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Solution of the NP-hard total tardiness minimization problem in scheduling theory

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Abstract

The classical NP-hard (in the ordinary sense) problem of scheduling jobs in order to minimize the total tardiness for a single machine 1‖ΣT j is considered. An NP-hard instance of the problem is completely analyzed. A procedure for partitioning the initial set of jobs into subsets is proposed. Algorithms are constructed for finding an optimal schedule depending on the number of subsets. The complexity of the algorithms is O(n 2Σp j ), where n is the number of jobs and p j is the processing time of the jth job (j = 1, 2, …, n).

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  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

    A. A. Lazarev

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  1. A. A. Lazarev
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Original Russian Text © A.A. Lazarev, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 6, pp. 1087–1098.

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Lazarev, A.A. Solution of the NP-hard total tardiness minimization problem in scheduling theory. Comput. Math. and Math. Phys. 47, 1039–1049 (2007). https://doi.org/10.1134/S0965542507060139

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