在當前製造實務上，供應鏈管理(SCM)與即時系統(JIT)的概念廣泛的被運用。在供應鏈環境中，利用即時的概念來獲得並維持競爭上的優勢。即時系統(JIT)是由下列幾項特徵組成：交貨頻率、較短的前置時間、與供應商緊密連結、小批量和一致的高品質。而整合存貨模型能有效的顧及買賣雙方利益平衡的考量下，尋求出最佳策略。潘昭賢博士與楊金山博士在2002年所發表的文章中，整合存貨模型是以明確值為輸入變數加以研究。在實際多樣少量生產的環境中，要準確地預測這些輸入變數的資訊是很困難的，所以我們以模糊的觀念來加以探討。因此，我們先不考慮趕工成本部分，將考慮品質改善投資的整合存貨模型用以模糊的觀念加以探討並藉由數據執行，觀察其特殊現象。這樣的做法能提供我們以另外一種角度來解決存貨問題。在本篇文章中，我們以模糊集合的概念，導入整合存貨模型中的三個變數，買方年需求、賣方年生產量以及製程脫離管制機率，並加以討論。

Supply chain and just-in-time (JIT) are popular concepts in manufacturing in practice. Using JIT concept in supply chain environment to gain and hold a competitive advantage is usually applied in manufacturing. Characteristics of JIT consist of frequent delivery, short lead time, close supplier ties, small lot sizes and consistent high quality. This integrated inventory model can be useful to find a optimal strategic alliance between the vendor and the purchaser for profit sharing. Pan and Yang (2002) studied integrated inventory with crisp value. In real environment, for purchaser and vendor, getting and predicting precisely and exactly the order information on large variety products with low quantity are very difficult. As the result, we discuss that the integrated inventory model without crashing cost and with quality improvement investment is considered by the concept of fuzzy sets in this paper and find the phenomena for the model by numerical data, which can give us another point of view to solve the problem with care. In this paper, we introduce the concept of fuzzy sets into the integrated inventory model with quality investment improvement by three fuzzy factors, annual demand, production rate and out-of-control probability.

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