
2.5. THE PLANARIZATION METHOD 63
because some constraints are missing?”), but also the pricing problem: “Is our solu tion too
bad because some variables are missi ng?” Observe the diffe r en ce in t h e ob taine d bounds
when con st r aints or variables are missing, which, in general, leads to weaker bounding
strategies than applicable to pure branch-and-cut approaches.
Following the traditional approach based on the Dantzig-Wolfe decomposition [DW60],
we can solve the pricing problem in a purely algebraic way by computing the reduced costs
of t he variables not already in the model and adding them based on their sign. It turns out
that this approach, ...