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Scheduling dedicated jobs with variative processing times

Author

Listed:
  • Maksim Barketau

    (United Institute of Informatics Problems of the National Academy of Sciences)

  • Erwin Pesch

    (University of Siegen)

  • Yakov Shafransky

    (United Institute of Informatics Problems of the National Academy of Sciences)

Abstract

We consider the following optimization problem. There is a set of $$n$$ n dedicated jobs that are to be processed on $$m$$ m parallel machines. The job set is partitioned into subsets and jobs of each subset have a common due date. Processing times of jobs are interconnected and they are the subject of the decision making. The goal is to choose a processing time for each job in a feasible way and to construct a schedule that minimizes the maximum lateness. We show that the problem is NP-hard even if $$m=1$$ m = 1 and that it is NP-hard in the strong sense if $$m$$ m is a variable. We prove that there is no approximate polynomial algorithm with guaranteed approximation ratio less than 2. We propose an integer linear formulation for the problem and perform experiments. The experiments show that the solutions obtained with CPLEX within the limit of 5 min are on average about 5 % from the optimum value for instances with up to 150 jobs, 16 subsets and 11 machines. Most instances were solved to optimality and the average CPLEX running time was 32 s for these instances.

Suggested Citation

  • Maksim Barketau & Erwin Pesch & Yakov Shafransky, 2016. "Scheduling dedicated jobs with variative processing times," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 774-785, February.
  • Handle: RePEc:spr:jcomop:v:31:y:2016:i:2:d:10.1007_s10878-014-9787-0
    DOI: 10.1007/s10878-014-9787-0
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    References listed on IDEAS

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    1. Nils Boysen & Florian Jaehn & Erwin Pesch, 2011. "Scheduling Freight Trains in Rail-Rail Transshipment Yards," Transportation Science, INFORMS, vol. 45(2), pages 199-211, May.
    2. Boysen, Nils & Fliedner, Malte, 2010. "Determining crane areas in intermodal transshipment yards: The yard partition problem," European Journal of Operational Research, Elsevier, vol. 204(2), pages 336-342, July.
    3. Nils Boysen & Malte Fliedner & Florian Jaehn & Erwin Pesch, 2013. "A Survey on Container Processing in Railway Yards," Transportation Science, INFORMS, vol. 47(3), pages 312-329, August.
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