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This study considered reorder point on the continuous review inventory model under controllable lead time with mixture of backorder price discounts and partial lost sales. We developed a continuous review inventory model where the lead time, the order quantity, backorder discount and safety factor were considered as the decision variables of a mixture of backorders and lost sales inventory model. The objective was to minimize the expected total annual cost with respect to related decision variables. The purpose model with lead time demand distribution was unknown. The author applies a minimax distribution free procedure to find the optimal solution and numerical example was included to illustrate the solution procedure of the proposed algorithms

Economic Ordering Quantity Model with Lead Time Reduction and Backorder Price Discount for Stochastic Demand