Abstract
We study the scheduling of a set of n jobs, each characterized by a release (arrival) time and a processing time, for a batch processing machine capable of running at most B jobs at a time. We obtain an O(n log n)-time algorithm when B is unbounded. When there are only m distinct release times and the inputs are integers, we obtain an O(n(BR max)m - 1 (2/m)m - 3 )-time algorithm where Rmax is the difference between the maximum and minimum release times. When there are k distinct processing times and m release times, we obtain an O(k k+2 B k+1 m 2 log m)-time algorithm. We obtain even better algorithms for m = 2 and for k = 1. These algorithms improve most of the corresponding previous algorithms for the respective special cases and lead to improved approximation schemes for the general problem.
This research was fully supported by a grant from City U. of Hong Kong (Project No. 7100068).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
P. Brucker, A. Gladky, H. Hoogeveen, M.Y. Kovalyov, C.N. Potts, T. Tautenhahn, and S.L. van de Velde. Scheduling a batching machine. Journal of Scheduling, 1:31–54, 1998.
X. Deng, C.K. Poon, and Y. Zhang. Approximation algorithms in batch processing. In The 8th Annual International Symposium on Algorithms and Computation, volume 1741 of Lecture Notes in Computer Science, pages 153–162, Chennai, India, December 1999. Spring-verlag.
R.L. Graham, Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling. Annals of Discrete Mathematics, 5:387–326, 1979.
Y. Ikura and M. Gimple. Scheduling algorithm for a single batch processing machine. Operations Research Letters, 5:61–65, 1986.
C.Y. Lee and R. Uzsoy. Minimizing makespan on a single batch processing machine with dynamic job arrivals. Technical report, Department of Industrial and System Engineering, University of Florida, January 1996.
C.Y. Lee, R. Uzsoy, and L.A. Martin Vega. Efficient algorithms for scheduling semiconductor burn-in operations. Operations Research, 40:764–775, 1992.
Z. Liu and W. Yu. Scheduling one batch processor subject to job release dates. To appear, Discrete Applied Mathematics.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Poon, C.K., Zhang, P. (2000). Minimizing Makespan in Batch Machine Scheduling. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_33
Download citation
DOI: https://doi.org/10.1007/3-540-40996-3_33
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41255-7
Online ISBN: 978-3-540-40996-0
eBook Packages: Springer Book Archive