[Help-glpk] MIP rounding

[Jean-Sebastien Roy]

Hi !

I recently found a strange behavior in GLPK. When I input the following
problem :

Minimize
obj: c
Subject To
cst: x - 1000000.0 c <= 0
Bounds
0.5 <= x
Binaries
c
End

Whose solution is c = 1, x = 0.5. (min = 1)
GLPK is quite happy to answer c = 0, x = 0.5. (min = 0 !)

I understand that the large (1e6) coefficient is the cause of the
problem (the relaxed having solution c=5e-7, x=0.5, and c being
assimilated as the integer 0), but a basic check for feasibility would
be nice (or trying to solve the LP with integer variables fixed to
their optimal values).

On more complex problem, it happens with much lower values of the
coefficient.

xpress-mp has the same problem, cplex seems not.

btw, when asked to output an MPS file for this problem, glpsol omits the
'RHS' part (which is empty) which is problem for some solvers (SBB,
LP_SOLVE).

Regards,

js