A heuristic solution procedure for an integrated inventory system under controllable lead-time with equal or unequal sized batch shipments between a vendor and a buyer

This paper develops a heuristic solution procedure to minimize the total cost of setup or ordering, inventory holding and lead-time crashing for an integrated inventory system under controllable lead-time between a vendor and a buyer. Recently, this system has been studied with an extra safety stock over the year and a technique to attain a minimum cost solution has been developed. In this paper, the shortcoming of this technique in providing minimum cost solution is demonstrated. In addition, an alternative generalized model, based on equal and unequal sized batch shipments of a lot from the vendor to the buyer, is developed. Restricting the safety stock for the time of satisfying demand by the lot, a number of properties that the optimal solution should satisfy are developed. Based on these properties an algorithm giving the optimal solution is then derived. The potential value of transferring the lot with equal and unequal sized batches in reducing the total annual cost is illustrated with the solution of two numerical examples.