Lecture16 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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Unformatted text preview: IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis Kara Lecture # 16 Date: 16th December 2008 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17        o.w selected is if 1 i X i 18 More on Knapsack Problem • Additional constraints: – Exactly p selections – If k is selected so is r – If k is selected r cannot – Either k or r not both – Total number of selections is either • at least u or • at most l 19 More on Knapsack Problem: Additional constraints • Exactly p selections 20 } 1 , { . . m ax 1 1       i m i i i m i i i X K X w t s X c    m i i p X 1 More on Knapsack Problem: Additional constraints • If k is selected so is r 21 } 1 , { . . m ax 1 1       i m i i i m i i i X K X w t s X c k r X X  More on Knapsack Problem: Additional constraints • If k is selected r cannot 22 } 1 , { . . m ax 1 1       i m i i i m i i i X K X w t s X c r k X X   1 More on Knapsack Problem: Additional constraints • Either k or r not both 23 } 1 , { . . m ax 1 1       i m i i i m i i i X K X w t s X c 1   r k X X More on Knapsack Problem: Additional constraints • Total number of selections is either: at least u or at most l 24 } 1 , { . . m ax 1 1       i m i i i m i i i X K X w t s X c ? ? More on Knapsack Problem: Additional constraints • Total number of selections is either: at least u or at most l Either: Or: Define 25    m i i u X 1    m i i l X 1               m i i m i i l X u X Z 1 1 i f i f 1 More on Knapsack Problem: Additional constraints...
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This note was uploaded on 04/15/2010 for the course INDUSTRIAL ie513 taught by Professor Zeynephuygur during the Spring '10 term at Bilkent University.

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Lecture16 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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