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[Bug-glpk] binary bug


From: Michael Hecht
Subject: [Bug-glpk] binary bug
Date: Sun, 21 Dec 2008 21:43:48 +0300

Hello,

the following problem written in CPLEX format results in a binary error with 
the variable RutilScBin/RutilscL.
Since glpk doesn't support semi-continuous variables I tried to simulate it - 
and got 
the described error. So where is the problem? By the way, CPLEX results in the 
same error
but SCIP from ZIB (scip.zib.de) not! The variable RutilScBin is written to be 
zero but seems
to be something like 0.000 ... 526547 (as I got from CPLEX) which destroyes the 
semi-continuity.
Is there a workaround for this behaviour or better a patch?

Problem:

Minimize
cost: +kostenLegmit -kostenSwitchLm +382762 slackUC +382762 slackOC +382762 
slackUSi +382762 slackOSi +382762 slackUMn +382762 slackOMn +382762 slackUP 
+382762 slackOP +382762 slackUS +382762 slackOS +382762 slackUCu +382762 
slackOCu +382762 slackUAl +382762 slackOAl +382762 slackUMo +382762 slackOMo 
+382762 slackUNi +382762 slackONi +382762 slackUCr +382762 slackOCr +382762 
slackUV +382762 slackOV +382762 slackUNb +382762 slackONb +382762 slackUTi 
+382762 slackOTi +382762 slackUB +382762 slackOB

Subject to

SummeLegmit: +Kohle +SiMn +FeSi +FeMnC +FeMnA +ElMn +Al +FeMo +Ni +FeCrCar +Cu 
+FeV +FeNb +FeB +FeTi +Rutil +FeS +SiMnS +FeCrAff -sumLegmit = 0

KostenLegierung: +  0.216000 Kohle +  1.769700 SiMn +  1.619000 FeSi +  
2.050000 FeMnC +  2.800000 FeMnA +  2.835000 ElMn +  1.740000 Al + 34.763000 
FeMo + 21.097000 Ni +  1.595000 FeCrCar +  4.812000 Cu + 19.575000 FeV + 
15.044000 FeNb +  1.495000 FeB +  3.619000 FeTi +  0.570000 Rutil +  9.000000 
FeS +  2.094000 SiMnS +  1.942000 FeCrAff -kostenLegmit = 0

KostenSchalter:  +  0.000000 Kohle +  0.000000 SiMn +  0.000000 FeSi +  
0.000000 FeMnC +  0.000000 FeMnA +  2.832165 ElMn +  0.000000 Al +  0.000000 
FeMo +  0.000000 Ni +  0.000000 FeCrCar +  0.000000 Cu +  0.000000 FeV +  
0.000000 FeNb +  0.000000 FeB +  0.000000 FeTi +  0.000000 Rutil +  0.000000 
FeS +  0.000000 SiMnS +  0.000000 FeCrAff -kostenSwitchLm = 0

 C1U:   +  0.810000 Kohle  +  0.016610 SiMn  +  0.000860 FeSi  +  0.070220 
FeMnC  +  0.016000 FeMnA  +  0.000830 ElMn  +  0.000000 Al  +  0.000380 FeMo  + 
 0.000000 Ni  +  0.079600 FeCrCar  +  0.000000 Cu  +  0.002100 FeV  +  0.000700 
FeNb  +  0.003960 FeB  +  0.003480 FeTi  +  0.000000 Rutil  +  0.000000 FeS  +  
0.000260 SiMnS  +  0.016340 FeCrAff  +slackUC -0.001200 sumLegmit  >= 165.020000
 C1O:   +  0.810000 Kohle  +  0.016610 SiMn  +  0.000860 FeSi  +  0.070220 
FeMnC  +  0.016000 FeMnA  +  0.000830 ElMn  +  0.000000 Al  +  0.000380 FeMo  + 
 0.000000 Ni  +  0.079600 FeCrCar  +  0.000000 Cu  +  0.002100 FeV  +  0.000700 
FeNb  +  0.003960 FeB  +  0.003480 FeTi  +  0.000000 Rutil  +  0.000000 FeS  +  
0.000260 SiMnS  +  0.016340 FeCrAff  -slackOC -0.001300 sumLegmit  <= 183.520000

