Another formulation possibility for the uncapacitated facility location problem is to "disaggregate" the capacity constraints (the big-formula_49 constraints). That is, replace the constraintsformula_55with the constraintsformula_56In practice, this new formulation performs significantly better, in the sense that it has a tighter Linear programming relaxation than the first formulation. Notice that summing the new constraints together yields the original big-formula_49 constraints. In the capacitated case, these formulations are not equivalent. More information about the uncapacitated facility location problem can be found in Chapter 3 of "Discrete location theory".