Journal of Scheduling

, Volume 18, Issue 2, pp 119–129 | Cite as

Split scheduling with uniform setup times

  • Frans Schalekamp
  • René Sitters
  • Suzanne van der Ster
  • Leen Stougie
  • Víctor Verdugo
  • Anke van Zuylen
Article

Abstract

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-, machine- and sequence-independent. Problems of this kind were encountered when modelling practical problems in planning disaster 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 problem with three machines 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-, machine- and sequence-independent setup times.

Keywords

Scheduling Job splitting Setup times Complexity theory Approximation algorithms 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Frans Schalekamp
    • 1
  • René Sitters
    • 2
    • 3
  • Suzanne van der Ster
    • 2
  • Leen Stougie
    • 2
    • 3
  • Víctor Verdugo
    • 4
  • Anke van Zuylen
    • 1
  1. 1.Department of MathematicsCollege of William & MaryWilliamsburgUSA
  2. 2.Department of Operations ResearchVU University AmsterdamAmsterdamThe Netherlands
  3. 3.CWIAmsterdamThe Netherlands
  4. 4.Department of Industrial EngineeringUniversity of ChileSantiagoChile

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