Si1U:   +  0.000000 Kohle  +  0.168168 SiMn  +  0.777630 FeSi  +  0.004900 
FeMnC  +  0.008624 FeMnA  +  0.005243 ElMn  +  0.029243 Al  +  0.009898 FeMo  + 
 0.000225 Ni  +  0.000843 FeCrCar  +  0.000000 Cu  +  0.013230 FeV  +  0.024108 
FeNb  +  0.019110 FeB  +  0.011466 FeTi  +  0.014132 Rutil  +  0.003410 FeS  +  
0.280182 SiMnS  +  0.008428 FeCrAff  +slackUSi -0.003350 sumLegmit  >= 
619.750000
Si1O:   +  0.000000 Kohle  +  0.168168 SiMn  +  0.777630 FeSi  +  0.004900 
FeMnC  +  0.008624 FeMnA  +  0.005243 ElMn  +  0.029243 Al  +  0.009898 FeMo  + 
 0.000225 Ni  +  0.000843 FeCrCar  +  0.000000 Cu  +  0.013230 FeV  +  0.024108 
FeNb  +  0.019110 FeB  +  0.011466 FeTi  +  0.014132 Rutil  +  0.003410 FeS  +  
0.280182 SiMnS  +  0.008428 FeCrAff  -slackOSi -0.003850 sumLegmit  <= 
712.250000

Mn1U:   +  0.000000 Kohle  +  0.733100 SiMn  +  0.003300 FeSi  +  0.787700 
FeMnC  +  0.800000 FeMnA  +  0.995400 ElMn  +  0.002230 Al  +  0.000300 FeMo  + 
 0.000420 Ni  +  0.001400 FeCrCar  +  0.000000 Cu  +  0.017200 FeV  +  0.017400 
FeNb  +  0.003600 FeB  +  0.003700 FeTi  +  0.000000 Rutil  +  0.002600 FeS  +  
0.619500 SiMnS  +  0.003200 FeCrAff  +slackUMn -0.014592 sumLegmit  >= 
2424.425000
Mn1O:   +  0.000000 Kohle  +  0.733100 SiMn  +  0.003300 FeSi  +  0.787700 
FeMnC  +  0.800000 FeMnA  +  0.995400 ElMn  +  0.002230 Al  +  0.000300 FeMo  + 
 0.000420 Ni  +  0.001400 FeCrCar  +  0.000000 Cu  +  0.017200 FeV  +  0.017400 
FeNb  +  0.003600 FeB  +  0.003700 FeTi  +  0.000000 Rutil  +  0.002600 FeS  +  
0.619500 SiMnS  +  0.003200 FeCrAff  -slackOMn -0.015168 sumLegmit  <= 
2530.985000

 P2O:   +  0.000000 Kohle  +  0.001400 SiMn  +  0.000300 FeSi  +  0.000800 
FeMnC  +  0.002100 FeMnA  +  0.000140 ElMn  +  0.000000 Al  +  0.000400 FeMo  + 
 0.000000 Ni  +  0.000100 FeCrCar  +  0.000000 Cu  +  0.000400 FeV  +  0.002000 
FeNb  +  0.000400 FeB  +  0.000500 FeTi  +  0.000000 Rutil  +  0.000100 FeS  +  
0.000800 SiMnS  +  0.000300 FeCrAff  -slackOP -0.000150 sumLegmit  <= 4.070000

 S3O:   +  0.000000 Kohle  +  0.000000 SiMn  +  0.000000 FeSi  +  0.000000 
FeMnC  +  0.000000 FeMnA  +  0.000000 ElMn  +  0.000000 Al  +  0.000000 FeMo  + 
 0.000000 Ni  +  0.000000 FeCrCar  +  0.000000 Cu  +  0.000000 FeV  +  0.000000 
FeNb  +  0.000000 FeB  +  0.000000 FeTi  +  0.000000 Rutil  +  0.321600 FeS  +  
0.000000 SiMnS  +  0.000000 FeCrAff  -slackOS -0.000034 sumLegmit  <= 3.019200

