Abstract: This paper studies the problem of the Economic Production Quantity（EPQ） with repairable imperfect items and fuzzy repairable rate; The optimal production policies are determined using fuzzy structured element theory to solve the fuzzy models; The optimal production quantity with fuzzy structured element is obtained; The positive definite characteristic of Hessian matrix shows that the objective function has the minamal production inventory cost at the optimal production quantity point; The relationship between model and classical EPQ is revealed through theoretical analysis; A numerical example is given to illustrate the feasibility of using the fuzzy mathematics to solve the inventory problem.

Key words: Economic Production Quantity（EPQ）, fuzzy structuring element, fuzzy defective rate, rework, shortage

摘要： 研究了缺陷产品可修复且修复速率为模糊变量情况下的生产库存模型；给出了基于模糊结构元理论的求解模糊库存总成本最小化的方法步骤；得到了含有模糊结构元的最佳生产批量的表达式；应用Hessian矩阵的正定性验证了最小成本的存在性；分析了其与经典EPQ公式之间的联系；最后通过具体算例，证明了模型求解方法的可行性。

关键词: 生产库存模型, 模糊结构元, 缺陷率, 修复, 缺货