Unformatted text preview: 4 and 5) as
active.
The above procedure is repeated until there is no active node, at which point the incumbent
solution will be optimal. Figure 2 gives an overview of the branch and bound tree for solving
Problem (1). As shown in the tree, the nodes 15,17,19,21 get pruned since the corresponding
linear program at these nodes are all infeasible. In addition, we get x(4) = (0, 0, 11) with
value ZLP (4) = 70 at node 4, so node gets pruned and the incumbent solution is updated.
Later on, we get an improved incumbent solution at node 20 since we have x(20) = (1, 1, 1, 0)
with value ZLP (20) = 73. This is the optimal solution. IP(1)
1 x1=0 x1=1 ZLP(2)=75.57 2 x2=0 x2=1 ZLP(4)=70 x2=1 x2=0 ZLP(4)=75 5 4 ZLP(3)=75 3 ZLP(6)=77 6 x3=0 x3=1 x3=0
ZLP(9) ZLP(8)=63 8 9 =74.53
x4=0
14 ZLP(14)=53 ZLP(7)=75.846 x4=1 10 x3=1 x3=0
ZLP(12)
=75.846 ZLP(11) 11
=75.846 ZLP(10)=59 x4=0 x4=1 x4=0 15 16 InFeas ZLP(16)=49 InFeas 17 18 x3=1
ZLP(13)
=75.846 12 x4=1
x4=0
19 20 13 x4=1
21 ZLP(18) InFeas ZLP(20) InFeas
=42
=73
Figure 2: Branch and Bound Tree for Problem 1. 4 7 MIT OpenCourseWare
http://ocw.mit.edu 15.053 Optimization Methods in Management Science
Spring 2013 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms....
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This note was uploaded on 03/18/2014 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.
 Spring '07
 JamesOrli
 Management

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