Cu3O:   +  0.000000 Kohle  +  0.000100 SiMn  +  0.000500 FeSi  +  0.001000 
FeMnC  +  0.000200 FeMnA  +  0.000470 ElMn  +  0.012400 Al  +  0.003900 FeMo  + 
 0.000090 Ni  +  0.000100 FeCrCar  +  0.999100 Cu  +  0.001600 FeV  +  0.000500 
FeNb  +  0.000000 FeB  +  0.003700 FeTi  +  0.000000 Rutil  +  0.004200 FeS  +  
0.000300 SiMnS  +  0.000200 FeCrAff  -slackOCu -0.000845 sumLegmit  <= 60.310000

Al1U:   +  0.000000 Kohle  +  0.000000 SiMn  +  0.006176 FeSi  +  0.000000 
FeMnC  +  0.000000 FeMnA  +  0.000000 ElMn  +  0.344462 Al  +  0.000357 FeMo  + 
 0.000000 Ni  +  0.000000 FeCrCar  +  0.000000 Cu  +  0.005712 FeV  +  0.003142 
FeNb  +  0.000714 FeB  +  0.010721 FeTi  +  0.000000 Rutil  +  0.001000 FeS  +  
0.000000 SiMnS  +  0.000000 FeCrAff  +slackUAl -0.000450 sumLegmit  >= 83.250000
Al1O:   +  0.000000 Kohle  +  0.000000 SiMn  +  0.006176 FeSi  +  0.000000 
FeMnC  +  0.000000 FeMnA  +  0.000000 ElMn  +  0.344462 Al  +  0.000357 FeMo  + 
 0.000000 Ni  +  0.000000 FeCrCar  +  0.000000 Cu  +  0.005712 FeV  +  0.003142 
FeNb  +  0.000714 FeB  +  0.010721 FeTi  +  0.000000 Rutil  +  0.001000 FeS  +  
0.000000 SiMnS  +  0.000000 FeCrAff  -slackOAl -0.000555 sumLegmit  <= 
102.675000

Mo1U:   +  0.000000 Kohle  +  0.000000 SiMn  +  0.000000 FeSi  +  0.000000 
FeMnC  +  0.000000 FeMnA  +  0.000000 ElMn  +  0.000000 Al  +  0.669900 FeMo  + 
 0.000000 Ni  +  0.000000 FeCrCar  +  0.000000 Cu  +  0.000800 FeV  +  0.000000 
FeNb  +  0.000000 FeB  +  0.005860 FeTi  +  0.000000 Rutil  +  0.000000 FeS  +  
0.000000 SiMnS  +  0.000000 FeCrAff  +slackUMo -0.003510 sumLegmit  >= 
198.875000
Mo1O:   +  0.000000 Kohle  +  0.000000 SiMn  +  0.000000 FeSi  +  0.000000 
FeMnC  +  0.000000 FeMnA  +  0.000000 ElMn  +  0.000000 Al  +  0.669900 FeMo  + 
 0.000000 Ni  +  0.000000 FeCrCar  +  0.000000 Cu  +  0.000800 FeV  +  0.000000 
FeNb  +  0.000000 FeB  +  0.005860 FeTi  +  0.000000 Rutil  +  0.000000 FeS  +  
0.000000 SiMnS  +  0.000000 FeCrAff  -slackOMo -0.003900 sumLegmit  <= 
271.025000

Ni1U:   +  0.000000 Kohle  +  0.000400 SiMn  +  0.000600 FeSi  +  0.000800 
FeMnC  +  0.000600 FeMnA  +  0.000070 ElMn  +  0.000200 Al  +  0.001000 FeMo  + 
 0.998400 Ni  +  0.003700 FeCrCar  +  0.000050 Cu  +  0.000300 FeV  +  0.000200 
FeNb  +  0.002500 FeB  +  0.002910 FeTi  +  0.000000 Rutil  +  0.006300 FeS  +  
0.000600 SiMnS  +  0.004000 FeCrAff  +slackUNi -0.006510 sumLegmit  >= 
489.510000
Ni1O:   +  0.000000 Kohle  +  0.000400 SiMn  +  0.000600 FeSi  +  0.000800 
FeMnC  +  0.000600 FeMnA  +  0.000070 ElMn  +  0.000200 Al  +  0.001000 FeMo  + 
 0.998400 Ni  +  0.003700 FeCrCar  +  0.000050 Cu  +  0.000300 FeV  +  0.000200 
FeNb  +  0.002500 FeB  +  0.002910 FeTi  +  0.000000 Rutil  +  0.006300 FeS  +  
0.000600 SiMnS  +  0.004000 FeCrAff  -slackONi -0.006900 sumLegmit  <= 
561.660000

