Minimizing Total Completion Time of Batch Scheduling with Nonidentical Job Sizes

• Published in: Combinatorial Optimization and Applications Vol. 10627; pp. 165 - 179
• Main Authors: Li, Rongqi, Tan, Zhiyi, Zhu, Qianyu
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2017; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Batch Scheduling Problem; Parallel Machine Case; Total Completion Time; Unit Processing Times; Worst-case Ratio
• ISBN: 3319711490; 9783319711492
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-71150-8_16

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 (FFI) lies in the interval [10982,2+22]≈[1.3293,1.7071] $$[\frac{109}{82}, \frac{2+\sqrt{2}}{2}]\approx [1.3293, 1.7071]$$ for the single machine case, and is no more than 6+24≈1.8536 $$\frac{6+\sqrt{2}}{4}\approx 1.8536$$ for the parallel machines case.