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A polynomially solvable case of the three machine johnson problem

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Abstract

Under study is the classical NP-hard problem with three machines: N tasks must be fulfilled at three machines in minimum time. The processing time is given of each task at each machine. The processing sequences of all tasks are identical. It is impossible to process two tasks at one machine at the same time. We address the properties of this problem, find a new polynomially solvable case, and discuss a corresponding algorithm.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Omsk Branch, ul. Pevtsova 13, Omsk, 644099, Russia

    V. V. Servakh

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  1. V. V. Servakh
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Correspondence to V. V. Servakh.

Additional information

Original Russian Text © V.V. Servakh, 2006, published in Diskretnyi Analiz i Issledovanie Operatsii, Ser. 2, 2006, Vol. 13, No. 2, pp. 44–55.

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Servakh, V.V. A polynomially solvable case of the three machine johnson problem. J. Appl. Ind. Math. 2, 397–405 (2008). https://doi.org/10.1134/S1990478908030101

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  • DOI: https://doi.org/10.1134/S1990478908030101

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