Abstract
The problem is to minimize the total weighted completion time on a single batch-processing machine with setup times. The machine can process a batch of at most B jobs at one time, and the processing time of a batch is given by the longest processing time among the jobs in the batch. The setup time of a batch is given by the largest setup time among the jobs in the batch. This batch-processing problem reduces to the ordinary uni-processor scheduling problem when B = 1. In this paper we focus on the extreme case of B = +∞, i.e. a batch can contain any number of jobs. We present in this paper a polynomial-time approximation algorithm for the problem with a performance guarantee of 2. We further show that a special case of the problem can be solved in polynomial time.
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Dang, C., Kang, L. Batch-Processing Scheduling with Setup Times. Journal of Combinatorial Optimization 8, 137–146 (2004). https://doi.org/10.1023/B:JOCO.0000031415.55216.2a
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DOI: https://doi.org/10.1023/B:JOCO.0000031415.55216.2a