branch_and_bound_1 - BRANCH AND BOUND METHOD FOR PURE IPs I...

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BRANCH AND BOUND METHOD FOR PURE IPs I The IP: max z = 8 x 1 +5 x 2 x 1 + x 2 6 9 x 1 +5 x 2 45 x 1 0 x 2 0 x 1 int x 2 int Saigal (U of M) IOE 310 1 / 23
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BRANCH AND BOUND METHOD FOR PURE IPs I Branching Tree. Bounding. Fathomed. LIFO Rule. Candidate solution and lower bound. Saigal (U of M) IOE 310 2 / 23
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SOLVED AS LP I Saigal (U of M) IOE 310 3 / 23
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SUBPROBLEM 2 I After adding the constraint x 1 4 the LP relaxation becomes: max z = 8 x 1 +5 x 2 x 1 + x 2 6 9 x 1 +5 x 2 45 x 1 4 x 1 0 x 2 0 and the solution is x 1 = 4 , x 2 = 1 . 8 , z = 41. Saigal (U of M) IOE 310 4 / 23
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SUBPROBLEM 2 SOLVED I Saigal (U of M) IOE 310 5 / 23
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SUBPROBLEM 2 I After adding constraint x 1 3 the LP relaxation becomes: max z = 8 x 1 +5 x 2 x 1 + x 2 6 9 x 1 +5 x 2 45 x 1 3 x 1 0 x 2 0 and the solution is x 1 = 3 , x 2 = 6 , z = 39. THIS SOLUTION NOW GIVES A LOWER BOUND. (WHY?) Saigal (U of M) IOE 310 6 / 23
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SUBPROBLEM 3 SOLVED I Saigal (U of M) IOE 310 7 / 23
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SUBPROBLEM 5 I Saigal (U of M) IOE 310 8 / 23
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BRANCHING TREE PART 1 I Saigal (U of M) IOE 310 9 / 23
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BRANCHING TREE PART 2 I Saigal (U of M) IOE 310 10 / 23
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FINAL BRANCHING TREE I Saigal (U of M) IOE 310 11 / 23
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