臺灣博碩士論文加值系統

我們考慮在具有工件釋放時限制下最小化提早與延遲成本之單機排程問
題。此問題為單一機台、n 的工件，此機台一次只能針對一個工件偍供服務，而
工件在被服務的過程中，不因其他因素而中斷。在我們的問題中，每一個工件有
不同的釋放時間，此釋放時間代表工件進入機台等待加工的時間點，只有在此時
間點或此時間點之後，工件才可進行加工。所有的工作有一個相同的到期日，在
到期日之前完工，會造成提早完工成本；在到期日之後完工，會造成延遲成本。
目的是找到一個提早時間與延遲時間最小的最佳解。
針對此問題，我們利用分枝定界法(Branch-and-Bound)來找尋最佳解，並提
出適用於此問題的分枝法則與定界法則。在實驗的部份，主要針對我們所建構的
分枝定界法進行正確性的驗證與效率性的評估。我們利用窮舉法與特例來驗證演
算法的正確性。而效率評估的部分，窮舉法與我們所提出之演算法進行比較。根
據實驗結果平均顯示，我們所提出演算法可有效地刪除超過99%的點。

We consider a single machine scheduling problem to minimize job-dependent
weighted earliness and tardiness penalties with distinct release dates. Each of n jobs is
to be processed without interruption on a single machine which can handle only one
job at a time. In our problem, each job becomes available for processing at its release
date. All jobs have common due date and each job has different weights for earliness
and tardiness. The objective is to find an optimal schedule that minimizes the sum of
job-dependent earliness and job-dependent tardiness.
For this problem, a branch-and-Bound Algorithm is proposed to find an optimal
schedule in this article, and some propositions are used to eliminate a large of
infeasible solutions. Computational experiments are proposed to validate and evaluate
our algorithm. In validation, a special case and enumeration are compared with our
algorithm. In evaluation, we compare effectiveness between our algorithm and
enumeration. In average, more than 99% of nodes are eliminated in test problems.

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Research Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4.1 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4.2 Research Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Chapter 2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Earliness and Tardiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Different Release Dates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Chapter 3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Basic Propositions of E/T Model . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Branch-and-Bound Scheme . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3.1 Propositions used in Branching Tree . . . . . . . . . . . . . . . . . 18
3.3.2 Branch-and-Bound Algorithm . . . . . . . . . . . . . . . . . . . . . . 31

Chapter 4 Computational analysis . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1 Validation of Branch-and-bound Algorithm . . . . . . . . . . . . . 37
4.2 Evaluation of Branch-and-Bound Algorithm . . . . . . . . . . . . . 39
4.2.1 Comparing the Enumeration . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.2 The Suitability of Algorithm Experiment . . . . . . . . . . . . . . . 41

Chapter 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
APPENDIX B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
APPENDIX C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

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