Approximation Algorithms for Scheduling Problems with Exact Delays

  • Alexander A. Ageev
  • Alexander V. Kononov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4368)


We give first constant-factor approximations for various cases of the coupled-task single machine and two-machine flow shop scheduling problems with exact delays and makespan as the objective function. In particular, we design 3.5- and 3-approximation algorithms for the general cases of the single-machine and the two-machine problems, respectively. We also prove that the existence of a (2−ε)-approximation algorithm for the single-machine problem as well as the existence of a (1.5−ε)-approximation algorithm for the two-machine problem implies P=NP. The inapproximability results are valid for the cases when the operations of each job have equal processing times and for these cases the approximation ratios achieved by our algorithms are very close to best possible: we prove that the single machine problem is approximable within a factor of 2.5 and the two-machine problem is approximable within a factor of 2.


Approximation Algorithm Completion Time Approximation Ratio Single Machine Feasible Schedule 
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  1. 1.
    Ageev, A.A., Baburin, A.E.: Approximation Algorithms for the Single and Two-Machine Scheduling Problems with Exact Delays. To appear in Operations Research LettersGoogle Scholar
  2. 2.
    Farina, A., Neri, P.: Multitarget interleaved tracking for phased array radar. IEEE Proc. Part F: Comm. Radar Signal Process 127(4), 312–318 (1980)CrossRefGoogle Scholar
  3. 3.
    Garey, M.R., Johnson, D.S.: Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Francisco (1979)MATHGoogle Scholar
  4. 4.
    Elshafei, M., Sherali, H.D., Smith, J.C.: Radar pulse interleaving for multi-target tracking. Naval Res. Logist. 51, 79–94 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Izquierdo-Fuente, A., Casar-Corredera, J.R.: Optimal radar pulse scheduling using neural networks. IEEE International Conference on Neural Networks 7, 4588–4591 (1994)MATHGoogle Scholar
  6. 6.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5, 287–326 (1979)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Orman, A.J., Potts, C.N.: On the complexity of coupled-task scheduling. Discrete Appl. Math. 72, 141–154 (1997)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Sherali, H.D., Smith, J.C.: Interleaving two-phased jobs on a single machine. Discrete Optimization 2, 348–361 (2005)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Yu, W.: The two-machine shop problem with delays and the one-machine total tardiness problem, Ph.D. thesis, Technische Universiteit Eindhoven (1996)Google Scholar
  10. 10.
    Yu, W., Hoogeveen, H., Lenstra, J.K.: Minimizing makespan in a two-machine flow shop with delays and unit-time operations is NP-hard. J. Sched. 7(5), 333–348 (2004)MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Alexander A. Ageev
    • 1
  • Alexander V. Kononov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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