A simple method to locate the optimal solution of the inventory model with variable lead time

Abstract This article tries to find the optimal order quantity and optimal lead time of a mixture inventory model. First, this article establishes a principle to compare the optimal order quantities at all the lengths of lead times with components crashed to their minimum duration. Second, some lemmas are developed to reveal the effects of parameters and to simplify the solution procedure of Ouyang, Yeh and Wu. Finally, some numerical examples are given to illustrate all lemmas in this article. Scope and purpose This article explores the problem of a continuous review inventory model in which both lead time and the order quantity are treated as decision variables and the shortages are allowed. In a recent paper, Ouyang, Yeh and Wu considered such problems. The purpose of this article is twofold. First, this article examines the effect of the fraction of the demand backordered during the stockout period on the minimum total expected annual costs at all the lengths of lead times with components crashed to their minimum duration. Second, a simple method to locate the optimal solution is developed to simplify the solution procedure.