Abstract
This paper studies a mixed batch scheduling problem with non-identical job sizes to minimize the makespan. Multiple jobs can be processed simultaneously as a batch on a mixed batch machine as long as the total size of the jobs in the batch does not exceed the machine capacity. The processing time of a batch is the weighted sum of the maximum processing time and total processing time of the jobs in the batch. We show that the problem is strongly NP-hard even with a single machine, and analyze the worst-case performance ratio of the longest processing time first fit (LPTFF) algorithm. Furthermore, we present the longest processing time first fit greedy (LPTFFG) algorithm, and show that the worst-case performance ratio of algorithm LPTFFG is better than that of algorithm LPTFF. Computational experiments show that algorithm LPTFFG fits the case with a large number of machines, small job sizes, and small weight of the maximum processing time.
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The data that support the findings of this study are available from the corresponding author upon request.
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Acknowledgements
The authors are grateful to the editors and anonymous reviewers for their valuable comments, which have significantly improved the quality of this work. The work of the first two authors was partly supported by the National Natural Science Foundation of China (Grant Nos. 52105529, 52075453, and 71931007), and the Fundamental Research Funds for the Central Universities (Grant No. ZYTS24049).
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Fan, GQ., Wang, JQ. & Liu, Z. Mixed batch scheduling with non-identical job sizes to minimize makespan. OR Spectrum 47, 105–127 (2025). https://doi.org/10.1007/s00291-024-00770-2
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DOI: https://doi.org/10.1007/s00291-024-00770-2