本研究以經濟生產批量(EPQ)且允許缺貨後補為基本架構，放寬部份傳統理論的假設限制並提出兩種模式來討論，一則是考慮生產過程中生產設備可能會有異常的狀況發生對整體生產總成本與生產週期時間的影響。其二為在具重修不良品模式下考慮保固成本對生產模式的影響。在實際生產實務上，製程並非一設置後就能運作到汰舊換新的階段而沒有出現任何異常狀況，因生產過程因為設備上的損耗而會造成不良品、報廢品的產生。故本研究的主要的目的在調整傳統EPQ模式，減少與實際情況的偏差。根據生產情況各項因素，設定最佳的生產時間，達到總成本為最小為目的。
本研究方法是將實際上會產生的問題導入數學模式呈現，由模式的推導與數學軟體的輔助來得到全域或局部之最佳化的生產時間、缺貨量與生產成本。根據數值分析的結果得知在兩種模式中其單位時間期望總成本均小於EPQ模式所獲得的成本。此外，經由敏感度分析可得到參數對決策變數的影響程度。就數據觀察得知，對整體生產系統的影響為單位生產率、單位需求率、整備成本、單位缺貨的影響程度較為明顯。相對地，其餘參數如製程退化平均次數對決策變數的影響程度較小。

Determining the economic production quantity (EPQ) or production cycle length under various conditions has considerable researches. Typical models for determining the EPQ assume that the quality of products and production process are perfect. In practice, due to the deterioration of production, generate of defective items is inevitable.
This paper presents two models to solve the economic production quantity with backorder under imperfect production process. The first EPQ model incorporates the effect of shift of production rate and the generation of defective items in production cycle time decision. The second model considers an unreliable production system with warranty cost.
This paper develops mathematical models to minimize total production cost per unit time via calculus and Mathematica. We obverse the two modified models are better then traditional EPQ models in the numerical examples. Sensitivity analysis is performed. The results indicate that production rate, demand rate, setup cost, shortage cost are sensitive to overall production system and other parameters are insensitive.

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