The effects of investing in lost sales reduction on the stochastic inventory models

This paper considers the continuous review, stochastic demand inventory model with a mixture of backorders and lost sales. It investigates the feasibility of investing in reducing the lost sales caused by stockout. We first assume that the lead time demand follows a normal distribution, then relax this assumption to consider the distribution free case where only the mean and standard deviation of lead time demand are known. An algorithm is developed to find the optimal ordering policy and the optimal investment strategy. Also, two numerical examples are provided to demonstrate the results.