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A mixture periodic review inventory model with fuzzy backorder rate where both lead time and review period are considered as decision variables is constructed. In the practical situation, the lead time demand distribution information and backorder rate are always unknown due to various uncertainties. Therefore, it is assumed that the first two moments of the protection interval demand are given and backorder rate is a fuzzy number. A minimax distribution free procedure is applied to find the optimal lead time and optimal review period. The effects of fuzziness of the backorder rate on the optimal procedure solution are discussed via numerical examples.