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On the Dual and Inverse Problems of Scheduling Jobs to Minimize the Maximum Penalty

Author

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  • Alexander A. Lazarev

    (Institute of Control Sciences, 117997 Moscow, Russia)

  • Nikolay Pravdivets

    (Institute of Control Sciences, 117997 Moscow, Russia)

  • Frank Werner

    (Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany)

Abstract

In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial time. Since the dual problem gives a lower bound on the optimal objective function value of the original problem, we use the optimal function value of a sub-problem of the dual problem in a branch and bound algorithm for the original single-machine scheduling problem. We present some initial computational results for instances with up to 20 jobs.

Suggested Citation

  • Alexander A. Lazarev & Nikolay Pravdivets & Frank Werner, 2020. "On the Dual and Inverse Problems of Scheduling Jobs to Minimize the Maximum Penalty," Mathematics, MDPI, vol. 8(7), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1131-:d:382811
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    References listed on IDEAS

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