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Critical objective function values in linear sum assignment problems

Author

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  • Ivan Belik

    (Norwegian School of Economics)

  • Kurt Jornsten

    (Norwegian School of Economics)

Abstract

The linear sum assignment problem has been well studied in combinatorial optimization. Because of the integrality property, it is a linear programming problem with a variety of efficient algorithms to solve it. In the given research, we present a reformulation of the linear sum assignment problem and a Lagrangian relaxation algorithm for its reformulation. An important characteristic of the new Lagrangian relaxation method is that the optimal Lagrangian multiplier yields a critical bottleneck value. Lagrangian relaxation has only one Lagrangian multiplier, which can only take on a limited number of values, making the search for the optimal multiplier easy. The interpretation of the optimal Lagrangian parameter is that its value is equal to the price that must be paid for all objects in the problem to be assigned.

Suggested Citation

  • Ivan Belik & Kurt Jornsten, 2018. "Critical objective function values in linear sum assignment problems," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 842-852, April.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:3:d:10.1007_s10878-017-0240-z
    DOI: 10.1007/s10878-017-0240-z
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    References listed on IDEAS

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