Cr1U:   +  0.000000 Kohle  +  0.000198 SiMn  +  0.002673 FeSi  +  0.000297 
FeMnC  +  0.000198 FeMnA  +  0.000871 ElMn  +  0.000624 Al  +  0.000990 FeMo  + 
 0.000000 Ni  +  0.699138 FeCrCar  +  0.000000 Cu  +  0.002871 FeV  +  0.000594 
FeNb  +  0.006435 FeB  +  0.004188 FeTi  +  0.000000 Rutil  +  0.003861 FeS  +  
0.000396 SiMnS  +  0.683397 FeCrAff  +slackUCr -0.003325 sumLegmit  >= 
538.720000
Cr1O:   +  0.000000 Kohle  +  0.000198 SiMn  +  0.002673 FeSi  +  0.000297 
FeMnC  +  0.000198 FeMnA  +  0.000871 ElMn  +  0.000624 Al  +  0.000990 FeMo  + 
 0.000000 Ni  +  0.699138 FeCrCar  +  0.000000 Cu  +  0.002871 FeV  +  0.000594 
FeNb  +  0.006435 FeB  +  0.004188 FeTi  +  0.000000 Rutil  +  0.003861 FeS  +  
0.000396 SiMnS  +  0.683397 FeCrAff  -slackOCr -0.003900 sumLegmit  <= 
645.095000

 V3O:   +  0.000000 Kohle  +  0.000000 SiMn  +  0.000000 FeSi  +  0.000000 
FeMnC  +  0.000000 FeMnA  +  0.000000 ElMn  +  0.000090 Al  +  0.000000 FeMo  + 
 0.000000 Ni  +  0.001300 FeCrCar  +  0.000000 Cu  +  0.810000 FeV  +  0.000400 
FeNb  +  0.000100 FeB  +  0.010280 FeTi  +  0.000000 Rutil  +  0.000000 FeS  +  
0.000000 SiMnS  +  0.001100 FeCrAff  -slackOV -0.000105 sumLegmit  <= 19.425000

Nb1U:   +  0.000000 Kohle  +  0.000000 SiMn  +  0.000000 FeSi  +  0.000000 
FeMnC  +  0.000000 FeMnA  +  0.000000 ElMn  +  0.000000 Al  +  0.000000 FeMo  + 
 0.000000 Ni  +  0.001000 FeCrCar  +  0.000000 Cu  +  0.000400 FeV  +  0.680000 
FeNb  +  0.000100 FeB  +  0.000820 FeTi  +  0.000000 Rutil  +  0.000000 FeS  +  
0.000000 SiMnS  +  0.001000 FeCrAff  +slackUNb -0.000080 sumLegmit  >= 14.615000
Nb1O:   +  0.000000 Kohle  +  0.000000 SiMn  +  0.000000 FeSi  +  0.000000 
FeMnC  +  0.000000 FeMnA  +  0.000000 ElMn  +  0.000000 Al  +  0.000000 FeMo  + 
 0.000000 Ni  +  0.001000 FeCrCar  +  0.000000 Cu  +  0.000400 FeV  +  0.680000 
FeNb  +  0.000100 FeB  +  0.000820 FeTi  +  0.000000 Rutil  +  0.000000 FeS  +  
0.000000 SiMnS  +  0.001000 FeCrAff  -slackONb -0.000130 sumLegmit  <= 23.865000

