I am observing something unusual : after solving a linear program, some basic variables have negative reduced costs (instead of $0$) :
CPLEX> display which sensitivity analysis: objective * Variable Name Reduced Cost Down Current Up Path_P168 zero -infinity 305767.0000 +infinity Path_P198 zero 1764192.0000 1790688.0000 +infinity Path_P203 -13636.0000 -infinity 58440.0000 72076.0000 Path_P204 -51212.0000 -infinity 207739.0000 258951.0000 Path_P205 -35112.0000 -infinity 247247.0000 282359.0000 CPLEX> display solution variables * Variable Name Solution Value Path_P168 1.000000 Path_P198 0.094203 Path_P203 1.000000 Path_P204 1.000000 Path_P205 1.000000
In the above sensitivity report generated by CPLEX, variable Path_P203 for example, has value $1$ and reduced cost $-13636$. The solution status is optimal.
I thought this was impossible (as basic variables should have reduced costs equal to $0$). Can someone provide an explanation ?