Geodesic
Comparison of Lagrangian bounds for one class of generalized assignment problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 779-787

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Classical and modified Lagrangian bounds for the optimal value of optimization problems with a double decomposable structure are examined. For the class of generalized assignment problems, this property of constraints is used to design a Benders algorithm for solving the modified dual problem. Numerical results are presented that compare the quality of classical and modified bounds. 
@article{ZVMMF_2008_48_5_a3,
     author = {I. S. Litvinchev and S. Rangel},
     title = {Comparison of {Lagrangian} bounds for one class of generalized assignment problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {779--787},
     publisher = {mathdoc},
     volume = {48},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a3/}
}
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I. S. Litvinchev; S. Rangel. Comparison of Lagrangian bounds for one class of generalized assignment problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 779-787. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a3/