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A Cutting Plane Algorithm for the Single Machine Scheduling Problem with Release Times

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Combinatorial Optimization

Part of the book series: NATO ASI Series ((NATO ASI F,volume 82))

Abstract

We propose a mixed integer programming formulation for the single machine scheduling problem with release times and the objective of minimizing the weighted sum of the start times. The basic formulation involves start time and sequence determining variables, and lower bounds on the start times. Its linear programming relaxation solves problems in which all release times are equal. For the general problem, good lower bounds are obtained by adding additional valid inequalities that are violated by the solution to the linear programming relaxation. We report computational results and suggest some modifications based on including additional variables that are likely to give even better results.

Supported by NATO Collaborative Research Grant No. 901057 and by NSF Research Grant No. ISI-8761183.

Supported by NATO Collaborative Research Grant No. 901057 and by the Netherlands Organization for Scientific Research through NATO Science Fellowship Grant No. N62-316.89.

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Author information

Authors and Affiliations

  1. Georgia Institute of Technology, Atlanta, USA

    G. L. Nemhauser

  2. Eindhoven University of Technology, The Netherlands

    M. W. P. Savelsbergh

Authors
  1. G. L. Nemhauser
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  2. M. W. P. Savelsbergh
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Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Bilkent University, 06533, Ankara, Turkey

    Mustafa Akgül

  2. Fachbereich Mathematik, Universität Kaiserslautern, Erwin-Schroedinger-Straße, W-6750, Kaiserslautern, Germany

    Horst W. Hamacher

  3. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, 32611-2083, Gainesville, FL, USA

    Süleyman Tüfekçi

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© 1992 Springer-Verlag Berlin Heidelberg

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Nemhauser, G.L., Savelsbergh, M.W.P. (1992). A Cutting Plane Algorithm for the Single Machine Scheduling Problem with Release Times. In: Akgül, M., Hamacher, H.W., Tüfekçi, S. (eds) Combinatorial Optimization. NATO ASI Series, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77489-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-77489-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77491-1

  • Online ISBN: 978-3-642-77489-8

  • eBook Packages: Springer Book Archive

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