Ti3O:   +  0.000000 Kohle  +  0.001176 SiMn  +  0.001120 FeSi  +  0.000070 
FeMnC  +  0.000000 FeMnA  +  0.000063 ElMn  +  0.000511 Al  +  0.000000 FeMo  + 
 0.000000 Ni  +  0.000070 FeCrCar  +  0.000000 Cu  +  0.000630 FeV  +  0.003850 
FeNb  +  0.000770 FeB  +  0.508340 FeTi  +  0.383208 Rutil  +  0.000490 FeS  +  
0.001680 SiMnS  +  0.000000 FeCrAff  -slackOTi -0.000026 sumLegmit  <= 3.376250

 B7O:   +  0.000000 Kohle  +  0.000240 SiMn  +  0.000000 FeSi  +  0.000000 
FeMnC  +  0.000000 FeMnA  +  0.000000 ElMn  +  0.000000 Al  +  0.000000 FeMo  + 
 0.000000 Ni  +  0.000000 FeCrCar  +  0.000000 Cu  +  0.000000 FeV  +  0.000000 
FeNb  +  0.156240 FeB  +  0.000000 FeTi  +  0.000000 Rutil  +  0.000000 FeS  +  
0.000220 SiMnS  +  0.000000 FeCrAff  -slackOB -0.000003 sumLegmit  <= 0.027750

KohlescL: Kohle -  50 KohleScBin >= 0
KohlescU: Kohle - 1e6 KohleScBin <= 0
SiMnscL: SiMn -  50 SiMnScBin >= 0
SiMnscU: SiMn - 1e6 SiMnScBin <= 0
FeSiscL: FeSi -  50 FeSiScBin >= 0
FeSiscU: FeSi - 1e6 FeSiScBin <= 0
FeMnCscL: FeMnC -  50 FeMnCScBin >= 0
FeMnCscU: FeMnC - 1e6 FeMnCScBin <= 0
FeMnAscL: FeMnA -  50 FeMnAScBin >= 0
FeMnAscU: FeMnA - 1e6 FeMnAScBin <= 0
ElMnscL: ElMn -  50 ElMnScBin >= 0
ElMnscU: ElMn - 1e6 ElMnScBin <= 0
AlscL: Al -  50 AlScBin >= 0
AlscU: Al - 1e6 AlScBin <= 0
FeMoscL: FeMo -  50 FeMoScBin >= 0
FeMoscU: FeMo - 1e6 FeMoScBin <= 0
NiscL: Ni -  50 NiScBin >= 0
NiscU: Ni - 1e6 NiScBin <= 0
FeCrCarscL: FeCrCar -  50 FeCrCarScBin >= 0
FeCrCarscU: FeCrCar - 1e6 FeCrCarScBin <= 0
CuscL: Cu -  50 CuScBin >= 0
CuscU: Cu - 1e6 CuScBin <= 0
FeVscL: FeV -  50 FeVScBin >= 0
FeVscU: FeV - 1e6 FeVScBin <= 0
FeNbscL: FeNb -  50 FeNbScBin >= 0
FeNbscU: FeNb - 1e6 FeNbScBin <= 0
FeBscL: FeB -  50 FeBScBin >= 0
FeBscU: FeB - 1e6 FeBScBin <= 0
FeTiscL: FeTi -  50 FeTiScBin >= 0
FeTiscU: FeTi - 1e6 FeTiScBin <= 0
RutilscL: Rutil -  50 RutilScBin >= 0
RutilscU: Rutil - 1e6 RutilScBin <= 0
FeSscL: FeS -  50 FeSScBin >= 0
FeSscU: FeS - 1e6 FeSScBin <= 0
SiMnSscL: SiMnS -  50 SiMnSScBin >= 0
SiMnSscU: SiMnS - 1e6 SiMnSScBin <= 0
FeCrAffscL: FeCrAff -  50 FeCrAffScBin >= 0
FeCrAffscU: FeCrAff - 1e6 FeCrAffScBin <= 0

