Abstract
We consider batch scheduling on m machines to minimize the makespan. Each job has a given set of machines to be assigned. Each machine can process several jobs simultaneously as a batch, and the machines may have different batch capacities. We study two models: (i) scheduling on equal-speed batch machines under a nested processing set restriction, where the machines have the same processing speed, and (ii) scheduling on uniform batch machines under a tree-hierarchical processing set restriction, where the machines have different processing speeds. For both models we design polynomial-time approximation algorithms to solve them. The algorithms have a worst-case ratio of 2 for non-identical batch capacities and a worst-case ratio of \(2-1/m\) for identical batch capacities.
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Acknowledgements
We thank two anonymous referees for their helpful comments. This research was supported in part by the National Natural Science Foundation of China under grant numbers 12001169, 11971443, 11771406, and 61971380. It was also supported in part by the University Grants Council of Hong Kong under grant number PolyU 152148/15E.
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Chai, X., Li, W., Ng, C.T. et al. Approximation algorithms for batch scheduling with processing set restrictions. J Sched 26, 523–533 (2023). https://doi.org/10.1007/s10951-022-00720-2
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DOI: https://doi.org/10.1007/s10951-022-00720-2