Abstract
A polynomial approximation scheme for minimizing makespan in a batch processing system under dynamic job arrivals is presented. A lower bound of \({{(\sqrt 5 + 2)} \mathord{\left/ {\vphantom {{(\sqrt 5 + 2)} 2}} \right. \kern-\nulldelimiterspace} 2}\) on the competitive ratio of any on-line algorithm is proved. This is matched by an on-line algorithm for the special case of unbounded machine capacity.
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Deng, X., Poon, C.K. & Zhang, Y. Approximation Algorithms in Batch Processing. Journal of Combinatorial Optimization 7, 247–257 (2003). https://doi.org/10.1023/A:1027316504440
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DOI: https://doi.org/10.1023/A:1027316504440