ORIE 3300/5300
Assignment 12 SOLUTION
Fall 2008
Problem 1
(a)
Since the variables are binary, on the left branch we place the restriction
x
= 0 and on the
right branch
x
= 1.
(b)
The branch-and-bound tree is here. The optimal solution is
x
= (1
,
1
,
0) with value
z
= 16.
(1)
Original problem
z=21.6
x=(F,1,1)
x
1
=1
(2)
z=20
x=(1,F,F)
x
2
=1
(3)
z=19.3
x=(1,1,F)
x
3
=1
(4)
infeasible
x
3
=0
(5)
z=16
x=(1,1,0)
current incumbent = 16
x
2
=0
(6)
z=18.5
x=(1,0,F)
x
3
=1
(7)
infeasible
x
3
=0
(8)
z=11
worse than incumbent
x
1
=0
(9)
z=15
worse than incumbent
1

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