Improved periodic review inventory model involving lead-time with crashing components and service level

A periodic review inventory model with backorders and lost sales in which both lead-time and the periodic review length are decision variables and the production interval demand follows a normal distribution is explored in this article. Ouyang and Chuang discussed this problem in a recent paper published in the International Journal of Systems Science. However, their algorithms might not, although intended to, find the optimal solution due to questionable results in their solution procedure. The purpose of this study is 3-fold. First, the criteria for the existence and uniqueness of the critical solution for minimising the total expected annual cost are determined. Second, a correct and efficient algorithm to improve their method is constructed to find the optimal lead-time and periodic review length simultaneously.