Abstract
The paper deals with a single machine scheduling problem for the maximum completion time (makespan) minimization subject to the constraint on the total amount of available resources. The job processing times are given by non-decreasing linear functions simultaneously dependent on the starting moment of their execution and on the amount of allocated resources. We prove the ordinary NP-completeness of the considered problem by reducing to it the ordinary NP-complete Partition Problem. We give also some properties of the optimal resource allocation. The optimal solutions for some special cases of the latter problem are also presented.
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Bachman, A., Janiak, A. (2001). Scheduling Deteriorating Jobs Dependent on Resources for the Makespan Minimization. In: Fleischmann, B., Lasch, R., Derigs, U., Domschke, W., Rieder, U. (eds) Operations Research Proceedings. Operations Research Proceedings, vol 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56656-1_5
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DOI: https://doi.org/10.1007/978-3-642-56656-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41587-9
Online ISBN: 978-3-642-56656-1
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