The lack of available historical data resulting from increasing market turbulence and very short product life cycles means that the demand in an inventory system varies nonstochastically and must therefore be subjectively determined. This paper investigates the economic production lot size inventory problem, in which a positive lead time and shortages are allowed, with fuzzy demands and an unknown explicit membership function. An analysis method based on an α-cut representation and fuzzy ranking is proposed to derive the optimal inventory policy. In addition, the necessary and sufficient conditions for the optimal inventory policy are determined. The merits of the proposed approach include the ability to obtain a numeric and precise optimal policy rather than a fuzzy policy and no requirement for explicit forms of the membership functions of the fuzzy demands, which increases the generality of the proposed model. Additionally, practical insights are provided.

中文翻译：

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无显式隶属函数的模糊经济生产批量库存问题分析


由于市场动荡加剧和产品生命周期非常短，导致缺乏可用的历史数据，这意味着库存系统中的需求是非随机变化的，因此必须主观确定。本文研究了经济生产批量库存问题，其中允许正的提前期和短缺，具有模糊需求和未知的显式隶属函数。提出了一种基于α-cut表示和模糊排序的分析方法来导出最优库存策略。此外，还确定了最优库存策略的充要条件。该方法的优点包括能够获得数字且精确的最优策略而不是模糊策略，并且不需要模糊需求的隶属函数的显式形式，这增加了所提出模型的通用性。此外，还提供了实用的见解。