Abstract
We study the scheduling of a set of n jobs, each characterized by a release (arrival) time and a processing time, for a batch processing machine capable of running at most B jobs at a time. We obtain an O(n log n)-time algorithm when B is unbounded. When there are only m distinct release times and the inputs are integers, we obtain an O(n(BRmax)m-1(2/m)m-3)-time algorithm where Rmax is the difference between the maximum and minimum release times. When there are k distinct processing times and m release times, we obtain an O(n log m + kk+2 Bk+1 m2 log m)-time algorithm. We obtain even better algorithms for m=2 and for k=1. These algorithms improve most of the corresponding previous algorithms for the respective special cases and lead to improved approximation schemes for the general problem.
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Poon, C., Zhang, P. Minimizing Makespan in Batch Machine Scheduling. Algorithmica 39, 155–174 (2004). https://doi.org/10.1007/s00453-004-1083-4
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DOI: https://doi.org/10.1007/s00453-004-1083-4