s2008.prelim1 - PRELIM 1 Closed book exam. Justify all...

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PRELIM 1 ORIE 321/521 February 26, 2008 Closed book exam. Justify all work. 1. Consider the following linear programming problem, to which the decomposition procedure is applied using two subproblems (SUB1, SUB2). The Frst two constraints are the linking constraints ; the next two constraints, along with x 1 , x 2 , x 3 0 , deFne SUB1; SUB2 is deFned by the Fnal two constraints and y 1 , y 2 0 . 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 0 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 0 corresponding to extreme point ( x 1 , x 2 , x 3 ) = (0 , 0 , 0) , and the SUB2 variable μ 0 corresponding to extreme point ( y 1 , y 2 ) = (0 , 0) . basis
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This note was uploaded on 05/10/2010 for the course OR&IE 3310 taught by Professor Trotter during the Spring '10 term at Cornell University (Engineering School).

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s2008.prelim1 - PRELIM 1 Closed book exam. Justify all...

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