Abstract
We consider batch processing of jobs to minimize the mean response time. A batch processing machine can handle up to B jobs simultaneously. Each job is represented by an arrival time and a processing time. The processing time of a batch of several jobs is the maximum of their processing times. In batch processing, non-preemptive scheduling is usually required and we discuss this case. The batch processing problem reduces to the ordinary uni-processor system scheduling problem if B = 1. We focus on the case B = +∞. Even for this seemingly simple extreme case, we are able to show that the problem is NP-hard. We further show that several important special cases of the problem can be solved in polynomial time.
Research partially supported by a CERG grant of Hong Kong UGC and an SRG grant of City University of Hong Kong
Research partially supported by Natural Science Foundation of China and Shandong
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Brucker, A. Gladky, C.N. Potts, H. Hoogeveen, M.Y. Kovalyov, C.N. Potts, T autenhahn and S.L. Van De Velde. Scheduling a batching machine, Journal of Scheduling, 1, 31–54,(1998).
V. Chandru, C.Y. Lee and R. Uzsoy, Minimizing total completion time on batch processing machine, International Journal of Production Research 31, 2097–2121 (1993).
V. Chandru, C.Y. Lee and R. Uzsoy, Minimizing total completion time on a batch processng machine with job family, Operations Research Letters 13, 61–65 (1993).
R.L., Graham, Lawler, J.K. Lenstra and Kan. Rinnooy, Optimization and approximation in deterministic sequencing and scheduling. Annal of Discrete Math. 5 (1979).
C.Y. Lee and Uzsoy, R., Minimizing makespan on single batch processing machine with dynamic job arrivals, Research Report, Dept. Industrial and System Engineering, Univ. Florida, Jan, 1996.
R. Uzsoy, Scheduling a single batch processing machine with non-idential job sizes, International J. Production Research 23, 1615–1635 (1994).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deng, X., Zhang, Y. (1999). Minimizing Mean Response Time in Batch Processing System. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_23
Download citation
DOI: https://doi.org/10.1007/3-540-48686-0_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66200-6
Online ISBN: 978-3-540-48686-2
eBook Packages: Springer Book Archive