本研究主要探討多資源種類排程問題(Multiple resource type scheduling
problem, MRTSP)，此問題為多資源限制下的平行機台生產排程，並考慮了因生
產不同工作(即訂單或是產品)而導致的資源(即設備)整備時間以及與工作和機
台兩者均相關的加工時間。目前較少研究平行機台排程問題的文獻考量到多資源
限制。同時，本研究考量順序相依的資源整備時間，但為了更加準確的對此問題
的整備時間進行建模，本研究將整備時間分成卸載時間(un-setup time)與裝設時
間(setup time)並設定兩者均為順序相依。卸載時間是指將前一個工作所使用之資
源拆除與清理以便之後裝設他種資源所需要的時間，而裝設時間則是將後一個工
作所需要的資源裝設完成以便開始加工所需要的時間。此外，資源的可用性與工
作的生產時窗亦列入本研究之考量。在資源可用性的限制下，並非所有資源都可
以對一個特定工作進行加工。而每個工作(訂單)均有其特定的生產時窗(為訂單
可開始加工時間與交期之間的時間區段)，其生產活動希望在其生產時窗內完成。
倘若完成時間晚於交期，則延遲的時間稱之為生產延遲時間(Tardiness)。因此，
本研究以最小化所有工作的總生產延遲時間做為研究目的。
本研究採用三階段求解方法：第一階段提出一種啟發式做法找出一個初始可
行的排程，作為第一階段之最終解；第二階段則是採用平行化的搜尋法來進一步
改善第一階段之解，並將搜尋後得到的解稱為第二階段的最終解；第三階段則使
用混整數規劃模型來最佳化第二階段的最終解。本研究比較兩種平行化的搜尋法
/三種混整數規劃模型來決定最終使用在三階段求解架構中的第二/三階段的方
法。根據實驗結果，三階段求解方法可以取得比單純的搜尋法與單純的混整數規
劃模型更好的排程結果。

Multiple resource type scheduling problem (MRTSP), the focus of this study, is a scheduling problem in which several groups of parallel machine have to be scheduled under sequence dependent un-setup and setup times. The processing time is determined by both job and used machine. Only few of existing literatures study on parallel schedule problems considered multiple resource types. In order to accurately model the setup times for multiple resource types in MRTSP, this study separates the traditional setup time into un-setup time and setup time. The former is used to clear up the processing of the previous job, whereas, the latter is used to prepare for the processing of the following job. Both of them can be modelled as sequence dependent. In addition, resource eligibility and job time window are also considered. With eligibility limitations, not all resource units can be used to process a specific job. A job should be processed within its time windows, the time interval between its ready and due dates. If the completion time of a job is late than its due date, the delay is called tardiness. Minimizing the total tardiness of all jobs is the objective of the scheduling problem in this study.
This study adopts a three stage solution approach. The first stage uses a heuristic method to find an initial feasible solution of MRTSP; the second phase introduce a parallel searching algorithm to further improve the initial solution from phase one; the third phase adopt three mix integer programming (MIP) models to optimize the solutions from phase two. According to the experiments, three-stage approach outperforms pure parallel searching algorithm and pure MIP model.

TABLE OF CONTENTS
摘要 ................................ ................................ ................................ ................................ . i
Abstract ................................ ................................ ................................ .......................... ii
TABLE OF FIGURESTABLE OF FIGURES TABLE OF FIGURES TABLE OF FIGURESTABLE OF FIGURESTABLE OF FIGURESTABLE OF FIGURESTABLE OF FIGURES TABLE OF FIGURESTABLE OF FIGURES ................................ ................................ ................................ ... v
TABLE OF TABLESTABLE OF TABLES TABLE OF TABLES TABLE OF TABLESTABLE OF TABLESTABLE OF TABLESTABLE OF TABLES TABLE OF TABLES ................................ ................................ ................................ .... vi
1. Introduction ................................ ................................ ................................ ............ 1
1.1. Production Scheduling ................................ ................................ ............... 1
1.2. Problem Description ................................ ................................ .................. 3
1.3. Research Method ................................ ................................ ....................... 7
2. Literature Review................................ ................................ ................................ ... 9
2.1. Parallel Machine Scheduling Problem (PMSP) with Multiple Resource Constraints ................................ ................................ ................................ ............. 9
2.2. Stochastic Local Search ................................ ................................ ........... 13
2.2.1. Simulated Annealing ................................ ................................ .... 13
2.2.2. Tabu Search ................................ ................................ .................. 16
2.3. Parallel Computing ................................ ................................ .................. 18
3. Methodology ................................ ................................ ................................ ........ 20
3.1. Assumptions and Input Parameters ................................ .......................... 20
3.2. Phase One: Heuristic Method ................................ ................................ .. 22
3.2.1. Discrete Event Simulation ................................ ........................... 23
3.3. Phase Two: Metaheuristic Searching Algorithm ................................ ..... 25
3.3.1. Neighborhood Solution Generation ................................ ............. 25
3.3.2. Single Simulated Annealing ................................ ........................ 29
3.3.3. Single Tabu Search ................................ ................................ ...... 32
3.3.4. Parallel Computation Procedure ................................ .................. 35
iv
3.4. Phase Three: Mix Integer Programming Model（MIP） ....................... 35
3.4.1. Network Model (M1) ................................ ................................ ... 36
3.4.2. Extended Hung’s Model (M2) ................................ ..................... 40
3.4.3. Position Assignment Model (M4) ................................ ................ 44
4. Computation Experiments ................................ ................................ ................... 49
4.1. Experimental Parameters ................................ ................................ ......... 49
4.2. Random Problem Generation Procedure ................................ ................. 51
4.2.1. Resource Attribute Generation Procedure ................................ ... 51
4.2.2. Job Attribute Generation Procedure ................................ ............. 53
4.3. Parameter Setting ................................ ................................ ..................... 55
4.4. The Results and Analysis ................................ ................................ ......... 57
4.4.1. The Performances of Heuristic Methods (Stage One) ................. 57
4.4.2. The Performances of Two Parallel Searching Algorithms (Stage Two) ................................ ................................ ................................ ...... 58
4.4.3. The Performances of Three MIP Models (Stage Three) .............. 62
4.4.4. The Performances of Three-stage Approach ................................ 66
4.4.5. The Factorial Analysis of Three-stage Approach ......................... 71
5. Conclusion ................................ ................................ ................................ ........... 74
Reference ................................ ................................ ................................ ..................... 76

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