Originally posted by: SystemAdmin

[BigInJapan said:]

Example:
[pre]
max  2x1 + 2x2 -  x3
s.t.  x1 +  x2 -  x3 = 0
      x1            <= 5<br />            x2      <= 4<br />                  x3<= 7<br />  (x1, x2, x3 >= 0)
The optimal solution is any x = (q1, q2, 7) where q1 + q2 = 7.
In this case how CPLEX finds optimal x?

If I want to adjust x1 is more preferable then x2, I have to set its TF (target function) coef to 2.0001 (for example).
After that solution would be single and equals to (5, 2, 7). But this operation may react dual variables to change. Am I right?

And my question is - can CPLEX order variables other way then TF? If yes, this is no need to set up TF coef for preferable variable.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

[BigInJapan said:]

Nobody knows? :(
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

[Sylvain said:]

The simplex does not actually do that.
There are some workarounds.
As you said you can change objective coefficients in order to give weights to your variables in some way.
But the marginal values may not be correct.
In this case, what you could do is resolve the original problem giving simplex a starting basis solution which corresponds to your "weight" optimal solution.
If you run a [u]basic[/u] simplex from this basis, no iteration should be performed and you should get correct marginal values...
#CPLEXOptimizers
#DecisionOptimization