A study of an integrated inventory with controllable lead time

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 associated 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. In most of the literature dealing with inventory problems, either a deterministic model or probabilistic model, lead time is viewed as a prescribed constant or a stochastic variable, and is not subject to control. However, in many practical situations, lead time can be reduced by an additional cost. Moreover, the successful implementation of JIT production in today's supply chain environment requires a new spirit of cooperation between the buyer and the vendor. A desirable condition in long time purchase agreements in such a manufacturing environment is the frequent delivery of small quantitites of items so as to minimize inventory holding cost for the buyer. The vendor also needs to minimize his or her total inventory costs. An integrated inventory model that allows the two trading parties to form a strategic alliance for profit sharing may prove helpful in breaking down the traditional barriers. This paper presents an integrated inventory model with controllable lead time. The model is shown to provide a lower total cost and shorter lead time compared with those of Banerjee and Goyal, and is useful for practical inventory problems.