Approximation algorithms for batch scheduling with processing set restrictions

Xing Chai, Wenhua Li (), C. T. Ng and T. C. E. Cheng
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Xing Chai: Zhengzhou University
Wenhua Li: Zhengzhou University
C. T. Ng: The Hong Kong Polytechnic University
T. C. E. Cheng: The Hong Kong Polytechnic University

Journal of Scheduling, 2023, vol. 26, issue 6, No 2, 523-533

Abstract: 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 $$2-1/m$$ 2 - 1 / m for identical batch capacities.

Keywords: Scheduling; Batch; Uniform machines; Processing set restrictions; Makespan (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10951-022-00720-2

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