零工式生產排程(job shop scheduling)在生產排程上佔了很重要的角色，很多產業的排程問題是屬於零工式生產型態。近年來，關於零工式生產問題的研究很多，這些研究大多只考慮單一資源(single-resource)。在製造業中，機台常是唯一被考慮的資源，我們需要決定各種工件在有限機台上的加工順序，例如半導體產業，機器通常是非常昂貴的，所以數量是有限的。
現實的生產環境中，單一資源的零工式生產模型簡化了實際的狀況，當工件在某台機器上作業時，常需要輔以夾具或特殊的技術人員同時對工件做加工，夾具和特殊技術人員也可視為資源的一種，當一個作業同時需要兩個或兩個以上的資源，我們將這樣的生產環境稱為多資源(multiple-resource)的生產環境。我們希望求解多資源的零工式生產排程問題，若能將所有的資源妥善的規劃，有效率地運用有限的資源，定能減少不必要的損失。本論文主要研究的方向為如何產生一個合理且最佳的排程，其目標為得到最短的完工時間(makespan)。Giffler and Thompson【1960】以離散圖形表示零工式生產排程問題，運用分支界限法(branch-and-bound technique)求解目標為最小化完工時間的單一資源零工式生產排程問題。在本論文中，我們修改離散圖形表示多資源零工式生產排程問題，並且發展新的分支界限技巧求解這類問題。我們針對問題做多因子的實驗設計，並且分析這些因子是否顯著影響解題的時間，分析結果顯示資源數、工件數、作業數和資源使用頻率這四個因子對於解題時間是影響是顯著的。

Job shop scheduling plays an important role in production scheduling. Many manufacturing scheduling problems can be modeled as a job shop scheduling problem. In recently years, there are many research works related to job shop scheduling, but most of theses works consider only single-resource on an operation. In high tech industries, such as semiconductor manufacturing, only machines are considered as limited resource.
But, in many cases, an operation requires more than one resource. We call this kind of problem as multiple-resource scheduling. This research intends to solve multiple-resource job shop scheduling problem with the objective of minimizing makespan. Giffler and Thompson【1960】 introduced the disjunctive graph technique to represent job shop scheduling and used branch-and-bound technique to solve single-resource job shop scheduling problem. In this study, we modify disjunctive graph to represent multiple-resource job shop scheduling and develop a branch-and-bound technique to solve this problem. Experimental designs and statistical methods are used to evaluate and analyze the performance of the method. The results show that the number of resources, the number of jobs, the number of operations and the utilizations of resources affect the solution time used by branch-and bound method.

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