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Scheduling in-line mulitple cluster tools: A decomposition approach

We examine a new scheduling problem of in-line multiple cluster tools. A cluster tool has been popularly used for wafer fabrication processes such as lithography, etching, deposition, and inspection. It consists of several processing modules (PMs), a wafer handling robot, and loadlocks. Each cluster tool also has its equipment front-end module (EFEM) that helps keep the cluster tool in a vacuum state. An EFEM has an aligner, a robot, and loadports where wafer cassettes arrive. Since overhead hoist transfers (OHTs) move wafer cassettes containing 25 wafers between EFEMs and there are a huge number of manufacturing tools in a fab, it is extremely complicated to schedule OHTs. Moreover, an arrival delay of cassettes can cause wafer quality degradation significantly. Therefore, fabs tend to reduce transportation tasks by arranging tools in a line with a buffer. In this paper, we address the new in-line multiple cluster tools' scheduling problem to minimize the makespan of a lot with 25 identical wafers. Since the problem is NP-complete, we decompose it into two parts; a PM assignment problem and a robot task sequence decision problem. We first develop mixed integer programming (MIP) models to decide the number of wafers that each PM processes based on the workloads and to assign each wafer to PMs. With the assignment information, we find a best robot task sequence priority experimentally.