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A New Semi-Lagrangean Relaxation for the K-Cardinality Assignment Problem

Author

Listed:
  • Belik, Ivan

    (Dept. of Business and Management Science, Norwegian School of Economics)

  • Jörnsten, Kurt

    (Dept. of Business and Management Science, Norwegian School of Economics)

Abstract

Recently Beltrán-Royo, Vial & Alonso-Ayuso (2012) presented a semi-Lagrangean relaxation for the classical p-median location problem and for the incapacitated facility location problem. The results, obtained using the semi-Lagrangean relaxation approach, were quite impressive. In this paper we use a semi-Lagrangean relaxation to obtain an efficient solution method for the kcardinality assignment problem. The method has only one semi-Lagrangean multiplier that can only take on a limited number of values, making the search for the optimal multiplier easy. Since the semi-Lagrangean relaxation closes the duality gap, this leads to an extremely reliable and easily implementable method for finding k-cardinality assignments in large-scale cases. The method is computationally tested on the examples commonly used in the literature.

Suggested Citation

  • Belik, Ivan & Jörnsten, Kurt, 2014. "A New Semi-Lagrangean Relaxation for the K-Cardinality Assignment Problem," Discussion Papers 2014/1, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2014_001
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    File URL: http://hdl.handle.net/11250/227006
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    References listed on IDEAS

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    1. C. Beltran-Royo & J.-P. Vial & A. Alonso-Ayuso, 2012. "Semi-Lagrangian relaxation applied to the uncapacitated facility location problem," Computational Optimization and Applications, Springer, vol. 51(1), pages 387-409, January.
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    Cited by:

    1. Kurt Jörnsten & Andreas Klose, 2016. "An improved Lagrangian relaxation and dual ascent approach to facility location problems," Computational Management Science, Springer, vol. 13(3), pages 317-348, July.
    2. Nitish Das & P. Aruna Priya, 2019. "A Gradient-Based Interior-Point Method to Solve the Many-to-Many Assignment Problems," Complexity, Hindawi, vol. 2019, pages 1-13, July.

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    More about this item

    Keywords

    K-cardinality assignment; Lagrangean Relaxation; Mathematical Programming;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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