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The value of the optimal LP-solution is υ LP (MTZ ) = 4 + 1 / n and the optimal value is OPT = L + 4, which gives ratio υ LP (MTZ ) / OPT ≈ 1 / L. □ The values of the LP-relaxation of the MTZ model can be arbitrarily bad.
The value of the optimal LP-solution is υ LP (MTZ ) = 4 + 1 / n and the optimal value is OPT = L + 4, which gives ratio υ LP (MTZ ) / OPT ≈ 1 / L. □ Note that for our computational experiments we replaced constraints (26) by the following stronger ones: (ˈ S ˈ − 2 ) · x ji + ˈ S ˈ · x ij + u i ≤ u j + ˈ S ˈ − 1 ∀ ij ∈ A S The polyhedral results in Section 4 are given for the weaker model.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com