Originally posted by: SystemAdmin

[anujiitm2004@gmail.com said:]

Hey folks,
            I am wondering after seeing solution of my optimization problem. I solved minimization problem with cplex 11.2 (by interactive optimizer ). i got the optimum solution for my problem, but at the [b]optimum condition[/b] for the [b]minimization[/b] problem, [b]reduced cost[/b] is coming [b]negative[/b]. How it is possible!!! Am i doing some mistake to solve the minimization problem in cplex ( by interactive optimizer), or is there any fundamental mistake ??

Here the minimization problem :
[b]minimize[/b]
-x1-2x2-3x3
st
x1-x2-x3>=-20
-x1+3x2-x3>=-30
3x1+2x2-x3>=100
-x3+4x4>=-40
bounds
0<=x1<=40<br />10<=x2<=10000<br />0<=x3<=100<br />0<=x4<=10000<br />


i am also putting things which i followed steps in interactive optimizer :

Welcome to CPLEX Interactive Optimizer 11.2.1
  with Simplex, Mixed Integer & Barrier Optimizers
Copyright (c) ILOG 1997-2008
CPLEX is a registered trademark of ILOG

Type 'help' for a list of available commands.
Type 'help' followed by a command name for more
information on commands.

CPLEX> enter
Enter name for problem: optimum
Enter new problem ['end' on a separate line terminates]:
minimize
-x1-2x2-3x3
st
x1-x2-x3>=-20
-x1+3x2-x3>=-30
3x1+2x2-x3>=100
-x3+4x4>=-40
bounds
0<=x1<=40<br />10<=x2<=10000<br />0<=x3<=100<br />0<=x4<=10000<br />end
CPLEX> optimize
Tried aggregator 1 time.
LP Presolve eliminated 1 rows and 1 columns.
Reduced LP has 3 rows, 3 columns, and 9 nonzeros.
Presolve time =  -0.00 sec.

Iteration log . . .
Iteration:    1  Dual infeasibility =            0.000000
Iteration:    2  Dual objective    =          -202.500000

Dual simplex - Optimal:  Objective = -2.0250000000e+002
Solution time =    0.00 sec.  Iterations = 2 (1)

[b]CPLEX> display solution reduced -
Variable Name            Reduced Cost
x1                          -3.500000[/b]
All other reduced costs in the range 1-4 are 0.


how can reduced cost can come negative in minimization problem at optimum???
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

[afleischer said:]

Hi,

don't you get this because x1 is at its upper bound?

Alex
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

[notdarkyet said:]

Hi,

the previous post clearly stated the reason: optimality conditions in simplex method with bounds depend on the bound the nonbasic variable is at! The same applies to the check for unboundedness , since a nonbasic at its upper bound can just be reduced in value instead of increased as in the standard textbook form Ax=b, x>=0.


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#DecisionOptimization