On solving structured integer programming problems with Lagrangean relaxation and/or decomposition

Lagrangean relaxation and Lagrangean decomposition are powerful tools for obtaining bounds for (mixed-)integer programming problems. It is assumed that the constraint set contains at least one, and in the case of Lagrangean decomposition, multiple structured subsets of constraints. The paper reviews conditions under which strong bounds can be obtained, presents some applications and reports computational results for some of these problems.