Improved inventory models with service level and lead time

This paper explores the mixed inventory backorder and lost sales problem in which both the lead time and order quantity are treated as decision variables. In a recent paper on Computers and Operations Research, Ouyang and Wu considered this problem. However, their algorithms might not find the optimal solution due to flaws in their solution procedure. We develop some lemmas to reveal the parameter effects and then present two complete procedures for finding the optimal solution for the models. The savings are illustrated by solving the same examples from Ouyang and Wu's paper to demonstrate the superiority of our revised algorithms.