生產排程(Production scheduling)是在各種有限的生產資源下來安排不同工件(job)的投入時間。本研究將機台視為生產資源，探討單一機台(Single-machine)的生產排程問題。各工件相關的屬性(Attributes)有可加工時間(Ready date)、工件交期(Due date)、加工時間(Processing time)及工件權重(Weight)。本研究假設每個工件有不同的可加工時間與交期，且工件只能在可加工時間到工件交期的時段內加工，不允許延期加工。因此，對於每一工件而言，我們僅能挑選來加工或是拒絕。此外，在工件加工期間，不允許中斷或被其他工件強占(Non-preemption)。本研究著重的生產排程問題為最大化權重排程問題(Weight maximization problem)，以往文獻將此問題稱為最大化產出量問題(Throughput maximization problem)。
本研究提出三個方法來求解最大化權重排程問題，分別是(1)啟發式演算法(Heuristic method)；(2)混合整數規劃(Mixed integer programming)及(3)分枝界限法(Brand-and-bound method)。其中，啟發式演算法可求得一初解供混合整數規劃及分枝界限法利用。本研究發展出兩個部份排序(Partial ordering)、四個支配法則(Dominance rule)以及利用線性規劃放鬆(Linear programming relaxation)模型求出界限，以降低分枝界限法的運算時間。
在本研究的研究結果中，於分枝界限法中使用部份排序，可在極短時間內求得一個鄰近最佳解，因此若在有限的時間內，我們可以利用部份排序來求解，而不需求得最佳解。此外，支配法則與線性規劃放鬆模型可降低分枝界限法中搜尋樹的節點數，有效縮減求解的運算時間。

Production scheduling arranges the production activities for various jobs under the limitation of scarce resources. This study discusses a single-machine production scheduling problem. The known attributes of a job include processing time, ready date, due date, and weight. Different jobs are allowed to have different ready dates and due dates. A job is either totally completed between its ready date and its due date on a single machine or totally rejected. The problem this study investigates is a non-preemptive single machine scheduling problem with the objective of maximizing total weight generated by completed jobs. Such a problem is called throughput maximization problem in previous literatures.
This study develops three methods to solve the problem: (1) a heuristic method; (2) a mixed integer programming; and (3) a brand-and-bound method. The heuristic method provides an initial solution for the mixed integer programming and the brand-and-bound method. To reduce computation time of the branch-and-bound method, this study develops four dominance rules and bounding approach using an LP-relaxation formulation.
From the results of experiments, the computation time of mixed integer programming is larger than other methods. Also, partial orderings can provide a solution near an optimal solution. This shows that if we use the partial orderings before solving a problem by the branch-and-bound method, we can immediately obtain an objective value near the optimal solution. Most of fathom rules are used in high frequency. Thus, two partial orderings, four dominance rules, and bounding approach using an LP-relaxation formulation can reduce computation time of the branch-and-bound method effectively.

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