Advertisement

Bounded Parallel-Batch Scheduling on Unrelated Parallel Machines

  • Cuixia Miao
  • Yuzhong Zhang
  • Chengfei Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)

Abstract

In this paper, we consider the bounded parallel-batch scheduling problem on unrelated parallel machines. Problems R m |B|F are NP-hard for any objective function F. For this reason, we discuss the special case with p ij  = p i for i = 1, 2, ⋯ , m , j = 1, 2, ⋯ , n. We give optimal algorithms for the general scheduling to minimize total weighted completion time, makespan and the number of tardy jobs. And we design pseudo-polynomial time algorithms for the case with rejection penalty to minimize the makespan and the total weighted completion time plus the total penalty of the rejected jobs, respectively.

Keywords

Parallel-batch scheduling Unrelated parallel machines Rejection penalty Pseudo-polynomial time 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., Stougie, L.: Multiprocessor scheduling with rejection. SIAM J. Discrete Math. 13, 64–78 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Brucker, P., Gladky, A., Hoogeveen, H., Kovalyov, M.Y., Potts, C.N., Tautenhahn, T., van de Velde, S.L.: Scheduling a batching machine. Journal of Scheduling 1, 31–54 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cao, Z.G., Yang, X.G.: A PTAS for parallel batch scheduling with rejection and dynamic job arrivals. Theoretical Computer Science 410(27-29), 2732–2745 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Chen, B., Deng, X.T., Zang, W.N.: On-line scheduling a batch processing system to minimize total weighted job completion time. Journal of Combinatorial Optimization 8, 85–95 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cheng, Y.S., Sun, S.J.: Scheduling linear deteriorating job with rejection on a single machine. European Journal of Operational Research 194, 18–27 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Deng, X.T., Zhang, Y.Z.: Minimizing mean response time in batch processing system. In: Asano, T., Imai, H., Lee, D.T., Nakano, S.-i., Tokuyama, T. (eds.) COCOON 1999. LNCS, vol. 1627, pp. 231–240. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Engels, D.W., Karger, D.R., Kolliopoulos, S.G., Sengupta, S., Uma, R.N., Wein, J.: Techniques for scheduling with rejection. Journal of Algorithms 49, 175–191 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Epstein, L., Noga, J., Woeginger, G.J.: On-line scheduling of unit time jobs with rejection: Minimizing the total completion time. Operations Research Lettars 30, 415–420 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Graham, R.L., Lawler, L.J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Disc. Math. 5, 287–326 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Lee, C.-Y., Uzsoy, R., Martin-Vega, L.A.: Efficient algorithms for scheduling semiconductor burn-in operations. Operations Research 40, 764–775 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Li, S.G., Li, G.J., Wang, X.H.: Minimizing total weighted completion time on parallel unbounded batch machines. Journal of Software 17, 2063–2068 (2006)zbMATHCrossRefGoogle Scholar
  12. 12.
    Lu, L.F., Cheng, T.C.E., Yuan, J.J., Zhang, L.Q.: Bounded single-machine parallel-batch scheduling with release dates and rejection. Computer and Operations Research 36, 2748–2751 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Miao, C.X., Zhang, Y.Z.: On-line scheduling with rejection on identical parallel machines. Journal of System Science and Complexity 19, 431–435 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Webster, S., Baker, K.R.: Scheduling groups of jobs on a single machine. Operations Research 43, 692–703 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Zhang, Y.Z., Wang, Z.Z., Wang, C.Y.: The “transform lemma” and its application in batch scheduling. Journal of Systems Science and Mathematical Sciences 22(3), 328–333 (2002)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Cuixia Miao
    • 1
    • 2
  • Yuzhong Zhang
    • 1
  • Chengfei Wang
    • 1
  1. 1.School of Operations Research and Management SciencesQufu Normal UniversityRizhaoChina
  2. 2.School of Mathematical SciencesQufu Normal UniversityQufuChina

Personalised recommendations