p1_sp2011 - PRELIM 1 ORIE 3310/5310 Feb. 17, 2011 Closed...

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Unformatted text preview: PRELIM 1 ORIE 3310/5310 Feb. 17, 2011 Closed book exam. Justify all work. 1. Consider again the following LP decomposition model from the homework assignment. The first two constraints are the linking constraints ; the remaining constraints define the two subproblems, SUB1 (variables x 1 ,x 2 ,x 3 ) and SUB2 (variables y 1 ,y 2 ). ORIGINAL PROBLEM max 15 x 1 + 7 x 2 + 15 x 3 + 20 y 1 + 12 y 2 s.t. x 1 + x 2 + x 3 + y 1 + y 2 ≤ 5 3 x 1 + 2 x 2 + 4 x 3 + 5 y 1 + 2 y 2 ≤ 16 4 x 1 + 4 x 2 + 5 x 3 ≤ 20 2 x 1 + x 2 ≤ 4 y 1 + 1 / 2 y 2 ≤ 3 1 / 2 y 1 + 1 / 2 y 2 ≤ 2 x 1 , x 2 , x 3 , y 1 , y 2 ≥ The following tableau is encountered for the restricted master program at an iteration of the decom- position procedure. The λ variables are from SUB1 and the μ variables from SUB2; s 1 ,s 2 are slack variables associated with the two linking constraints. The initial basis for the restricted master con- sisted of s 1 ,s 2 , the SUB1 variable λ corresponding to extreme point ( x 1 ,x 2 ,x 3 ) = (0 , , 0) , and the SUB2 variable μ corresponding to extreme point ( y 1 ,y 2 ) = (0 , 0) ....
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This note was uploaded on 02/09/2012 for the course OR&IE 3310 taught by Professor Trotter during the Spring '10 term at Cornell University (Engineering School).

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p1_sp2011 - PRELIM 1 ORIE 3310/5310 Feb. 17, 2011 Closed...

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