全自動化晶圓廠需詳細考量規劃組成因素（Fab設計、自動化材料處理系統(automated material handling systems, AMHS)）、工具規格和軟體應用程式，工廠製造晶圓過程中，屬於半成品的材料多裝於標準的密封運載工具中，而這些載滿貨物的桶狀工具重量時而高達十公斤，難以採用人為運輸，因此常利用AMHS高空運輸系統，完成晶圓桶在中央主通道、加工裝置站點、儲料器之間的移動過程。當晶圓廠規模日益擴大，AMHS搬運問題也日益複雜。本篇研究旨在探討AMHS指派問題，在晶圓桶起訖點已知的情形下，最有效率地指派AMHS系統，期能最小化完成晶圓桶搬運整體之時間。本篇研究將AMHS系統搬運晶圓之最佳化問題構建為多元商品最小成本流量問題 (multi-commodity minimum cost flow problem, MCMCFP)，並據此開發優化演算法以求得最佳解。研究分為兩個部分，首先構建此問題的數學模型，並利用商用軟體求得最佳解以作為演算法之比較基礎。多元商品最小成本流量類型之問題在研究中已被證明為具備NP-complete之複雜度，當數學模型隨著規模漸漸擴大時，預期商用求解軟體遭遇瓶頸，本研究整合拉格朗日鬆弛法(Lagrangian relaxation heuristic)將多元商品最小成本流量問題鬆弛為多個單一商品最小成本流量問題，並利用容量縮放演算法(capacity scaling)做為求解單一商品最小成本流量問題之演算法求解多元商品最小成本流量問題，數值分析發現，本研究開發之演算法能夠在求解軟體求解過程發生瓶頸時，求得AMHS指派問題之最佳解，同時能求解實務規模之問題。

Fully automated fab should carefully considered the planning components (Fab design, automated material handling systems (AMHS)), tool specifications and software applications. In the process of manufacturing wafers in the factory, most of the semi-finished materials are packed in standard sealed vehicles, and these barrel-shaped tools loaded with goods weigh up to more than ten kilograms. It is difficult to use human transportation, so the AMHS high-altitude transportation system is often used to complete the movement of the semi-finished materials between the central main channel, processing device site, and stocker. As the scale of the factory gradually expanded, AMHS handling problems became more complicated. The purpose of this study is to discuss the AMHS assignment problem. Under the condition where the starting and ending points of the semi-finished materials are known, we hope to assign the AMHS system most efficiently, hoping to minimize the time required to complete the overall wafer handling. In this research, the optimization problem of AMHS system handling wafers is constructed as a multi-commodity minimum cost flow problem (MCMCFP), and an algorithm is developed to find the optimal solution. The research is divided into two parts. First, the mathematical model of this problem is constructed, and the optimal solution is obtained using commercial software as the basis for comparison of the developed algorithm. Multi-commodity minimum cost flow problem has been proved to be NP-complete. When the mathematical model gradually expands, the commercial solution software is expected to encounter difficulties in solving the problem. This study integrates the Lagrangian relaxation heuristic method to relax the multi-commodity minimum cost flow problem into multiple single commodities minimum cost flow problem, and use capacity scaling to solve the single commodities minimum cost flow problem. Numerical analysis found that the algorithm developed in this research could obtain the optimal solution to the AMHS assignment problem when the software encounters difficulties, and can solve the problem of real-world scale at the same time.

洪友芳、高嘉和（2017，7月13日）。台積電先進廠，人機比達1:75。自由時報。
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