Abstract
We investigate the following two semi-on-line scheduling problems with machine activation cost. We are given two potential identical machines to non-preemptively process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and activation cost of machines. For the first semi-on-line problem with known the sum size of all jobs P in advance , we present an semi-on-line algorithm which is optimal for every P > 0. For the second problem with known the largest size of all jobs L in advance, we present an optimal semi-on-line algorithm for every L > 0.
Research supported by Natural Science Foundation of China(10671177), Natural Science Foundation of Zhejiang Province (Y605316), and Natural Science Foundation of Education Department of Zhejiang Province (20060578).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cao, D., Chen, M., Wan, G.: Parallel machine selection and job scheduling to minimize machine cost and job tardiness. Comput. & Oper. Res. 32, 1995–2012 (2005)
Dósa, G., He, Y.: Better on-line algorithms for scheduling with machine cost. SIAM Journal on Computing 33, 1035–1051 (2004)
Graham, R.L.: Bounds on muliprocessing finishing anomalies. SIAM Journal on Applied Mathematics 17, 416–429 (1969)
Han, S.G., Jiang, Y.W., Hu, J.L.: On-line algorithms for scheduling with machine activation cost on two uniform machines. Journal of Zhejiang University SCIENCE 8(1), 127–133 (2007)
He, Y., Han, S.G., Jiang, Y.W.: On-line algorithms for scheduling with machine activation cost. Asia-Pacific Journal of Operations research 24(2), 263–277 (2007)
He, Y., Zhang, G.: Semi-on-line scheduling on two identical machines. Computing 62, 179–187 (1999)
Imreh, C., Noga, J.: Scheduling with machine cost. In: Hochbaum, D.S., Jansen, K., Rolim, J.D.P., Sinclair, A. (eds.) RANDOM 1999 and APPROX 1999. LNCS, vol. 1671, pp. 168–176. Springer, Heidelberg (1999)
Jiang, Y.W., He, Y.: Preemptive on-line algorithms for scheduling with machine cost. Acta Informatica 41, 315–340 (2005)
Kellerer, H., Kotov, V., Speranza, M.R., Tuza, Z.: Semi on-line algorithms for the partition problem. Operation Research Letters 21, 235–242 (1997)
Panwalker, S., Liman, S.D.: Single operation earliness-tardiness scheduling with machine activation cost. IIE Transactions 34, 509–513 (2002)
Tan, Z.Y., He, Y.: Semi-on-line problems on two identical machines with combined partial information. Operation Research Letters 30, 408–414 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Han, S., Jiang, Y., Hu, J. (2007). Optimal Semi-online Algorithms for Scheduling with Machine Activation Cost. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-74450-4_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74449-8
Online ISBN: 978-3-540-74450-4
eBook Packages: Computer ScienceComputer Science (R0)