MIT15_053S13_iprefguide

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online