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This note examines the inventory model with service level constraint in which the lead time, the reordered point and order quantity are treated as decision variables. The previous researchers believed that the objective function is concave in the lead time such that the minimummust occur on the boundary points of each sub-domain. In this note, we will show that their belief contains questionable results. In a recent paper in Journal of the Operations Research Society of Japan, Ouyang and Chuang studied this problem. However, their algorithm might not find the optimal solution due to flaws in their solution procedure. We developed some lemmas to reveal the parameter effects and then presented the complete procedures for finding the optimal solution for the inventory model in which the lead time demand is unknown and for solving by the Gallego’s minimax distribution free procedure. The savings are illustrated by solving the same examples from Ouyang and Chuang’s paper to demonstrate a 30% improvement by our revised algorithm.

NOTE ON STOCHASTIC INVENTORY MODELS WITH SERVICE LEVEL CONSTRAINT