Periodic review stochastic inventory models with service level constraint

This article considers the periodic review stochastic inventory models with service level constraint to provide an improved solution procedure. The previous researchers assumed that the objective function is concave down in the lead time so that the minimum must occur on the boundary points of each sub-domain. In this article, we will show that their assumption is questionable since the minimum might not occur at the boundary points of each sub-domain. In a recent paper in International Journal of Systems Science, Ouyang and Chuang studied this problem. However, their solutions contained questionable results and their algorithm 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 our improved solution procedures for finding the optimal solution for periodic review stochastic inventory models in which the lead time demand is a normal distribution. The savings are illustrated by solving the same examples from Ouyang and Chuang's paper to demonstrate the improvement using our revised algorithm. In the direction of future research, we discuss the comparison between the reordered point being fixed and the reordered point as a new variable.