Abstract
In this paper, we study the problem of cost constrained fixed job scheduling (CCFJS). In this problem, there are a number of processors, each of which belongs to one of several classes. The unit time processing cost for a processor varies with the class to which the processor belongs. There are N jobs, each of which must be processed from a given start time to a given finish time without preemption. A job can be processed by any proc- essor, and the cost of that processing is the product of the processing time and the processor’s unit time process- ing cost. The problem is to find a feasible scheduling of the jobs such that the total processing cost is within a given cost bound. This problem (CCFJS) arises in several applications, including off-line multimedia gateway call routing. We show that CCFJS can be solved by a network flow based algorithm when there are only two classes of processors. For more than two classes of processors, we prove that CCFJS is not only NP-Complete, but also that there is no constant ratio approximation algorithm. Finally, we present an approximation algorithm, derive its worst-case performance ratio (non constant), and show that it has a constant approximation ratio in several special cases.
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
Fischetti, M., Martello, S., Toth, P.: The Fixed Job Schedule Problem with Spread-Time Constraints. Operations Research 35(6), 849–858 (1987)
Fischetti, M., Martello, S., Toth, P.: The Fixed Job Schedule Problem with Working-Time Constraints. Operations Research 37(3), 395–403 (1989)
Kolen, A.W.J., Kroon, L.G.: On the Computational Complexity of (Maximum) Class Scheduling. European Journal of Operational Research 54, 23–38 (1991)
Kolen, A.W.J., Kroon, L.G.: License Class Design: Complexity and Algorithms. European Journal of Operational Research 63, 432–444 (1992)
Kolen, A.W.J., Kroon, L.G.: On the Computational Complexity of (Maximum) Shift Class Scheduling. European Journal of Operational Research 64, 138–151 (1993)
Kolen, A.W.J., Kroon, L.G.: An Analysis of Shift Class Design Problems. European Journal of Operational Research 79, 417–430 (1994)
Kroon, L.G., Sen, A., Deng, H., Roy, A.: The optimal cost chromatic partition problem for trees and interval graphs. In: D’Amore, F., Marchetti-Spaccamela, A., Franciosa, P.G. (eds.) WG 1996. LNCS, vol. 1197, Springer, Heidelberg (1997)
Jansen, K.: Approximation Results for the Optimal Cost Chromatic Partition Problem. Journal of Algorithms 34, 54–89 (2000)
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice-Hall, Englewood Cliffs (1993)
Garey, M.R., Johnson, D.S.: Computer and Intractability, A Guide to the Theory of NP-Completeness (2000) (Twenty-second printing)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Huang, Q., Lloyd, E. (2003). Cost Constrained Fixed Job Scheduling. In: Blundo, C., Laneve, C. (eds) Theoretical Computer Science. ICTCS 2003. Lecture Notes in Computer Science, vol 2841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45208-9_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-45208-9_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20216-5
Online ISBN: 978-3-540-45208-9
eBook Packages: Springer Book Archive