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The stochastic inventory models analyzed in this paper explore the problem of lead time associated with setup cost reductions for the continuous review and periodic review inventory models. For these two models with a mixture of backorders and lost sales, we respectively assume that their mean and variance of the lead time demand and protection interval (i.e., lead time plus review period) demand are known, but their probability distributions are unknown. We develop a minimax distribution free procedure to find the optimal solution for each case.

SETUP COST AND LEAD TIME REDUCTIONS ON STOCHASTIC INVENTORY MODELS WITH A SERVICE LEVEL CONSTRAINT