4QA3 F12 Week 12 Lecture Notes

Gandomi 10 amsterdam a 500 antwerp b 700 tilburg

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Unformatted text preview: twerp (B) 700 Tilburg (4) 500 Leipzig (1) 400 Liege (3) 200 Le Havre (C) 800 Total Supply (2000) = Total Demand (2000) 4QA3 F12 Balanced A. Gandomi Nancy (2) 900 11 min 120 xA1 + 130 xA2 + 41 xA3 + … + 122 xC3 + 42 xC4 Subject to: For Amsterdam: xA1 + xA2 + xA3 + xA4 < 500 For Antwerp: xB1 + xB2 + xB3 + xB4 < 700 For Le Havre: xC1 + xC2 + xC3 + xC4 < 800 For Leipzig: xA1 + xB1 + xC1 > 400 For Nancy: xA2 + xB2 + xC2 > 900 For Liege: xA3 + xB3 + xC3 > 200 For Tilburg: xA4 + xB4 + xC4 > 500 All variables nonnegative Excel Solver 4QA3 F12 A. Gandomi 12 ●  ●  ●  ●  Maximization Problem o  Same constraints Total Supply ≠ Total Demand o  If Total Supply > Total Demand, no modicication, o  If Total Supply < Total Demand, add a dummy origin. Route Capacities and Route Minimum o  Capacities: add a ≤ constraint o  Minimum: add a ≤ constraint Unacceptable Routes o  3 techniques: •  Drop it •  Assign a very large cost •  Assign 0 to the corresponding decision variable 4QA3 F12 A. Gandomi 13 ●  Total Supply < Total Demand: In the AutoPower example, suppose that supply in Antwerp (B) is 600 instead of 700. Now, total supply is 1900 and total demand is 2000. min 120xA1 + 130xA2 + 41xA3 + … + 122xC3 + 42xC4 s.t. Cost of shipping from D is zero xA1 + xA2 + xA3 + xA4 < 500 xB1 + xB2 + xB3 + xB4 < 600 xC1 + xC2 + xC3 + xC4 < 800 xD1 + xD2...
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