Scheduling of Dual Resource Constrained Lithography Production: Using CP and MIP/CP

Abstract

A dual resource constrained (DRC) scheduling problem arises at the photolithography area in semiconductor manufacturing wherein reticles are required as an auxiliary resource. Reticles are transferred from one place to another. While this shared resource gives the manufacturer a flexibility, it certainly gives rise to a complex DRC scheduling problem surrounded by jobs, machines, and reticles, restricted by sequence-dependent setup-time and location-dependent reticle transfer-time. This study proposes a constraint programming (CP) approach and investigates methods for improving our initial CP using a hybrid method and variable ordering heuristic. Experiments indicate the variable ordering heuristic brings a significant improvement over a pure CP. Note to Practitioners —There has been yet no successful exact approach that addresses litho scheduling problem, covering jobs, machines, and reticles. This study demonstrates CP is able to find an optimal solution for most of realistic industry-size test problems. In a future smart semiconductor factory, seamlessly orchestrating machines, reticles, and jobs would not be the end state. The next level is to integrate material handling system to this already overcrowded production scheduling problem. The specialized keywords of CP, as demonstrated in this study, will enable practitioners to develop a concise code of integrating vehicles, jobs, machines, and reticles.