Unrelated Parallel Machine Photolithography Scheduling Problem With Dual Resource Constraints

This paper studies an unrelated parallel machine photolithography scheduling problem with dual resource constraints (DRC). This is an emerging problem in the semiconductor industry, where the masks can be transferred from one working station to another, increasing the flexibility of production through sharing the auxiliary resource. It gives rise to a complex DRC scheduling problem involving jobs, machines, and masks, restricted by sequence-dependent setup time and station-dependent mask transfer time. This study proposes two mixed-integer programming (MIP) models (Model 1 and Model 2) and an improved naked mole-rat algorithm that hybrids with a genetic algorithm (GA) and variable neighborhood search algorithm (VNS). Numerical experiments show that Model 2 performs better compared with Model 1, and the improved naked mole-rat algorithm brings a significant improvement over GA and VNS.