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A Lagrangian bound for many-to-many assignment problems

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Abstract

A simple procedure to tighten the Lagrangian bounds is proposed. The approach is interpreted in two ways. First, it can be seen as a reformulation of the original problem aimed to split the resulting Lagrangian problem into two subproblems. Second, it can be considered as a search for a tighter estimation of the penalty term arising in the Lagrangian problem. The new bounds are illustrated by a small example and studied numerically for a class of the generalized assignment problems.

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Authors and Affiliations

  1. Department of Mechanical and Electrical Engineering, UANL, Monterrey, Mexico

    Igor Litvinchev & Jania Saucedo

  2. São Paulo State University–UNESP, Rua Cristóvão Colombo, 2265, S.J. do Rio Preto, 15054000, Brazil

    Socorro Rangel

Authors
  1. Igor Litvinchev
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  2. Socorro Rangel
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  3. Jania Saucedo
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Corresponding author

Correspondence to Socorro Rangel.

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Litvinchev, I., Rangel, S. & Saucedo, J. A Lagrangian bound for many-to-many assignment problems. J Comb Optim 19, 241–257 (2010). https://doi.org/10.1007/s10878-008-9196-3

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  • DOI: https://doi.org/10.1007/s10878-008-9196-3

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