MIT15_053S13_iprefguide

Where 52 x 500 if x 1 1 1 f1 x1 0 if x1 0

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Unformatted text preview: At least one of the following two constraints is satisfied: x1 + 4x2 + 2x4 ≥ 7 or 3x1 - 5x2 ≤ 12. This logical condition is equivalent to: x1 + 4x2 + 2x4 ≥ 7 - Mw 3x1 - 5x2 ≤ 12 + M(1- w) w ∈ {0,1} Section 5. Fixed costs Here we consider an integer program in which there are fixed costs on variables. For example, consider the following integer program: Maximize f ( x1 ) + f 2 ( x2 ) + f3 ( x3 ) 2 x1 + 4 x2 + 5x3 ≤ 100 subject to x1 + x2 + x3 ≤ 30 10 x1 + 5x2 + 2 x3 ≤ 204 xi ≥ 0 and integer for i = 1 to 3. where ⎧ 52 x − 500 if x ≥ 1 ⎪ 1 1 f1 ( x1 ) = ⎨ 0 if x1 = 0 ⎪ ⎩ ⎧ 30 x − 400 if x ≥ 1 ⎧ 20 x − 300 ⎪ ⎪ 2 2 3 , f 2 ( x2 ) = ⎨ , f3 ( x3 ) = ⎨ 0 if x2 = 0 0 ⎪ ⎪ ⎩ ⎩ if x3 ≥ 1 if x3 = 0 . The IP formulation is as follows: Maximize subject to 52 x1 − 500 w1 + 30...
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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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