Originally posted by: Mimmo88

main.cpp:(.text+0x0): multiple definition of `MCFCallback(IloEnv, ...

Did you use the same name for the two different callback classes?

This errors messages looks like a genuine C++ programming error, not like something specific to CPLEX. Somehow you managed to define the MCFCallback function (or constructor) twice.

Originally posted by: Mimmo88

//UpperBoundLazyConstraintCallback.h

class UpperBoundLazyConstraintCallbackI : public IloCplex::LazyConstraintCallbackI {
...
};

IloCplex::Callback UpperBoundLazyConstraintCallback(IloEnv env, IloNumVarArray z, IloNumVarArray w, const std::map<char, int> params) {
    return (IloCplex::Callback(new (env) UpperBoundLazyConstraintCallbackI(env, z, w, params)));
}
...

//MCFCallback.h
class MCFCallbackI : public IloCplex::LazyConstraintCallbackI {
...
};

IloCplex::Callback MCFCallback(IloEnv env, const std::set<teseo::Arc<unsigned int>*> edges, IloNumVarArray x_ij, IloNumVarArray x_ji, const std::map<int, int> x_ij_map, const std::map<int, int> x_ji_map) {
    return (IloCplex::Callback(new (env) MCFCallbackI(env, edges, x_ij, x_ji, x_ij_map, x_ji_map)));
}
...

I use different names.

Do you include MCFCallback.h from more than one file? If yes, do you use proper include guards in MCFCallback.h?