Effective investment to reduce lost-sales rate in a periodic review inventory model

In 1973 Montgomery et al. proposed an (R, T) type of a periodic review inventory model in which the lost-sales rate caused by stockout is given. The purpose of this article is to investigate in this heuristic periodic review inventory model with partial lost-sales to effectively increase investment and to reduce the lost-sales rate. We discuss two models: complete (normal distribution) and partial (distribution free) information about the protection interval (i.e., review period plus lead time) demand distribution. For each model, two commonly used investment cost functional forms, logarithmic and power, are employed for lost-sales rate reduction. That is, for these two investment cost functions, we first assume that the protection interval demand follows a normal distribution, and then we assume that only first and second moments of the probability distribution of protected interval demand are known. Two algorithms are developed to find the optimal investment decision, and six numerical examples are given to illustrate the results.