Minimax distribution free procedure with backorder price discount

The inventory models analyzed in this paper explore the problem in which the lead time and ordering cost reductions are inter-dependent in the continuous review inventory model with backorder price discount. The objective is to minimize total related cost by simultaneously optimizing the order quantity, reorder point, lead time and backorder price discount. Moreover, we assume that the mean and variance of the lead time demand are known, but its probability distribution is unknown. We apply a minimax distribution free procedure to find the optimal solution, and three numerical examples are given to illustrate the results.