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Unformatted text preview: f the integer programming algorithm
may depend on the choice of M. Choosing M very large (e.g., M = 1 trillion) will lead to valid
formulations, but the overly large value of M may slow down the solution procedure. ⎧1
⎪
if x ≥ a w =
⎨
otherwise. ⎪ 0
⎩
Here we assume that x is an integer variable that is bounded from above, but we donCt specify the bound.
Big M: example 2. Equivalent constraints: x : a  M(1w)
x : (a1) + Mw
w E {0,1}, where M is chosen sufficiently large. In any feasible solution, the definition of w is correct. If x � a,
then the first constraint is satisfied whether w = 0 or w = 1, and the second constraint forces w to be
1. If x : a1, then the first constraint forces w to be 0, and the second constraint is satisfied. ⎧1
⎪
if x ≤ a
w= ⎨
otherwise.
⎪0
⎩
Here we assume that x is an integer variable that is bounded from above, but we donCt specify the
bound. Big M: example 3. Equivalent constraints: x 5 a  M(1w)
x ≥ (a+1) + Mw
�
w E {0,1}, where M is chosen sufficiently large. In the case that w depends on an inequal...
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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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