An Open Challenge for Exact Job Scheduling with Reticle Batching in Photolithography

Abstract

We consider scheduling solutions for photolithography, an im- portant sub-task in semi-conductor production, where patterns are transferred to wafers using reticles. The problem can be modelled as job scheduling on unrelated parallel machines with sequence-dependent setup times and release dates. The reticles add auxiliary-resource constraints for processing jobs. Equipping machines with the right reticles using transport robots from stockers in time renders this problem extremely difficult for exact solvers that use a declarative model. The lat- ter would be attractive as such models tend to be compact and easy to maintain. We present a solver-independent MiniZinc model and provide 500 new benchmark instances. However, only small instances can be solved with state-of-the-art MIP and CP solvers. Consequently, we present this problem as an open challenge with considerable potential for driving im- provements towards industrial applications.