I have implemented a model in cplex and even if I give it an initial feasible solution of a heuristic programmed elsewhere, it gives me the error "the model is infeasible". Please if someone can explain what is exactly the problem ?
Short answer: The model is wrong. :-)
Longer answer: After attempting to solve the model and being told it is infeasible, run the conflict refiner to get an set of mutually inconsistent constraints. Plug your heuristic solution into each of those constraints, and see which are violated. Assuming your heuristic solution really is feasible, those constraints must be incorrect.
Alternate approach: You can fix all variables at their values in the heuristic solution (by setting lower bound = upper bound = heuristic value) and then try to solve, which presumably will result in CPLEX saying the model is infeasible. Then ask CPLEX for the value of the expression in each constraint. Compare those values with the right-hand sides to see where there are constraint violations. As in the previous case, constraints that are violated are presumably incorrect.