'Why the reduced cost for the nonbasic variable can be negative?
I am working the column generation with the IP solver CPLEX.
When the master problem was solved to optimal, I output the basis information, and I found that there is a nonbasic varible takes value 1.0, and its reduced cost is negative, although the status of the cplex model is optimal.
I can't really understand what happen to this phenomenon. Maybe it is because that the solver can attach both the lower and upper bounds on a variable (eg. [0,1] in my experiment), so the reduced cost of a nonbasic variable can be negative, and its value reaches the upper bound. But I don't know how to prove it.
Any help would be greatly appreciated. Thank you very much!
Solution 1:[1]
Depends on maximization or minimization and on whether the variable is at lower bound or at upper bound.
Sources
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