In this paper, we are going to exhibit an inventory model in which shortages are permitted and that can be completely replaced. The model is derived to compute the economic order quantity and to minimize the total cost. To get the optimal solution closer to the reality, the fuzzy techniques are applied. We use the octagonal fuzzy numbers to fuzzify the inventory quantities like ordering cost, holding cost and backorder cost. The ranking function of octagonal fuzzy numbers is used here for

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... ification. The optimal solutions are verified with the help of numerical illustrations.