在此研究中，我們研究 n 個可以進行批次加工的工作跟 m 台平行機台的排程問題，不同批次加工的工作有著不同的加工配方，即是說工作有適合自己加工的機台，在符合的機台環境下，該工作才能加工，再加上不同工作有著一些時間上的限制，因此我們研究的目標是在符合這些限制條件下找出最小化最後一個離開系統工作的完工時間。
為了求出這個問題的最佳解，本研究提出了一個混整數規劃的模型，並加上時間限制、機器合適度、批次加工與平行機台加工以及在物料使用上的限制…等等的限制條件。在本研究的環境設置上，我們所提出的環境假設是與實際半導體產業的生產情況更加相近，最後使用的方法是以線性規劃來求解此排程問題。
;In this research, we research the scheduling problem with n lots that can be divided into batches and m parallel machines under availability constraint. Due to the eligibility constraint, each lots has its own recipe, not all m machines can process the all recipes. And the lots have the waiting time before the processing, they can process together when their arrival time smaller than the batch’s waiting time. Therefore, the goal of our research is to find the minimum completion time for the last system to leave the system, subject to these constraints.
In order to find the optimal solution to this problem, this study proposes a model for mixed integer programming. And with time constraints, machine eligibility constraint, batch processing constraint, and parallel machine processing constraint. In our environment settings. The assumptions we put forward are more similar to the actual environment of the semiconductor industry. Finally, we use mixed integer programming to solve this scheduling problem.
