Does anybody see an example for hybrid of Lagrangian relaxation and Benders decomposition in MIP?
These two papers might be interesting, allthough not completely what you are looking for:
http://link.springer.com/article/10.1007%2Fs10732-007-9064-9
http://link.springer.com/chapter/10.1007%2F978-1-4419-1306-7_5
Dear Hossein,
You might have better luck if you search for "Cross Decomposition", as this is usually how this mixed application of Benders and Lagrangean relaxation is referred to. For example, one nice application in the context of a facility location problem can be found at http://www.jstor.org/stable/170679.
The following papers might interesting in this context, allthough they might not fully answer your question.
http://link.springer.com/article/10.1007%2Fs10732-007-9064-9
http://link.springer.com/chapter/10.1007%2F978-1-4419-1306-7_5
In the paper "A decomposition approach for the integrated vehicle-crew-roster problem with days-off pattern" of Marta Mesquita, Margarida Moz, Ana Paias, Margarida Pato a kind of hybrid is discussed. The problem is modeled as a MIP, then it is decomposed by Benders decomposition and the master problem is approximated by Lagrangean relaxation, while the Benders cuts are relaxed.
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