[Help-glpk] Failure with a basic LP problem

[Jean-Sebastien Roy]

I've just come across the following problem :

Minimize
test: a
Subject To
c1: - a + b >= -6909301372.79
c2: - a + c >= -6919351684.21
c3: - a + d >= -6930335991.34
End

for which a=b=c=d=0 seems to be an obvious solution (cplex agrees).
Yet glpk (4.0) gives the following answer :

lpt_read_prob: reading LP data from `bug-glpk2.lp'...
lpt_read_prob: 4 variables, 3 constraints
lpt_read_prob: 7 lines were read
lpx_simplex: original LP has 3 rows, 4 columns, 6 non-zeros
lpx_simplex: presolved LP has 3 rows, 4 columns, 6 non-zeros
gm_scal: max / min = 1.000e+00
gm_scal: max / min = 1.000e+00
lpx_adv_basis: size of triangular part = 3
      0:   objval =   0.000000000e+00   infeas =   1.000000000e+00 (0)
      1:   objval =   0.000000000e+00   infeas =   9.999999856e-01 (0)
      2:   objval =   0.000000000e+00   infeas =   1.000000000e+00 (0)
      3:   objval =   0.000000000e+00   infeas =   9.999999855e-01 (0)
PROBLEM HAS NO FEASIBLE SOLUTION
lpx_simplex: cannot recover undefined or non-optimal solution
Time used:   0.0 secs
Memory used: 0.1M (72700 bytes)

The previous failures I had with glpk came from scaling problems. Is it
still the case is this problem ?

Thank you very much in advance,

Regards,

js