在排程的領域，以最佳解方法解決小規模的問題並不是難題，但隨著環境的複雜度上升，問題也相對越來越難求得最佳解，使用派工法則等啟發式演算法，在可接受的時間內求得近似最佳解已是學者們致力多年的目標。本研究探討的系統為兩階段之混合流程式生產，因需求不同使得某些工件在第一階段作業時間為零之情形，稱之為不完全作業模式(missing operations)，若以過往方式產生作業排班，將導致第二階段機台空閒之情形過長，為了改善此類情形，將這些工件直接移至第二階段進行加工，產生非排列式(non-permutation)工作序列，便可得到更好之績效。然而過去文獻中鮮少討論此類情形，其中以交期指標做為目標之研究更為稀少，因此本研究提出三個以交期指標做為目標之啟發式演算法，使此生產系統能快速回應客戶需求，本研究提出之演算法1藉由以多種派工法則產生第一階段排序，計算工件在第二階段釋放時間後，再以其他派工法則產生一組解，從不同組合中選擇最小的總延遲時間排程；演算法2亦以四種排列組合方式產生初始解，並以遞迴方式持續向下搜尋是否有較低的延遲工件數，最後回傳找到的最佳序列；演算法3則是由演算法2的步驟中，利用多個儲存空間記取所有符合最低延遲工件數的排序，從中選擇總延遲時間最低的序列，此三種演算法皆利用有效率地步驟求得近似解。
本研究先以小問題測試本研究提出之啟發式演算法有效性，再以多種參數組合之實驗，探討不同生產環境下演算法之適用性。最後根據分析結果發現，隨著不完全作業比率以及工件數的增加，本研究提出之演算法1與演算法2改善排列式排程狀況也隨之明顯。並在不同資料實驗設計的環境下，分析與交期相關之派工法則，發現當工件數較少時使用SPT派工法則；而工件數提升時使用EDD派工法則，更能快速地找到品質較佳的可行解。

This study discusses two-stage hybrid flow shop with missing operations, which means some jobs do not have to be processed at some stages. The production system we studied is composed of two stages in series. In this system some of jobs could pass over the first stage and only need to be processed on the second stage. Generally, we use the permutation scheduling (PS) method to tackle flow shop scheduling problem, but this doesn’t work effectively when jobs with missing operations. In this study, we proposed three heuristic algorithms to generate a non-permutation scheduling (NPS) from various dispatching rules for problems with due dates related objectives--minimizing the total tardiness and the number of tardy jobs. The computational experiments show that the proposed algorithms find near optimal solution efficiently in small scale problems and outperform PS methods in large scale problems.

中文部分：
賴士葆，2004年，生產與作業管理－理論與實務，第三版。台北市：華泰。
陳俊吉，2008年，以啟發式方法解決具迴流性質之彈性流程式排程問題，國立政治大學資訊管理學系碩士班論文。
黃世傑，2010年，不完全作業下兩工作站混合流程式排程研究-最小化總完工時間，國立成功大學工業與資訊管理學系碩士班論文。

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