Characterizing complete weak efficiency in multple objective linear programming

The phenomenon consisting in all the feasible region of a multiple objective linear programming problem being weakly efficient, may be less unlikely than has been believed, particularly for problems whose feasible regions have no interior. To deal with such possibility of complete weak efficiency, we would want to have at our disposal proficient methods to check this situation. So, in this paper we give a few characterizations of that kind. The provided tests are easily put into practice and can lead us to important procedural simplifications and computational savings, specially if vector maximum or interactive approaches are going to be used in the resolution of a multiple objective linear program.