生產批量問題是製造業中十分基礎且重要的問題，在有限的產能下最小化相關生產成本，此種問題可被稱為產能限制批量排程問題（CLSP）。本研究探討考量四項重要裝設因素的CLSP，此四項因素包含：（1）裝設時間會占用產能（2）順序相依的裝設成本及時間（3）允許裝設延續至下一期，亦即，若下期第一個生產產品與本期最後一個產品相同，不需再重新裝設，以及（4）允許裝設時間跨期，亦即，一次裝設不限定於要在同一期內完成，可以跨越多期。由於此問題本就複雜度高，若同時多考量此四項裝設因素，會再大幅增加問題的難度，故目前文獻中鮮少能夠完善涵蓋此四項裝設因素。且顧及在現實生產環境中的實用性，本研究不僅考量如何正確的求解問題，更考量如何有效率的求解。
本研究將以兩種啟發式搜尋演算法求解此問題，包含塔布搜尋法以及模擬退火法。且將總體解決方案分為離散決策以及連續決策，離散決策包含每個批量生產的產品以及生產次序，連續決策則是每個批量開始以及結束的時間點。在給定一離散決策後，透過求解線性規劃問題可求得連續決策。為提升求解過程在程式中的效率，本研究提出一特殊方式來在程式中建構數學模型，鄰近解可使用現行解的數學模型進行調整，以有效運用本研究使用之線性規劃求解程式中的單形法敏感度分析。本研究也將平行運算的技術導入啟發式搜尋法，來進一步增進求解效率。

Lot sizing is an essential decision in many manufacturing environments. With the objective to minimize relevant costs within limited capacity, this problem is also called capacitated lot sizing and scheduling problem (CLSP). This study investigates CLSP with four comprehensive setup considerations, including: (1) setup times; (2) sequence-dependence for both setup costs and times; (3) setup carryover, avoiding duplicate setups of a same item in adjacent periods; and (4) setup crossover, allowing setups to run across the boundary of two adjacent periods. The complexity of CLSP has been proven to be NP-hard. Considering these four setup features simultaneously further increases the complexity of CLSP and existing study on this problem is rare. Because of the practicality in manufacturing environments, solving the problem not only correctly but also efficiently is the main focus of this study.
Two metaheuristic algorithms, Tabu search (TS) and simulated annealing (SA), are experimented in this study. An overall solution of a problem is divided into two kinds of decision: discrete decision and continuous decision. Discrete decision contains the item produced in each batch, and the sequence of epochs, which include the start and end epochs of batches and boundaries of periods. Continuous decision refers to the exactly start and end times of each batch. With a discrete decision, a linear programming (LP) model can be solved to obtain continuous decisions. To improve solution efficiency and take advantage of post-optimization techniques of the Simplex method of the LP solver used in this study, various methods are proposed to generate the LP instance of a neighborhood solution by few modifications of the LP instance of a current solution. To further improve the solution efficiency, TS and SA are both implemented with parallel computing technique.

摘要 I
Abstract II
圖目錄 V
表目錄 VII
1. 緒論 1
1.1. 問題背景及應用 1
1.2. 產能限制批量排程問題之分類 2
1.3. 產能限制批量排程問題之延伸與複雜度 2
1.4. 問題假設與求解方法 4
2. 文獻探討 6
2.1. CLSP之歷史概述及經典文獻 6
2.2. 裝設時間及成本的相關之文獻 7
2.2.1. 允許裝設延續之CLSP 7
2.2.2. 允許裝設時間跨期之CLSP 8
2.3. 啟發式搜尋演算法之相關文獻 9
2.3.1. 禁忌搜索法及CLSP之相關應用 9
2.3.2. 模擬退火法及CLSP之相關應用 9
2.4. 平行運算及生產排程相關應用 10
3. 研究方法 11
3.1. 混合整數規劃數學模型 11
3.2. 產生起始解：啟發式方法 14
3.3. 離散決策與連續決策 18
3.3.1. 離散決策與連續決策之概念 18
3.3.2. 連續決策：線性規劃數學模型 19
3.4. 探索鄰近解流程 21
3.4.1. 四種探索鄰近解方法 21
3.4.2. 確認鄰近解可行性之方法 25
3.4.3. 基於影子價格資訊之局部搜索演算法 26
3.5. 在程式中建構線性規劃數學模型方法 29
3.6. 啟發式搜尋演算法 32
3.6.1. 禁忌搜索法 32
3.6.2. 模擬退火法 34
3.7. 平行運算 37
3.7.1. 產生平行啟發式搜尋演算法之起始解方法 37
3.7.2. 平行啟發式搜尋演算法 38
4. 實驗結果與探討 40
4.1. 實驗問題產生流程 40
4.2. 實驗參數設定 42
4.3. 實驗結果分析 43
4.3.1. 建立數學模型方法對於程式求解效率之影響 43
4.3.2. 各控制變因對目標值之影響 44
4.3.3. 各方法求解效率之評估及探討 49
5. 結論與未來研究方向 53
參考文獻 54

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