MIT15_053S13_iprefguide

G m 1 trillion will lead to valid formulations but the

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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(1-w) x : (a-1) + 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 : a-1, 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(1-w) 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.

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