An inventory policy for the lead time demand with compound Poisson process and controllable lead time

Abstract

The Japanese experience of Just-in-Time (JIT) production has shown that there are advantages and benefits associated with the efforts to reduce inventory lead time and the inventory cost. The length of lead time directly affects the customer service level, inventory investment in safety stock, and the competitive abilities of a business. 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. This article relaxes the assumption that lead time demand is deterministic and assumes that it is a compound Poisson process. Also, the article assumes that lead time can be reduced at an added cost. A model is derived to determine an optimal integrated inventory policy with controllable lead time. The expected annual integrated total cost function in derived and a solution procedure is established to find out the optimal solution.