在紡織產業中，由於大量的訂單及染缸數量，染色排程往往是一項瓶頸作業，且其排程的最佳化是一項複雜且困難的任務。因此，本研究以最小化延遲成本及染缸生產成本為目標，提出了混整數規劃模型以求解此染色排程問題。在本研究中，所有訂單的開始生產時間皆被限制不得早於其可以開始生產的時間。在理想情況下，訂單的完工時間需早於其承諾交付予顧客之時間，倘若不可實現，將因延遲交貨而必須支付額外的賠償費用。在本研究中，染缸的規格容量越小，所需的生產成本也越低。因此，一筆訂單通常會先被指派至規格容量最小但足以生產該筆訂單的染缸。數量小的訂單可以被允許在容量較大的染缸內進行染色，然而，此情況會產生額外的生產成本，因此須盡量避免。在染色排程問題中，順序相依的裝設時間也是一項很重要的特性。將顏色較淺之訂單排在顏色較深之訂單之前可以省略清洗染缸的過程，反之，在為下一筆訂單進行染色之前將會需要一段時間清洗染缸。此外，由於每筆訂單的布種及數量皆不同，並非每台染缸均能生產某筆特定的訂單。因此，此研究亦須將機台限制的特性納入考量。據知，目前並沒有文獻以本研究提出之混整數規劃模型完整地探討此類染色排程問題。
本研究提出了四種方法以求解此類問題，包括緊鄰變數的混合整數規劃（immediate precedence mixed integer programming, IPMIP）、非緊鄰變數的混合整數規劃（linear ordering mixed integer programming, LOMIP）、以啟發式方法提供起始解的緊鄰變數的混合整數規劃（HIPMIP），以及以啟發式方法提供起始解的非緊鄰變數的混合整數規劃（HLOMIP）。此外，為比較上述四種方法之優劣，本研究設計了運算實驗以比較及分析不同的方法。根據本研究之實驗結果，HIPMIP的求解效率在上述四種方法中最好。

Since dye operation is often a bottleneck in the textile manufacturing and there are large numbers of jobs and dye vats in a practical dye scheduling environment, its scheduling problem is a complicated optimization task. Therefore, this study presents effective mixed integer programming (MIP) models for scheduling dye operation with the objective of minimizing the overall tardiness and production costs. In this study, each job is restricted to be started later than its ready date, and it is desired to be completed before its due date; otherwise, penalty cost will be calculated in proportion to its tardiness. Besides, the smaller dye vat, the lower production costs. Hence, a job will normally be assigned to a smallest available dye vat that is large enough to process the job. Upgrading to a larger size dye vat is allowable, but should be avoided due to a higher production cost. In addition, setup time in dye scheduling highly depends on the job sequence. The required setup time for dyeing darker colored fabric after lighter colored fabric is more than vice versa. Finally, because the size and fabric of a job determine the qualification of dye vat; not all of the dye vats are qualified to process a particular job, machine eligibility is also taken into consideration. To our best knowledge, no existing literature has used MIP models to solve such dye scheduling problem.
This study proposes and tests four methods, including immediate precedence mixed integer programming (IPMIP), linear ordering mixed integer programming (LOMIP), IPMIP with initial solution provided by a heuristic method (HIPMIP), and LOMIP with initial heuristic solution (HLOMIP). Based on the experimental results in this study, HIPMIP is the most effective and efficient method to solve the problem.

摘要 I
Abstract II
LIST OF FIGURES V
LIST OF TABLES VI
1. Introduction 1
1.1. Textile Industry 1
1.2. Dye Scheduling 2
1.3. Problems Statement and Research Approach 4
2. Literature Review 7
3. Solution Methods 11
3.1. Heuristic Method 11
3.2. IPMIP 15
3.2.1. IPMIP Formulation 15
3.2.2. Determine Initial Integer Variable Values of IPMIP based on Heuristic Method 18
3.3. Linear Ordering MIP (LOMIP) 21
3.3.1. LOMIP Formulation 21
3.3.2. Determine Initial Integer Variable Values of LOMIP based on Heuristic Method 25
3.4. Numerical Example 27
4. Computation Experiments 30
4.1. Experimental Parameters 32
4.2. Problem Generation Procedure 34
4.3. Parameter Setting 35
4.4. Experimental Results 37
4.4.1. Performance Evaluation 37
4.4.2. Factorial analyses 44
5. Conclusions and Future Research 50
Reference 51

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