Infinitesimal Dividing Method: Sole Supplier Inventory Cost Model with Random Lead Times

This paper considers the inventory model with random procurement lead time. Using infinitesimal dividing method, the exact (Q,r) inventory cost model of single supplier procurement is presented, which is proved equal to the traditional model. Main properties of the model are analyzed strictly. The convexity of the cost function per unit time is proved. Then the optimal solution can be easily obtained by applying the classical convex optimization methods. Finally, numerical examples are given to verify the main conclusions in this paper