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Unformatted text preview: ity constraint involving more than one variable, the
previous two transformations can modified in a straightforward manner. ⎧
⎪1
w= ⎨
⎪0
⎩ Big M: example 4. Here we assume that
bound. ∑ Equivalent constraints: n if ∑ n ax ≤b i =1 i i otherwise. a x is integer valued and is bounded from above, but we donCt specify the i =1 i i ∑
∑ n a x ≤ b + M (1 − w). i =1 i i
n a x ≥ b + 1 − Mw. i =1 i i w ∈{0,1}.
In any feasible solution, the definition of w is correct. If ∑ n a x ≤ b, , then the first constraint is i =1 i i satisfied whether w = 0 or w = 1, and the second constraint forces w to be 1. If
the first constraint forces w to be 0, and the second constraint is
satisfied. ∑ n a x ≥ b + 1, , then i =1 i i At least one of three inequalities is satisfied.
Suppose that we wanted to model the logical constraint that at least one of three inequalities is
satisfied. For example, x1 + 4x2 + 2x4 ≥ 7 or 3x1  5x2 ≤ 12 or 2x2 + x3 ≥ 6. We...
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This note was uploaded on 03/18/2014 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.
 Spring '07
 JamesOrli
 Management

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