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MIE376 Lec9 DWD Incomplete.page5

# MIE376 Lec9 DWD Incomplete.page5 - B B-1 N – c N = as 80...

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MIE376 Mathematical Programming Lecture Notes Daniel Frances 2011 5 I B = = 1 0 0 0 1 0 0 0 1 Thus I B = 1 so that shadow prices = ( ) 0 0 0 1 = B c B Thus with this offer from Pike and Quid their resources are not worth anything, and no reason for compensating them. The next plant offers (round 1) Observing their resources have no value with their current null offers, they next have to each think of their first real offer, associated with µ 1, for Pike, and λ 1 for Quid. The Pike and Quid perspective is to think of a new offer (P 1 , P 2 ) and (Q 1 , Q 2 ), respectively, which will be most attractive to the coordinator. As before in CG we can think of designing the offer (P 1 1 , P 2 1 ) associated with the non-basic variable u 1 , to generate the largest +ve or –ve z-coefficient. This time the main LP is maximizing so that we want the z-coefficient (c B B -1 N – c N ) associated with u 1 to be as –ve as possible By examining the master LP we identify that the u 1 element of c
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Unformatted text preview: B B-1 N – c N = as ( ) ) 80 90 ( ) 80 90 ( 1 6 8 1 2 1 1 1 2 1 1 1 2 1 1 P P P P P P + − = + − + Thus the most attractive offer from Pike at this stage would be simply derived as Min – (90P 1 1 + 80P 2 1 ) subject to the local coal and furnace constraint. Since the iron constraint was now jointly shared with the other plant it would be managed by the coordinator. Max 90 P 1 1 + 80P 2 subject to 3 P 1 1 + P 2 ≤ 12; 2 P 1 1 + P 2 ≤ 10; P i 1 ≥ 0 P 1 1 = 0 @90 \$/ton, P 2 1 = 10 @ 80 \$/ton z-coeff of u 1 = - 800 Similarly for Quid Max 70Q 1 1 + 60Q 2 1 subject to 3Q 1 1 +2 Q 2 1 ≤ 15; Q 1 1 + Q 2 1 ≤ 4; Q i 1 ≥ 0 Q 1 1 = 4 @ 70 \$/ton, Q 2 1 = 0 @ 60 \$/ton z-coeff of λ 1 = - 280 Back to the coordinator (round 1) The non-basic variable with the most –ve coefficient enters the basis u 1 enters...
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