Batch scheduling of nonidentical job sizes with minsum criteria

Rongqi Li, Zhiyi Tan () and Qianyu Zhu
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Rongqi Li: Zhejiang University
Zhiyi Tan: Zhejiang University
Qianyu Zhu: Zhejiang University

Journal of Combinatorial Optimization, No 0, 22 pages

Abstract: Abstract This paper concerns the problem of scheduling jobs with unit processing time and nonidentical sizes on single or parallel identical batch machines. The objective is to minimize the total completion time of all jobs. We show that the worst-case ratio of the algorithm based on the bin-packing algorithm First Fit Increasing lies in the interval $$\left[ \frac{109}{82}, \frac{2+\sqrt{2}}{2}\right] \approx [1.3293, 1.7071]$$ 109 82 , 2 + 2 2 ≈ [ 1.3293 , 1.7071 ] for the single machine case, and is no more than $$\frac{6+\sqrt{2}}{4}\approx 1.8536$$ 6 + 2 4 ≈ 1.8536 for the parallel machines case.

Keywords: Scheduling; Bin-packing; Worst-case ratio; Batch machine (search for similar items in EconPapers)
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DOI: 10.1007/s10878-019-00419-9

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