Inventory model involving lead time as a decision variable with a mixture of lost sales and backorders

Abstract

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 can be reduced at an added cost. The purposes of this study are to incorporate both the penalty of lead time reduction and allow for the shortages into the inventory model and to develop a solution procedure to determine the optimal inventory policy. This article explores the problem of a continuously reviewed inventory model, in which both lead time 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 and lead time. Finally, to illustrate the solution procedure, numerical examples are provided.

Keywords:

• inventory
• lead time
• optimal order quantity