Inventory model involving lead time and setup cost as decision variables

Almost all inventory models assume that lead time is prescribed, regardless of whether it is deterministic or probabilistic, and thus is not subject to control. However, in many practical situations, lead time and setup cost can be reduced at added costs. This article combines the concept of capital investment allocated to reducing lead time and setup cost. This article explores the problem of a continuously reviewed inventory model, in which lead time, setup cost and order quantity are decision variables with permitted shortages. The correct total expected annual cost is derived, and a solution procedure is presented to determine the optimal order quantity, lead time and setup cost. Finally, to illustrate the solution procedure, numerical examples are provided.