  Dantzig-Wolfe (DW) decomposition is a well-known technique in mixed-integer
programming (MIP) for decomposing and convexifying constraints to obtain
potentially strong dual bounds. We investigate cutting planes that can be
derived using the DW decomposition algorithm and show that these cuts can
provide the same dual bounds as DW decomposition. More precisely, we generate
one cut for each DW block, and when combined with the constraints in the
original formulation, these cuts imply the objective function cut one can
simply write using the DW bound. This approach typically leads to a formulation
with lower dual degeneracy that consequently has a better computational
performance when solved by standard MIP solvers in the original space. We also
discuss how to strengthen these cuts to improve the computational performance
further. We test our approach on the Multiple Knapsack Assignment Problem and
the Temporal Knapsack Problem, and show that the proposed cuts are helpful in
accelerating the solution time without the need to implement branch and price.
