Split Scheduling with Uniform Setup Times

Frans Schalekamp; Rene Sitters; Suzanne van der Ster; Leen Stougie; Victor Verdugo; Anke van Zuylen

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arXiv · 1212.1754

Split Scheduling with Uniform Setup Times

Frans Schalekamp·Rene Sitters·Suzanne van der Ster·Leen Stougie·Victor Verdugo·Anke van Zuylen

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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 objective minimising weighted total 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.

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Frans Schalekamp, Rene Sitters, Suzanne van der Ster, Leen Stougie, Victor Verdugo, Anke van Zuylen. 2012-12-08. Split Scheduling with Uniform Setup Times. https://arxiv.org/abs/1212.1754

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