Abstract
The preemptive single machine scheduling problem of minimizing the total weighted completion time with equal processing times and arbitrary release dates is one of the four single machine scheduling problems with an open computational complexity status. In this chapter we present lower and upper bounds for the exact solution of this problem based on the assignment problem. We also investigate properties of these bounds and worst-case behavior.
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Acknowledgements
The authors are partially supported by LATNA Laboratory, National Research University Higher School of Economics (NRU HSE), Russian Federation government grant, ag. 11.G34.31.0057.
Boris Goldengorin’s research was partially supported by the Exchange Visiting Program Number P-1-01285 carried out at the Center of Applied Optimization, University of Florida, USA.
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Batsyn, M., Goldengorin, B., Sukhov, P., Pardalos, P.M. (2013). Lower and Upper Bounds for the Preemptive Single Machine Scheduling Problem with Equal Processing Times. In: Goldengorin, B., Kalyagin, V., Pardalos, P. (eds) Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8588-9_2
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