Unformatted text preview: a constraint is satisfied, and 0
otherwise. In each case, we need bounds on how much the constraint could be violated in a solution
that satisfies every other constraint of the problem.
Example 1. ⎧1
⎪
w= ⎨
⎪0
⎩ if x ≥ 1
if x = 0. In this example, x is an integer variable. And suppose that we know x is bounded above by 100. (We
may know the bound on x because it is one of the constraints of the problem. We may also know the
bound of 100 on x because it is implied by one or more of the other constraints. For example,
suppose that one of the constraints was "3x + 4y + w : 300." We could infer from this constraint
that 3x : 300 and thus x : 100. Equivalent constraint: w : x : 100w.
w E {0,1}. In any feasible solution, the definition of w is correct. If x � 1, then the first constraint is satisfied
whether w = 0 or w = 1, and the second constraint forces w to be 1. If x = 0, then the first constraint
forces w to be 0, and the second constraint is satisfied.
⎧1
⎪
if x ≥ 7 Example 2. w =
⎨
otherwise. ⎪ 0
⎩
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 Spring '07
 JamesOrli
 Management

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