Cost Constrained Fixed Job Scheduling

  • Qiwei Huang
  • Errol Lloyd
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2841)


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.


Finish Time Feasible Schedule Total Processing Time Minimum Cost Flow Partition Property 
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  1. 1.
    Fischetti, M., Martello, S., Toth, P.: The Fixed Job Schedule Problem with Spread-Time Constraints. Operations Research 35(6), 849–858 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Fischetti, M., Martello, S., Toth, P.: The Fixed Job Schedule Problem with Working-Time Constraints. Operations Research 37(3), 395–403 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Kolen, A.W.J., Kroon, L.G.: On the Computational Complexity of (Maximum) Class Scheduling. European Journal of Operational Research 54, 23–38 (1991)zbMATHCrossRefGoogle Scholar
  4. 4.
    Kolen, A.W.J., Kroon, L.G.: License Class Design: Complexity and Algorithms. European Journal of Operational Research 63, 432–444 (1992)zbMATHCrossRefGoogle Scholar
  5. 5.
    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)zbMATHCrossRefGoogle Scholar
  6. 6.
    Kolen, A.W.J., Kroon, L.G.: An Analysis of Shift Class Design Problems. European Journal of Operational Research 79, 417–430 (1994)zbMATHCrossRefGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    Jansen, K.: Approximation Results for the Optimal Cost Chromatic Partition Problem. Journal of Algorithms 34, 54–89 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice-Hall, Englewood Cliffs (1993)Google Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computer and Intractability, A Guide to the Theory of NP-Completeness (2000) (Twenty-second printing)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Qiwei Huang
    • 1
  • Errol Lloyd
    • 2
  1. 1.UTStarcom Inc.IselinUSA
  2. 2.Dept. of Computer and Information SciencesUniversity of DelawareNewarkUSA

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