Split scheduling with uniform setup times

نویسندگان

  • Frans Schalekamp
  • René Sitters
  • Suzanne van der Ster
  • Leen Stougie
  • Victor Verdugo
  • Anke van Zuylen
چکیده

We study a scheduling problem in which jobs may be split into parts, where the parts of a split job may be processed simultaneously on more than one machine. Each part of a job requires a setup time, however, on the machine where the job part is processed. During setup, a machine cannot process or set up any other job. We concentrate on the basic case in which setup times are job-, machineand sequence-independent. Problems of this kind were encountered when modelling practical problems in planning disR. Sitters, S. van der Ster, L. Stougie, Research partially supported by the Tinbergen Institute. V. Verdugo, Research supported by EU-IRSES grant EUSACOU. F. Schalekamp · A. van Zuylen Department of Mathematics, College of William & Mary, Williamsburg, VA, USA e-mail: [email protected] A. van Zuylen e-mail: [email protected] R. Sitters · S. van der Ster · L. Stougie Department of Operations Research, VU University Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] S. van der Ster e-mail: [email protected] L. Stougie e-mail: [email protected] R. Sitters · L. Stougie (B) CWI, Amsterdam, The Netherlands e-mail: [email protected] R. Sitters e-mail: [email protected] V. Verdugo Department of Industrial Engineering, University of Chile, Santiago, Chile e-mail: [email protected] aster relief operations. Our main algorithmic result is a polynomial-time algorithm for minimising total completion time on two parallel identical machines. We argue, why the same problemwith threemachines is not an easy extension of the two-machine case, leaving the complexity of this case as a tantalising open problem. We give a constant-factor approximation algorithm for the general case with any number of machines and a polynomial-time approximation scheme for a fixed number of machines. For the version with the objective to minimise total weighted completion time, we prove NP-hardness. Finally, we conclude with an overview of the state of the art for other split scheduling problems with job-, machineand sequence-independent setup times.

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عنوان ژورنال:
  • J. Scheduling

دوره 18  شماره 

صفحات  -

تاریخ انتشار 2015