Approximation Algorithms in Batch Processing

  • Xiaotie Deng
  • Chung Keung Poon
  • Yuzhong Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)

Abstract

We study the scheduling of a set of jobs, each characterised by a release (arrival) time and a processing time, for a batch processing machine capable of running (at most) a fixed number of jobs at a time. When the job release times and processing times are known a-priori and the inputs are integers, we obtained an algorithm for finding a schedule with the minimum makespan. The running time is pseudo-polynomial when the number of distinct job release times is constant. We also ob- tained a fully polynomial time approximation scheme when the number of distinct job release times is constant, and a polynomial time approxi- mation scheme when that number is arbitrary. When nothing is known about a job until it arrives, i.e., the on-line setting, we proved a lower bound of \( (\sqrt 5 + 1)/2 \) on the competitive ratio of any approximation al- gorithm. This bound is tight when the machine capacity is unbounded.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.H. Ahmadi, R.H. Ahmadi, S. Dasu, and C.S. Tang. Batching and scheduling jobs on batch and discrete processors. Operations Research, 40:750–763, 1992.MATHMathSciNetGoogle Scholar
  2. 2.
    J.J. Bartholdi. unpublished manuscript, 1988.Google Scholar
  3. 3.
    P. Brucker, A. Gladky, H. Hoogeveen, M.Y. Kovalyov, C.N. Potts, T. Tautenhahn, and S.L. van de Velde. Scheduling a batching machine. Journal of Scheduling, 1:31–54, 1998.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    V. Chandru, C.Y. Lee, and R. Uzsoy. Minimizing total completion time on a batch processing machine with job families. Operations Research Letters, 13:61–65, 1993.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    V. Chandru, C.Y. Lee, and R. Uzsoy. Minimizing total completion time on batch processing machines. International Journal of Production Research, 31:2097–2121, 1993.CrossRefGoogle Scholar
  6. 6.
    G. Dobson and R.S. Nambinadom. The batch loading scheduling problem. Technical report, Simon Graduate School of Business Administration, University of Rochester, 1992.Google Scholar
  7. 7.
    C.R. Glassey and W.W. Weng. Dynamic batching heuristics for simultaneous processing. IEEE Transactions on Semiconductor Manufacturing, pages 77–82, 1991.Google Scholar
  8. 8.
    R.L. Graham, Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling. Annals of Discrete Mathematics, 5:387–326, 1979.MathSciNetGoogle Scholar
  9. 9.
    Y. Ikura and M. Gimple. Scheduling algorithm for a single batch processing machine. Operations Research Letters, 5:61–65, 1986.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    C.Y. Lee and R. Uzsoy. Minimizing makespan on a single batch processing machine with dynamic job arrivals. Technical report, Department of Industrial and System Engineering, University of Florida, January 1996.Google Scholar
  11. 11.
    C.Y. Lee, R. Uzsoy, and L.A. Martin Vega. Efficient algorithms for scheduling semiconductor burn-in operations. Operations Research, 40:764–775, 1992.MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    C.L. Li and C.Y. Lee. Scheduling with agreeable release times and due dates on a batch processing machine. European Journal of Operational Research, 96:564–569, 1997.MATHCrossRefGoogle Scholar
  13. 13.
    R. Uzsoy. Scheduling batch processing machines with incompatible job families. International Journal of Production Research, pages 2605–2708, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Xiaotie Deng
    • 1
  • Chung Keung Poon
    • 1
  • Yuzhong Zhang
    • 2
  1. 1.Department of Computer ScienceCity University of Hong KongHong KongChina
  2. 2.Institute of Operations ResearchQufu Normal UniversityQufuChina

Personalised recommendations