I am solving a model with GAMS/CPLEX and CPLEX claims it to be infeasible. The same behaviour shows the solver BDMLP.
I am solving the exact same model with GAMS/XPRESS and it provides the (known) optimal solution. The solvers BONMIN and CBC solve the model as well.
Any hint why this happens? Is it a question of tolerance values? But which tolerances would explain that behaviour?
I set the default integrality tolerance for CPLEX (= 1E-05) to the default value of XPRESS ( = 5E-06) but this doesn't change anything. The default optimality and feasibility tolerances for XPRESS and CPLEX have the same value (= 1E-06).
EDIT
The trouble starts when I add the following constraints Eq1, Eq2
Eq1: - sum_{i = 1}^{5} B_{i} + (50 - epsilon) \ge (- M Z )
Eq2: - sum_{i = 1}^{5} W_{i} + 2.0 \le (M (1.0 - Z))
Where,
epsilon = 0.0001
M = 1000 (BigM Value)
0 \le B_{i} \le 50.0 real variable
W_{i} binary variable
Z binary variable
What I am trying to say is:
IF sum_{i = 1}^{5} B_{i} > 50 THEN sum_{i = 1}^{5} W_{i} \ge 2