A minimax distribution free procedure for stochastic inventory models with a random backorder rate

The stochastic inventory models analyzed in this paper involve two models: continuous review and periodic review in which the backorder rate is a random variable. For these two models with a mixture of backorders and lost sales, we respectively assume that their mean and variance of lead time demand and review period demand are known, but their probability distribution, are unknown. Instead of having a stockout cost term in the objective function, a service level constraint is added to the models. We develop a procedure to find the optimal solution for each case. Furthermore, the sensitivity analysis is performed.