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Parallel batch scheduling of equal-length jobs with release and due dates

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Abstract

In this paper we study parallel batch scheduling problems with bounded batch capacity and equal-length jobs in a single and parallel machine environment. It is shown that the feasibility problem 1|p-batch,b<n,r j ,p j =p,C j ≤d j |− can be solved in O(n 2) time and that the problem of minimizing the maximum lateness can be solved in O(n 2log n) time. For the parallel machine problem P|p-batch,b<n,r j ,p j =p,C j ≤d j |− an O(n 3log n)-time algorithm is provided, which can also be used to solve the problem of minimizing the maximum lateness in O(n 3log 2 n) time.

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References

  • Baptiste, P. (2000). Batching identical jobs. Mathematical Methods of Operations Research, 52, 355–367.

    Article  Google Scholar 

  • Brucker, P. (2007). Scheduling algorithms. Berlin: Springer.

    Google Scholar 

  • Cheng, T. C. E., Yuan, J. J., & Yang, A. F. (2005). Scheduling a batch-processing machine subject to precedence constraints, release dates and identical processing times. Computers and Operations Research, 32, 849–859.

    Article  Google Scholar 

  • Garey, M. R., Johnson, D. S., Simons, B. B., & Tarjan, R. E. (1981). Scheduling unit-time tasks with arbitrary release times and deadlines. SIAM Journal on Computing, 10, 256–269.

    Article  Google Scholar 

  • Ikura, Y., & Gimple, M. (1986). Efficient scheduling algorithms for a single batch processing machine. Operations Research Letters, 5, 61–65.

    Article  Google Scholar 

  • Lageweg, B. J., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1976). Minimizing maximum lateness on one machine: computational experience and some applications. Statistica Neerlandica, 30, 25–41.

    Article  Google Scholar 

  • Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., & Shmoys, D. B. (1993). Sequencing and scheduling: algorithms and complexity. In Graves, S. C., Rinnooy Kan, A. H. G., & Zipkin, P. H. (Eds.) Handbooks in operations research and management science, logistics of production and inventory (Vol. 4, pp. 445–522). Amsterdam: North-Holland.

    Chapter  Google Scholar 

  • Lee, C. Y., Uzsoy, R., & Martin-Vega, L. A. (1992). Efficient algorithms for scheduling semiconductor burn-in operations. Operations Research, 40, 764–775.

    Article  Google Scholar 

  • Simons, B. B. (1978). A fast algorithm for multiprocessor scheduling of unit-length jobs. In IEEE 19th annual symposium on foundations of computer science (pp. 246–252).

  • Simons, B. B. (1983). Multiprocessor scheduling of unit-time jobs with arbitrary release times and deadlines. SIAM Journal on Computing, 12, 294–299.

    Article  Google Scholar 

  • Simons, B. B., & Warmuth, M. K. (1989). A fast algorithm for multiprocessor scheduling of unit-length jobs. SIAM Journal on Computing, 18, 690–710.

    Article  Google Scholar 

  • Ullman, J. D. (1975). NP-complete scheduling problems. Journal of Computer and System Sciences, 10, 384–393.

    Article  Google Scholar 

  • Vakhania, N. (2003). A better algorithm for sequencing with release and delivery times on identical machines. Journal of Algorithms, 48, 273–293.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Computing, University of Leeds, Leeds, LS2 9JT, UK

    Alessandro Condotta & Natalia V. Shakhlevich

  2. Institute of Mathematics, Technical University of Clausthal, 38678, Clausthal-Zellerfeld, Germany

    Sigrid Knust

Authors
  1. Alessandro Condotta
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  2. Sigrid Knust
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  3. Natalia V. Shakhlevich
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Correspondence to Natalia V. Shakhlevich.

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Condotta, A., Knust, S. & Shakhlevich, N.V. Parallel batch scheduling of equal-length jobs with release and due dates. J Sched 13, 463–477 (2010). https://doi.org/10.1007/s10951-010-0176-y

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  • DOI: https://doi.org/10.1007/s10951-010-0176-y

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