The fixed-charge ILP min 60x1 + 78x2 + 200y1 + 400y2 s.t. 12x1 + 20x2 64
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The fixed-charge ILP min 60x1 + 78x2 + 200y1 + 400y2 s.t. 12x1 + 20x2 Ú 64 15x1 + 10x2 … 60 x1 + x2 … 10 0 … x1 … 100y1 0 … x2 … 100y2 y1, y2 = 0 or 1 has LP relaxation optimum x = 10, 3.22, y
= 10, 0.0322.
(a) Compute the smallest replacements for big-M values of 100 in this formulation that can be inferred simply by examining constraints of the model.
(b) Show that the LP relaxation optimum will change if the lower big-M’s of part
(a) are employed.
(c) Verify part
(b) by solving the model having smaller big-M’s with class optimization software.
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