In this study, we investigate the periodic review inventory models with a mixture of backorders and lost sales by controlling lead time and setup cost simultaneously to reduce the inventory operating cost. It is assumed that the probability distribution of the protection interval, i.e., review period plus lead time, demand is unknown but its first two moments are given, we apply the minimax distribution free procedure to solve this problem. An algorithm to find the optimal solutions is developed. Specifically, from the results of numerical examples, it can be shown that, the significant savings can be achieved through the reductions of lead time and setup cost.
