在真實製造過程裡，當製程在管制內可生產出高品質或完美品質的產品；然而，當製程不在管制內，則容易產出品質有瑕疵的產品。因此，在任一生產週期中，產品的品質是不可能總是完美的，產出有瑕疵之產品是不可避免的。在傳統的經濟生產批量(EPQ)模式中，往往假設所有的產品都是良好的，這其實是很難符合真實的生產狀況。為反映現實中不可避免之有瑕疵的生產程序，本研究首先構建一新的數學模式，探討在產出品質有瑕疵的情況下，經濟生產批量模式的最適生產策略。在此模式中，假設產品的不良率為一隨機變數，針對不良品將予以一次的修復再決定是否視為廢料。此外，亦將缺貨及部分補貨的情況列入考慮。因此，修復成本、檢查成本、廢料損失、缺貨損失及銷售損失等相關成本皆被涵蓋於本模式中。接著，為避免繁複的微分過程及代數運算，本研究將採用算數-幾何平均數不等式的方法決定最佳解。最後，利用數值範例和敏感度分析驗證及說明此最佳解在管理上的運用及其意涵。 In the real production environment, a production process may be in either a “in-control” state, items produced maybe of high or of perfect quality, or a “out-of-control” state and produce defective items. Hence, it is inevitable that the production process generates defective items. In the traditional economic production quantity (EPQ) model, it is assumed that production process functions perfectly at all times. This assumption does not conform to the practical manufacturing environment. To reflect the real word situation, we develop a new mathematical model to study the optimal production policy for an imperfect quality EPQ model with partial backlogging and failure in repair. We assume that the defective rate is a random variable, all items produced are screened and all defective items are reworked. In addition, the assumption that shortages are allowed and partially backlogged is also considered in this study. Repair, inspection, disposal, shortage and lost sales costs are all included in the proposed model. An arithmetic-geometric mean inequality mothod is employed to determine the optimal solution without taking differential calculus or using complex algebraic manipulation. Finally, the model proposed is illustrated through numerical examples and sensitivity analysis is reported.
