Scheduling a Real-World Photolithography Area with Constraint Programming

Deenen, P. C., Nuijten, W. P. M., & Akcay, A. (2023). Scheduling a Real-World Photolithography Area with Constraint Programming. IEEE Transactions on Semiconductor Manufacturing, 36(4), 590-598. Article 10214506.


This paper studies the problem of scheduling machines in the photolithography area of a semiconductor manufacturing facility. The scheduling problem is characterized as an unrelated parallel machine scheduling problem with machine eligibilities, sequence- and machine-dependent setup times, auxiliary resources and transfer times for the auxiliary resources. Each job requires two auxiliary resources: a reticle and a pod. Reticles are handled in pods and a pod contains multiple reticles. Both reticles and pods are used on multiple machines and a transfer time is required if transferred from one machine to another. A novel constraint programming (CP) approach is proposed and is benchmarked against a mixed-integer programming (MIP) method. The results of the study, consisting of a real-world case study at a global semiconductor manufacturer, demonstrate that the CP approach significantly outperforms the MIP method and produces high-quality solutions for multiple real-world instances, although optimality cannot be guaranteed.

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