BOUNDS
0 <= slackUC <= 10000
0 <= slackOC <= 10000
0 <= slackUSi <= 10000
0 <= slackOSi <= 10000
0 <= slackUMn <= 10000
0 <= slackOMn <= 10000
0 <= slackUP <= 10000
0 <= slackOP <= 10000
0 <= slackUS <= 10000
0 <= slackOS <= 10000
0 <= slackUCu <= 10000
0 <= slackOCu <= 10000
0 <= slackUAl <= 10000
0 <= slackOAl <= 10000
0 <= slackUMo <= 10000
0 <= slackOMo <= 10000
0 <= slackUNi <= 10000
0 <= slackONi <= 10000
0 <= slackUCr <= 10000
0 <= slackOCr <= 10000
0 <= slackUV <= 10000
0 <= slackOV <= 10000
0 <= slackUNb <= 10000
0 <= slackONb <= 10000
0 <= slackUTi <= 10000
0 <= slackOTi <= 10000
0 <= slackUB <= 10000
0 <= slackOB <= 10000
0 <= Kohle <= 20000
0 <= SiMn <= 20000
0 <= FeSi <= 20000
0 <= FeMnC <= 20000
0 <= FeMnA <= 20000
0 <= ElMn <= 20000
0 <= Al <= 20000
0 <= FeMo <= 20000
0 <= Ni <= 20000
0 <= FeCrCar <= 20000
0 <= Cu <= 20000
0 <= FeV <= 20000
0 <= FeNb <= 20000
0 <= FeB <= 20000
0 <= FeTi <= 20000
0 <= Rutil <= 20000
0 <= FeS <= 20000
0 <= SiMnS <= 20000
0 <= FeCrAff <= 20000

BINARY
KohleScBin
SiMnScBin
FeSiScBin
FeMnCScBin
FeMnAScBin
ElMnScBin
AlScBin
FeMoScBin
NiScBin
FeCrCarScBin
CuScBin
FeVScBin
FeNbScBin
FeBScBin
FeTiScBin
RutilScBin
FeSScBin
SiMnSScBin
FeCrAffScBin


End

SOLUTION:
Problem:    
Rows:       63
Columns:    69 (19 integer, 19 binary)
Non-zeros:  408
Status:     INTEGER OPTIMAL
Objective:  cost = 3905701.725 (MINimum) 25573.07126 (LP)

   No.   Row name        Activity     Lower bound   Upper bound
------ ------------    ------------- ------------- -------------
     1 SummeLegmit                 0             0             =
     2 KostenLegierung
                                   0             0             =
     3 KostenSchalter
                                   0             0             =
     4 C1U                   184.158        165.02
     5 C1O                    183.52                      183.52
     6 Si1U                  715.441        619.75
     7 Si1O                   712.25                      712.25
     8 Mn1U                  2534.66       2424.43
     9 Mn1O                  2530.99                     2530.99
    10 P2O                      4.07                        4.07
    11 S3O                 -0.216956                      3.0192
    12 Cu3O                    60.31                       60.31
    13 Al1U                  103.345         83.25
    14 Al1O                  102.675                     102.675
    15 Mo1U                  273.514       198.875
    16 Mo1O                  271.025                     271.025
    17 Ni1U                  564.149        489.51
    18 Ni1O                   561.66                      561.66
    19 Cr1U                   538.72        538.72
    20 Cr1O                  535.051                     645.095
    21 V3O                  0.409939                      19.425
    22 Nb1U                  34.2847        14.615
    23 Nb1O                   23.865                      23.865
    24 Ti3O                  3.37625                     3.37625
    25 B7O                   0.02775                     0.02775
    26 KohlescL                    0             0
    27 KohlescU                    0                           0
    28 SiMnscL                     0             0
    29 SiMnscU                     0                           0
    30 FeSiscL               850.455             0
    31 FeSiscU               -999100                           0
    32 FeMnCscL              1417.03             0
    33 FeMnCscU              -998533                           0
    34 FeMnAscL              1469.94             0
    35 FeMnAscU              -998480                           0
    36 ElMnscL               201.408             0
    37 ElMnscU               -999749                           0
    38 AlscL                 241.296             0
    39 AlscU                 -999709                           0
    40 FeMoscL               391.724             0
    41 FeMoscU               -999558                           0
    42 NiscL                 550.551             0
    43 NiscU                 -999399                           0
    44 FeCrCarscL            745.156             0
    45 FeCrCarscU            -999205                           0
    46 CuscL                 7.92135             0
    47 CuscU                 -999942                           0
    48 FeVscL                      0             0
    49 FeVscU                      0                           0
    50 FeNbscL                     0             0
    51 FeNbscU               -999950                           0
    52 FeBscL                0.30012             0
    53 FeBscU                      0                           0
    54 FeTiscL                     0             0
    55 FeTiscU                     0                           0
    56 RutilscL              5.26547             0
    57 RutilscU                    0                           0
    58 FeSscL                      0             0
    59 FeSscU                      0                           0
    60 SiMnSscL                    0             0
    61 SiMnSscU                    0                           0
    62 FeCrAffscL                  0             0
    63 FeCrAffscU                  0                           0

