branch_and_bound_2

# branch_and_bound_2 - Saigal(U of M IOE 310 2 1 AN EXAMPLE...

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KNAPSACK BY BRANCH AND BOUND Section 9.5 I The Problem: max z = c 1 x 1 + c 2 x 2 + · · · + c n x n a 1 x 1 + a 2 x 2 + · · · + a n x n b and in addition x j = 0 or 1 , for each j = 1 , · · · , n . Saigal (U of M) IOE 310 1 / 1

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KNAPSACK LP RELAXATION I The LP relaxation is solved by inspection, since there is only a single variable: 1 Order c j a j . 2 Put items with the largest fractions into knapsack until no more full items can be put in. 3 Put in as much of last item as possible.
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Unformatted text preview: Saigal (U of M) IOE 310 2 / 1 AN EXAMPLE OF LP RELAXATION I The Problem: max z = 16 x 1 +22 x 2 +12 x 3 +8 x 4 5 x 1 +7 x 2 +4 x 3 +3 x 4 ≤ 14 and in addition x j = 0 or 1 , for each j = 1 , ··· , 4 . j c j a j Rank 1 16 5 1 2 22 7 2 3 12 4 3 4 8 3 4 The LP solution is: x 1 = 1, x 2 = 1, x 3 = 0 . 50, x 4 = 0. Saigal (U of M) IOE 310 3 / 1...
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