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178
CHAPTER
3
In the following example, an integer program with optimal value 15 is first solved with the default
setting of BIP. LINDO finds four integer solutions requiring 30 branches and 88 pivots. When BIP is
set to 10, the optimal solution is found in 43 branches and 110 pivots. When BIP is set to 14.5, the
optimal solution is found in only 13 branches and 41 pivots. Thus, a bad bound may not be helpful
while a good bound can be very helpful.
: retr trybip.lnd
: look all
MAX
9 X1 - X2 - 4 X3 - 2 X4 + 8 X5 - 2 X6 SUBJECT TO
2)
2 X1 + X2 - 2 X3 - X4 + 2 X5 - X6 - 2 X7 3)
X1 - 3 X2 + 2 X3 + 3 X4 - X5 + 2 X6 + X7 +
4) - X1 + X3 + X5 = - 9
5)
X1 - X2 + X4 =
3
6)
X2 - X3 + X6 - X7 =
12
7) - X4 - X6 + X8 =
9
8) - X5 + X7 - X8 = - 15
END
GIN
8
: ters
: go
LP OPTIMUM FOUND AT STEP
5
OBJECTIVE VALUE =
19.3000000
NEW INTEGER SOLUTION OF -1.00000000
AT BRANCH
BOUND ON OPTIMUM: 16.82500
NEW INTEGER SOLUTION OF 3.00000000
AT BRANCH
BOUND ON OPTIMUM: 16.82500
NEW INTEGER SOLUTION OF 9.00000000
AT BRANCH
BOUND ON OPTIMUM: 16.30000
NEW INTEGER SOLUTION OF 15.0000000
AT BRANCH
BOUND ON OPTIMUM: 16.30000
ENUMERATION COMPLETE. BRANCHES=
30 PIVOTS=
LAST INTEGER SOLUTION IS THE BEST FOUND
RE-INSTALLING BEST SOLUTION...
: retr trybip.lnd
: bip 10
: go
LP OPTIMUM FOUND AT STEP
5
OBJECTIVE VALUE =
19.3000000
NEW INTEGER SOLUTION OF 14.0000000
AT BRANCH
BOUND ON OPTIMUM: 18.00000
NEW INTEGER SOLUTION OF 15.0000000
AT BRANCH
BOUND ON OPTIMUM: 17.07500
ENUMERATION COMPLETE. BRANCHES=
43 PIVOTS=
LAST INTEGER SOLUTION IS THE BEST FOUND
RE-INSTALLING BEST SOLUTION...
8 X7 - 12 X8
3 X8 <= 13.1
X8 <= -6.1
14 PIVOT 43
20 PIVOT 59
25 PIVOT 69
29 PIVOT 81
88
35 PIVOT 85
41 PIVOT 103
110