A multistage mathematical programming based scheduling approach for the photolithography area in semiconductor manufacturing

Facilities for wafer fabrication are one of the most complex manufacturing systems. Typically, the bottleneck of such facilities is the photolithography area because of its highly expensive tools and complex resource constraints. In this research, a multistage mixed integer programming based optimization approach for planning of such an area is presented. Thereby, several existing process constraints like equipment dedications, resist allocation, vertical dedications, mask availability are taken into account on the basis of different granularity levels. Altogether eleven different optimization models are presented within four different decomposition stages. Thereby, objected goals are the maximization of throughput, the minimization of setup costs and a balancing of machine utilization. On the basis of real manufacturing data the benefit of the proposed approach is evaluated within a first prototype.