A Lagrangian bound for many-to-many assignment problems

@article{Litvinchev2010ALB,
  title={A Lagrangian bound for many-to-many assignment problems},
  author={Igor S. Litvinchev and Socorro Rangel and Jania Saucedo},
  journal={J. Comb. Optim.},
  year={2010},
  volume={19},
  pages={241-257}
}
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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