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Minimizing total weighted completion time with uncertain data: A stability approach

  • Scheduling Problems on a Single Machine
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Abstract

A single-machine scheduling problem is investigated provided that the input data are uncertain: The processing time of a job can take any real value from the given segment. The criterion is to minimize the total weighted completion time for the n jobs. As a solution concept to such a scheduling problem with an uncertain input data, it is reasonable to consider a minimal dominant set of job permutations containing an optimal permutation for each possible realization of the job processing times. To find an optimal or approximate permutation to be realized, we look for a permutation with the largest stability box being a subset of the stability region. We develop a branch-and-bound algorithm to construct a permutation with the largest volume of a stability box. If several permutations have the same volume of a stability box, we select one of them due to one of two simple heuristics. The efficiency of the constructed permutations (how close they are to a factually optimal permutation) and the efficiency of the developed software (average CPU-time used for an instance) are demonstrated on a wide set of randomly generated instances with 5 ≤ n ≤ 100.

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Authors and Affiliations

  1. United Institute of Informatics Problems, Belarussian National Academy of Sciences, Minsk, Belarus

    Yu. N. Sotskov & N. G. Egorova

  2. Otto-von-Guericke-University, Magdeburg, Germany

    F. Werner

Authors
  1. Yu. N. Sotskov
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  2. N. G. Egorova
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  3. F. Werner
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Additional information

Original Russian Text © Yu.N. Sotskov, N.G. Egorova, F. Werner, 2010, published in Avtomatika i Telemekhanika, 2010, No. 10, pp. 26–49.

The research of the first author was supported by Belorussian Republican Foundation for Fundamental Research.

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Sotskov, Y.N., Egorova, N.G. & Werner, F. Minimizing total weighted completion time with uncertain data: A stability approach. Autom Remote Control 71, 2038–2057 (2010). https://doi.org/10.1134/S0005117910100048

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  • DOI: https://doi.org/10.1134/S0005117910100048

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