I have a small problem and I want have the dual solution.
But I find that the GLPK and LP-solve give me 2 different dual solution (the
primal solution and the objective value is the same).
Could someone help to explain the reason??
( I give the mps file. )
Thanks
GLPK:
Problem:
No. Row name St Activity Lower bound Upper bound Marginal
------ ------------ -- ------------- ------------- ------------- -------------
1 R0 B 2071..61
2 R1 NS 100 100 = 5.12392
3 R2 NS 150 150 = 6.80022
4 R3 NS 200 200 = 7.35016
5 R4 NS 130 130 = -4.45249
6 R5 B 180 180 =
7 R6 NS 140 140 = -2.51445
No. Column name St Activity Lower bound Upper bound Marginal
------ ------------ -- ------------- ------------- ------------- -------------
1 x1 B 100 0
2 x2 NL 0 0 0.576412
3 x3 NL 0 0 6.39053
4 x4 B 30 0
5 x5 B 120 0
6 x6 NL 0 0 1.93804
7 x7 NL 0 0 0.28821
8 x8 B 60 0
9 x9 B 140 0
LP-solve :
Primal variables:
Column name Value Slack Min Max
--------------------------------------------------------------------------
x1 100 0 -1e+030 1e+030
x2 0 0.576412 -30 100
x3 0 6.39053 -30 100
x4 30 0 -1e+030 1e+030
x5 120 0 -1e+030 1e+030
x6 0 1.93804 -60 120
x7 0 0.28821 -120 30
x8 60 0 -1e+030 1e+030
x9 140 0 -1e+030 1e+030
Dual variables:
Row name Value Slack Min Max
--------------------------------------------------------------------------
R1 0.671428 100 100 100
R2 2.34773 150 150 150
R3 2.89767 200 200 200
R4 0 130 -1e+030 1e+030
R5 4.45249 180 180 180
R6 1.93804 140 140 140
*<meta creator='lp_solve v5.5'>
*<meta rows=6>
*<meta columns=9>
*<meta equalities=6>
*<meta integers=0>
*<meta origsense='MIN'>
*
NAME
ROWS
N R0
E R1
E R2
E R3
E R4
E R5
E R6
COLUMNS
x1 R0 0.6714280000 R1 1.0000000000
x1 R4 1.0000000000
x2 R0 5.7003300000 R1 1.0000000000
x2 R5 1.0000000000
x3 R0 9.0000000000 R1 1.0000000000
x3 R6 1.0000000000
x4 R0 2.3477300000 R2 1.0000000000
x4 R4 1.0000000000
x5 R0 6.8002200000 R2 1.0000000000
x5 R5 1.0000000000
x6 R0 6.2238100000 R2 1.0000000000
x6 R6 1.0000000000
x7 R0 3.1858800000 R3 1.0000000000
x7 R4 1.0000000000
x8 R0 7.3501600000 R3 1.0000000000
x8 R5 1.0000000000
x9 R0 4.8357100000 R3 1.0000000000
x9 R6 1.0000000000
RHS
RHS R1 100.00000000 R2 150.00000000
RHS R3 200.00000000 R4 130.00000000
RHS R5 180.00000000 R6 140.00000000
ENDATA
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