   No. Column name       Activity     Lower bound   Upper bound
------ ------------    ------------- ------------- -------------
     1 kostenLegmit          40268.8             0
     2 kostenSwitchLm
                             712.028             0
     3 slackUC                     0             0         10000
     4 slackOC                     0             0         10000
     5 slackUSi                    0             0         10000
     6 slackOSi                    0             0         10000
     7 slackUMn                    0             0         10000
     8 slackOMn                    0             0         10000
     9 slackUP                     0             0         10000
    10 slackOP                     0             0         10000
    11 slackUS                     0             0         10000
    12 slackOS                     0             0         10000
    13 slackUCu                    0             0         10000
    14 slackOCu                    0             0         10000
    15 slackUAl                    0             0         10000
    16 slackOAl                    0             0         10000
    17 slackUMo                    0             0         10000
    18 slackOMo                    0             0         10000
    19 slackUNi                    0             0         10000
    20 slackONi                    0             0         10000
    21 slackUCr                    0             0         10000
    22 slackOCr                    0             0         10000
    23 slackUV                     0             0         10000
    24 slackOV                     0             0         10000
    25 slackUNb                    0             0         10000
    26 slackONb              10.1006             0         10000
    27 slackUTi                    0             0         10000
    28 slackOTi                    0             0         10000
    29 slackUB                     0             0         10000
    30 slackOB                     0             0         10000
    31 Kohle                       0             0         20000
    32 SiMn                        0             0         20000
    33 FeSi                  900.455             0         20000
    34 FeMnC                 1467.03             0         20000
    35 FeMnA                 1519.94             0         20000
    36 ElMn                  251.408             0         20000
    37 Al                    291.296             0         20000
    38 FeMo                  441.724             0         20000
    39 Ni                    600.551             0         20000
    40 FeCrCar               795.156             0         20000
    41 Cu                    57.9214             0         20000
    42 FeV                         0             0         20000
    43 FeNb                       50             0         20000
    44 FeB                  0.300135             0         20000
    45 FeTi                        0             0         20000
    46 Rutil                 5.26574             0         20000
    47 FeS                         0             0         20000
    48 SiMnS                       0             0         20000
    49 FeCrAff                     0             0         20000
    50 sumLegmit             6381.05             0
    51 KohleScBin   *              0             0             1
    52 SiMnScBin    *              0             0             1
    53 FeSiScBin    *              1             0             1
    54 FeMnCScBin   *              1             0             1
    55 FeMnAScBin   *              1             0             1
    56 ElMnScBin    *              1             0             1
    57 AlScBin      *              1             0             1
    58 FeMoScBin    *              1             0             1
    59 NiScBin      *              1             0             1
    60 FeCrCarScBin *              1             0             1
    61 CuScBin      *              1             0             1
    62 FeVScBin     *              0             0             1
    63 FeNbScBin    *              1             0             1
    64 FeBScBin     *              0             0             1
    65 FeTiScBin    *              0             0             1
    66 RutilScBin   *              0             0             1
    67 FeSScBin     *              0             0             1
    68 SiMnSScBin   *              0             0             1
    69 FeCrAffScBin *              0             0             1

Integer feasibility conditions:

INT.PE: max.abs.err. = 5.27e+000 on row 57
        max.rel.err. = 5.27e+000 on row 57
        SOLUTION IS WRONG

INT.PB: max.abs.err. = 4.65e-017 on row 58
        max.rel.err. = 4.65e-017 on row 58
        High quality

End of output

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