Inventory models with fixed and variable lead time crash costs considerations

Most of the literature pertaining to inventory problems assumes lead time to be a prescribed parameter and thus not subject to control. In many practical situations, inventory lead time can be shortened at the expense of additional cost. Hence, the variable lead time can be regarded as a decision variable since it can be decomposed into several components, each having a crash cost function for the respective reduced lead time. However, in the related research each such crash cost is often treated only as a function of the reduced lead time. In this paper, crash cost is represented as a function of both the order quantity and the reduced lead time. An inventory model with normal demand is first presented and another model with unknown demand distribution is also discussed. Numerical examples are included to illustrate the procedures of the algorithms. These examples also show that the crash priority changes as the demand changes.