具X-因子目標限制的差別服務混合比例規劃之研究

Abstract

市場的全球化迫使半導體製造業者必須極力去尋求可以增進他們競爭力的管理方法，而晶圓廠在半導體供應鏈中佔了關鍵的地位，因為它代表的是龐大的投資，所以我們會把重點集中在晶圓廠上。而且晶圓廠通常都會有不同服務等級(Priority)的訂單，等級越高則可以得到優先加工的權利，因而增加了顧客提早進入市場的優勢，所以如何規劃不同服務等級訂單之間的比例將會帶給晶圓廠極大的挑戰。 為了能夠規劃不同服務等級訂單之間的比例，我們必須了解晶圓廠績效指標的變化。在晶圓廠眾多的指標之中，產品停滯於系統的時間(Cycle time)對於晶圓廠的生產力與顧客的服務率有重大的影響。為了管理與量測Cycle time，我們使用X-Factor來當作評估Cycle time變化的指標。 所以在本篇論文裡，為了得到最佳獲利我們把注意力放在利用具優先順序的(Priority) X-Factor設置目標的產能規劃上。因此，我們便需要一個晶圓廠X-Factor的模型來分析PXF、各種服務等級的比例及產能利用率三者的關係。現在有很多種方法被用來模擬晶圓廠的行為，而其中一種十分常見的方法就是排隊理論。而我們把晶圓廠的XF分成三個層次：整個晶圓廠、每個製程階段、不同服務等級的產品。首先，我們利用排隊理論中具優先權(Priority)的M/G/1近似法去計算每個加工階段的PXF。我們也提出了利用修正投料變異的係數去修正M/G/1精準度的方法(Model Fitting)。最後，提出了可以描述整個晶圓廠、每個製程階段及每種不同服務等級的產品三者X-Factor之間的關係的方法(PXFC and XFC Theories)，有了這個方法，我們便可以計算這三者的XF。 為了把產能規劃這個問題公式化，我們必須先了解PXF、各種服務等級的比例及產能利用率三者的關係，因此，我們會先對PXF模型做了一些數值的實驗，並且順便利用模擬網路PXF模型的結果跟我們的近似法比較精準度。 此外，我們將會把差別服務混合比例規劃(Priority Mix Planning)問題公式化並且藉由控制每種不同服務等級的投料速率來得到最佳獲利。我們會考慮PXF標的、產能利用率及機台工作小時等多項限制。在我們的規劃問題裡必須考慮價格跟成本兩個部份，對於價格，我們沒有多做討論只是單純以每片晶圓的價格來計算，主要是把重心放在成本計算上，不過忽略了成本中的固定成本 - 機器成本，因為機器成本並不會隨著投料速率而變動，它是一個常數，而我們把變動成本分成庫存成本與製造成本。最後，我們將會利用一些數值的實驗來觀察我們的數學模型在實務管理上能有什麼樣的潛力，比如說: 藉由控制優先混合比例(Priority Mix)或是產能利用率(Utilization)來獲得利潤並在一定的XF目標之下，甚至可以觀察成本、收入以及利潤這三者如何受我們的模型影響。

The globalization of markets is forcing the semiconductor manufacturers to look for ways to improve their competitive advantages by focusing on supply chain management. The foundry fab is particularly critical in semiconductor supply chain because that represents large capital investments, usually in the range of US$1-1.5 Billion. Foundry fabs often have multiple priority levels of orders, and higher priority must be given to some urgent lots to be competitive and to satisfy customers’ demand of accelerating the speed of products entering into the market so a product mix with different multiple priority lots has different and great influence on the production system and poses a great challenge to wafer fabrication. In order to plan priority mix, we need to know the performance of fab. To evaluate the performance of the current factory, we need to model fab performances. Among the many fab performance indices, cycle time has a significant impact on productivity learning and customer serviceability. To measure and manage cycle times, the notion of X-factor = cycle time/raw processing time has been introduced to provide a sensitive performance indicator, which is standardized across different products. In this thesis, we consider the priority mix planning under X-Factor target constrains to obtain the best profit because that makes sure the best solution of planning problem above the specific quality of service. To mathematically formulate the priority mix planning problem, we need a fab Priority X-Factor (PXF) model to analyze the relationship between PXF, release rate and capacity utilization. In view of the modeling power of Queueing models in describing fab performances is only to give mean and variance of release rate and service time. Our key ideas of modeling fab X-Factor are divided fab into three levels: overall fab, stages of process and individual priorities. For single stage, we adopt M/G/1: PR model as an approximation. It has a closed form to calculate for convenience but its disadvantages are ignoring the variance of release rate and cause calculation of the residual service time to lose accuracy for X-Factor we then propose ideas of modifying fab PXF model from M/G/1: PR to G/G/1: PR by adding variance term of release rate in residual service time. To calculate fab network X-Factor, we propose Priority X-Factor Contribution (PXFC) theory that describes the relationship of X-Factor between fab, stage and individual priorities. We can calculate fab X-Factor by summing stages X-Factor multiplied by relative processing time and calculate stage X-Factor by summing individual priorities’ X-Factor multiplied by relative utilization. To obtain issues of PXF modeling for planning problem, we study some numerical experiments of PXF model to analyze the influence of release rate of each priority, numbers of priority and capacity utilization on XF. And try to compare our network PXF model to simulation results from eM-Plant under the same input data but verification is not our major goal. We then incorporate the PXF model and issues of PXF numerical studies to formulate the planning problem. To consider the price of orders and cost in our problem formulation; for price, we calculate revenue by multiplying release rate and unit price of wafer; for cost, we ignore the fixed cost – machine cost because it is a constant and isn’t changed by release rate. We divide variable cost into inventory cost and manufacturing cost; inventory cost is controlled by WIP and manufacturing cost is calculated by multiplying release rate and unit cost of wafer. Finally, we make some numerical studies on our formulation to analyze the relation between profit, cost, revenue, and release rate of individual priorities and obtain insights of this research for managements.