MIE376 Lec9 DWD Incomplete.page8

MIE376 Lec9 DWD Incomplete.page8 - This time 2 enters Now...

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MIE376 Mathematical Programming Lecture Notes Daniel Frances 2011 8 Current Profit = ( ) 1000 1 1 80 0 200 10 = with solution = = 28 / 8 1 28 / 20 1 1 80 1 28 / 60 28 / 1 0 1 0 0 28 / 60 28 / 1 0 1 1 λ µ Since s 1 = 0 we have run out of iron, and can only accept (20/28) of the new Pike offer. The next plant offers (round 3) For Pike the u 2 element of c B B -1 N – c N is ( ) ) 20 10 ( 200 ) 80 90 ( 0 1 6 8 0 200 10 2 2 2 1 2 2 2 1 2 2 2 1 P P P P P P + = + + Max 10P 1 2 + 20 P 2 2 subject to 3 P 1 2 + P 2 2 ≤ 12; 2 P 1 2 + P 2 2 ≤ 10; P i 2 ≥ 0 P 1 2 = 0, P 2 2 = 10 @ 20 $/ton z-coeff of u 2 = 0 no good offer For Quid the λ 2 element of c B B -1 N – c N is ( ) 2 2 2 2 2 1 2 2 2 1 10 ) 60 70 ( 1 0 5 7 0 200 10 Q Q Q Q Q = + + Max 10Q 2 2 subject to 3 Q 1 2 +2 Q 2 2 ≤ 15; Q 1 2 + Q 2 2 ≤ 4; Q i 2 ≥ 0 Q 1 2 = 0, Q 2 2 = 4 @ 10 $/ton z-coeff of λ 2 = - 40 Back to the coordinator (round 3)
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Unformatted text preview: This time 2 enters Now we need to determine which of B = { 1 , 1 , } departs? As before we need to calculate B-b/B-1 (entering column) = = = 1 1 28 / 8 28 / 20 / 28 / 8 1 28 / 20 1 20 1 28 / 60 28 / 1 1 28 / 60 28 / 1 / 1 1 80 1 28 / 60 28 / 1 1 28 / 60 28 / 1 departs (or 1 ) Please stay tuned. ......
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