在迴流式生產系統中，同一工件因製程上之需要，必須在相同機台重複進行多次加工，且通常為有限產能之瓶頸機台，因此，決定各產品在此類機台之生產週期與生產批量，以有效利用產能並滿足顧客需求為重要議題。在現有相關文獻中，大多針對迴流製程或生產系統，探討不同訂單指派與排程問題，在生產規劃層面上，探討其不同產品之經濟生產批量決策極為少見，本論文針對多產品於單一機台迴流加工之經濟批量排程問題，以數學分析建構成本模式，並發展求解方法。
本研究考慮多產品於單一機台進行多次加工之迴流製程，當產品尚未完成其所有迴流加工程序前僅為半成品，在最後一次迴流加工後才成為成品，故考量之持有存貨包含半成品與成品。模式中考量機台整備成本與存貨持有成本，並考慮產品於每次迴流加工所增加之存貨價值，即階層存貨價值之概念，以估計該批量產品於整個生產過程所累積增加之存貨持有成本；此外，亦考量製程中暫存區或物料搬運系統之容量上限，即在製品數量或其容量具上限；並以最小化單位時間總成本為目標，決定在長期規劃時程下各產品之生產週期與生產批量，藉以建構可行之生產作業。
以文獻中不考慮迴流生產之共同週期法為基礎，本研究首先建構迴流式經濟批量排程問題之單位時間總成本模式，進而發現其目標式為共同週期之嚴格凸函數，並依據所發現之理論性質設計一快速求解方法。由64組演算實驗結果顯示，產品種類總數與加工次數對單位時間總成本之影響最大，其次為存貨相關成本參數；對共同週期決策而言，則以加工次數影響最大，且整備時間亦影響顯著；在成本偏差部分，當成本函數最小值之共同週期為可行時，其成本值與獨立解法目標值之平均成本偏差約1.88%，表示透過本模式所得之共同週期與未知最佳解間之平均成本偏差甚小；而當共同週期決策非該值時，其平均成本偏差則較大，需另發展一較佳成本下界之估計式。

An Economic Lot Scheduling Problem (ELSP) in a re-entrant production system is investigated in this thesis. Raw material enters the system, work-in-process (WIP) accumulates in the re-entrant stage, where multiple, repetitive processing is required to complete a finished product. Demand must be satisfied with finished goods and no shortage is allowed. Echelon value of a product at different processing stages are modeled, and buffer capacity is considered in the analysis. The optimal cycle time and the economic production quantity of each product are to be determined to minimize the total relevant cost per unit time, which consists of setup cost and inventory holding costs of WIP and finished product.
Via the Common Cycle (CC) approach, the per unit time cost model for the Re-entrant Economic Lot Scheduling Problem (RELSP) is analyzed. The cost model can be shown to be convex with respect to the common cycle time. Using this property, an efficient solution procedure to find the optimal common cycle time is developed. Computational results with 64 instances have demonstrated that the numbers of product types and processing stages have the most significant impact on the total relevant cost per unit time, followed by the setup cost and the echelon inventory holding cost of WIP. When the common cycle time with the minimum cost value is the optimum control policy, the average deviation of total cost per unit time for the proposed approach from those found with the Independent Solution (IS) approach is approximately 1.88%. It indicates that solution quality of the proposed approach is excellent.

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