光阻噴管配置模型之構建

Abstract

This study addresses the allocation of photoresists’ nozzles problem. Wen proposed a mathematical model to solve this problem in 2011. However, we find there are some errors in her mathematical model for some cases and we revised her model in this study. Given the demands of the products in the planning period, the allocation of the photoresist nozzle in previous period and the relationship among each type of photoresist, considered the constraints of machine capacity and the processing quantity of photoresist related to the relationships among each type of photoresist, we formulate a linear integer programming (IP) model for minimizing the non-productive consumption costs we consider in this study to determine the allocation of the photoresist nozzle in the planning period. The non-productive consumption costs include dummy cost of photoresist nozzles, maintenance cost and purge cost. We use LINGO to solve this linear IP mathematical model. The computational time is in exponentially growing with the number of machine and photoresist. In order to reduce the computational time, we propose a heuristic by adding some additional constraints to the IP model to reduce the computational time. Then we verify the accuracy of the heuristic. The worst relative error in testing cases is no more than 4%.

This study addresses the allocation of photoresists’ nozzles problem. Wen proposed a mathematical model to solve this problem in 2011. However, we find there are some errors in her mathematical model for some cases and we revised her model in this study. Given the demands of the products in the planning period, the allocation of the photoresist nozzle in previous period and the relationship among each type of photoresist, considered the constraints of machine capacity and the processing quantity of photoresist related to the relationships among each type of photoresist, we formulate a linear integer programming (IP) model for minimizing the non-productive consumption costs we consider in this study to determine the allocation of the photoresist nozzle in the planning period. The non-productive consumption costs include dummy cost of photoresist nozzles, maintenance cost and purge cost. We use LINGO to solve this linear IP mathematical model. The computational time is in exponentially growing with the number of machine and photoresist. In order to reduce the computational time, we propose a heuristic by adding some additional constraints to the IP model to reduce the computational time. Then we verify the accuracy of the heuristic. The worst relative error in testing cases is no more than 4%.