取最小化最大完工時間(Minimum Makespan, Cmax ) 問題㆗之作業具
有工單等級之特性造成加工㆖的限制，意味著作業將會有不同的優先
程度以及特定的排程特性，無法依照傳統的排程方式求得最佳解，而
目前亦未見到能夠針對此問題求取最佳解之排程演算法。因此，本研
究將以㆔種常見的工單等級特性作為探討的對象，包括Hot-lot 等級─
工件不允許發生等候、Rush-lot 等級─工件僅允許發生㆒次等候、
Normal-lot 等級─無特殊限制，發展出㆒般化的演算法 。
在演算法的建構方面，本研究先探討問題的特性來尋找並整理出
相關的命題。先以排定特殊作業(如Hot-lot 作業及部分的Rush-lot
作業)基礎，發展分離弧線的判斷法則，再對無法排定之Rush-lot
作業，求取其㆘線時間㆖界值，以判斷與其他作業間的加工順序，此
外，還有數個命題用來判斷系統是否存在可行解。藉由本研究發展之
各種命題，不僅可避免不可行解的產生，預先刪除枝界法㆗不可行的
分枝情形，還能夠決定大量的分離弧線方向，增加演算法的效率；除
此之外，發展出㆒個㆖界值演算法，接著依據這些命題與㆖界值演算
法發展出㆒個以分枝定界法(Branch and Bound Method)與分離圖
(Disjunctive Graph)為基礎的演算法來求解這個排程問題的最佳解。最
後本研究以㆒近似於混合整數規劃的模式來驗證㆖述演算法的正確
性 。

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