Lecture6

Mathematically this constraint can be stated as xa xd

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Unformatted text preview: ∗ ∗ ∗ Optimal solution: xA = 1, xB = xC = 0, xD = 1, PW ∗ = 34. SEEM5740/ECLT5930 42 Example 6.8 Now suppose A and D are mutually exclusive. Mathematically this constraint can be stated as xA + xD ≤ 1 If xA = 1 (select A) then the constraint implies xD = 0 (do not select D). The problem becomes maximize 21xA + 16xB + 12xC + 13xD subject to 10xA + 5xB + 5xC ≤ 10 − 30xA − 5xB − 5xC + 40xD ≤ 10 xA + xD ≤ 1 xA , xB , xC , xD is either 0 or 1 ∗ ∗ ∗ ∗ Optimal solution: xA = 0, xB = xC = 1, xD = 0, PW ∗ = 28. SEEM5740/ECLT5930 43 Constraints for dependencies among projects If projects A, B, and C are mutually exclusive then XA + XB + XC ≤ 1. If project B can be chosen only if A has been selected, then XB ≤ XA . If project C is dependent on the acceptance of A or B, then XC ≤ XA + XB . SEEM5740/ECLT5930 44 Mutually exclusive is a special case Suppose A, B, C and D are mutually exclusive. The problem becomes maximize 21xA + 16xB + 12xC + 13xD subject to xA + xB + xC + xD ≤ 1 xA , xB , xC , xD is either 0 or 1 ∗ ∗ ∗ ∗ Optimal solution from the solver: xA = 1, xB = xC = xD = 0, ∗ = 21. This is consistent with PW analysis by choosing the PW project with the largest positive PW. Question: If A, B, C, D are cost alternatives and mutually exclusive. What is the constraint? SEEM5740/ECLT5930 45 Mutually exclusive is a special case Suppose A, B, C and D are mutually exclusive. The problem becomes maximize 21xA + 16xB + 12xC + 13xD subject to xA + xB + xC + xD ≤ 1 xA , xB , xC , xD is either 0 or 1 ∗ ∗ ∗ ∗ Optimal solution from the solver: xA = 1, xB = xC = xD = 0, ∗ = 21. This is consistent with PW analysis by choosing the PW project with the largest positive PW. Question: If A, B, C, D are cost alternatives and mutually exclusive. What is the constraint? xA + xB + xC + xD = 1. We have “=” instead of “≤” because we must choose one. SEEM5740/ECLT5930 45...
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