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Unformatted text preview: n, we assume here that x is an integer variable, and that x is bounded above by 100.
Equivalent constraints: x : 7  7(1w)
x : 6 + 94 w
w E {0,1}. In any feasible solution, the definition of w is correct. If x � 7, then the first constraint is satisfied
whether w = 0 or w = 1, and the second constraint forces w to be 1. If x : 6, then the first constraint
forces w to be 0, and the second constraint is satisfied.
Big M: example 1. ⎧1
⎪
w =
⎨
⎪ 0
⎩ if x ≥ 7 otherwise. Here we assume that x is an integer variable that is bounded from above, but we donCt specify the bound.
Equivalent constraints: x : 7  M(1w)
x : 6 + Mw
w E {0,1}, where M is chosen sufficiently large. In this way, we donCt concern ourselves with the value of the
bound. We just write M. In fact, we could have written 7 instead of M in the first constraint, and it
would have also been valid. But writing big M means not having to think about the best bound.
The disadvantage of this approach is that the running time o...
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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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