand

Almost all inventory models assume that lead time is prescribed and thus is not subject to control. In many practical situations, however, lead time is controllable; that is, lead time can be shortened, at the expense of extra costs, so as to improve customer service, reduce inventory investment in safety stocks, and improve system responsiveness. Although some authors recognise the advantage of short lead time and suggest that it should be considered a variable for management to control instead of a given, there is a lack of a suitable inventory model for determining the optimal lead time. A probabilistic inventory model in which the lead time is a decision variable is presented. It is assumed that the demand follows normal distribution and the lead time consists of n components each having a different cost for reduced lead time. The objective is to determine the lead time that minimises the sum of the expected holding cost and the additional cost.