Abstract
We consider parallel machine scheduling problems with identical machines and preemption allowed. It is shown that every such problem with chain precedence constraints and release dates and an integer-concave objective function satisfies the following integrality property: for any problem instance with integral data there exists an optimal schedule where all interruptions occur at integral dates. As a straightforward consequence of this result, for a wide class of scheduling problems with unit processing times a so-called preemption redundancy property is valid. This means that every such preemptive scheduling problem is equivalent to its non-preemptive counterpart from the viewpoint of both its optimum value and the problem complexity. The equivalence provides new and simpler proofs for some known complexity results and closes a few open questions.
Research of the Russian authors is supported by RFBR grant no. 08-01-00370 and Russian-Taiwan grant no. 08-06-92000. Research of the third author is partially supported by ADTP grant 2.1.1/3235.
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Baptiste, P., Carlier, J., Kononov, A., Queyranne, M., Sevastyanov, S., Sviridenko, M. (2009). Integrality Property in Preemptive Parallel Machine Scheduling. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03351-3_6
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DOI: https://doi.org/10.1007/978-3-642-03351-3_6
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