# American Institute of Mathematical Sciences

October  2007, 3(4): 685-692. doi: 10.3934/jimo.2007.3.685

## Duplicating in batch scheduling

 1 School of Operations Research and Management Sciences, Qufu Normal University, Rizhao, Shandong, 276826 2 Department of Mathematics, Fuyang Teachers College, Fuyang, Anhui, 236032, P.R., China 3 School of Operations Research and Management Sciences, Qufu Normal University, Rizhao, Shandong, 276826, P.R., China 4 School of Management, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, P.R., China

Received  November 2006 Revised  July 2007 Published  October 2007

In this paper, we firstly propose a technique named Duplicating , which duplicates machines in batch scheduling environment. Then we discuss several applications of Duplicating in solving batch scheduling problems. For the batch scheduling problem on unrelated parallel machines to minimize makespan, we give a $(4 - \frac{2}{B})$- approximation algorithm and a $(2 - \frac{1}{B} + \epsilon)$ algorithm when $m$ is fixed. We also present a $4(2 - \frac{1}{B} + \epsilon)$-competitive algorithm for the on-line scheduling problem on identical machines to minimize total weighted completion time by another technique-$\rho-dual$, which is proposed originally by Hall et al.(1997).
Citation: Yuzhong Zhang, Chunsong Bai, Qingguo Bai, Jianteng Xu. Duplicating in batch scheduling. Journal of Industrial and Management Optimization, 2007, 3 (4) : 685-692. doi: 10.3934/jimo.2007.3.685
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