MIT15_053S13_iprefguide

If w2 1 then 3x1 5x2 12 if w3 1 then 2x2 x3

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Unformatted text preview: then create three new binary variables w1, w2, and w3 and reformulate the above constraint as the following system of logical, linear, and integer constraints. If w1 = 1, then x1 + 4x2 + 2x4 ≥ 7. If w2 = 1, then 3x1 - 5x2 ≤ 12. If w3 = 1, then 2x2 + x3 ≥ 6. w1 + w2 + w3 ≥ 1. wi ∈ {0,1} for i = 1 to 3. This above system of constraints is equivalent to the following. x1 + 4x2 + 2x4 ≥ 7 - M(1- w1) ≤ 12 + M(1- w2) 3x1 - 5x2 2x2 + x3 ≥ 6 - M(1- w3) w1 + w2 + w3 ≥ 1. (Using an equality would also be valid.) wi ∈ {0,1} for i = 1 to 3. At least one of two inequalities is satisfied. In the case of two inequalities, it suffices to create a single new variable w. For example, suppose that we want to satisfy the following logical condition....
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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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