Background: In this paper we developed a fuzzy two-warehouse (one is OW, the own warehouse and other is RW, the rented warehouse) inventory model of deteriorating items with price dependent demand rate and allowed shortages under partially backlogged conditions. Since the capacity of any warehouse is limited, the supplier has to rent a warehouse for keeping the excess units over the fixed capacity W of the own warehouse in practice. The rented warehouse owed higher holding cost than the own warehouse. In this paper we considered holding cost, deterioration rate, shortages cost and lost sales as triangular fuzzy numbers. Methods: Graded Mean Integration Representation is used to defuzzify the total cost function. The result obtained by this method is compared with crisp model with the help of a numerical example. Sensitivity analysis is accomplished to changing one parameter at a time and keeping others at their archetypal. Results and conclusions: It has been proved that graded mean integration representation method gives more accurate result as compare to crisp model.

中文翻译：

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带有部分积压的价格依赖需求和短缺的变质物品的两仓库库存模型

背景：在本文中，我们开发了一种模糊的两仓库库存模型（一个是OW，自己的仓库，另一个是RW，租用仓库），该模型具有价格依赖的需求率并且在部分积压条件下允许短缺的变质物品。由于任何仓库的容量都是有限的，因此供应商实际上必须租用一个仓库以使多余的单元保持在其自身仓库的固定容量W之上。租来的仓库比自己的仓库拥有更高的持有成本。在本文中，我们将持有成本，恶化率，短缺成本和销售损失视为三角模糊数。方法：使用分级均值积分表示法对总成本函数进行模糊化处理。借助数值示例，将通过此方法获得的结果与清晰模型进行比较。灵敏度分析可以一次更改一个参数，而另一个参数保持原型。结果与结论：已经证明，与均值模型相比，分级均值积分表示法给出的结果更为准确。