In this paper, supervisory control of (max,+) automata is studied. The synthesis of maximally permissive and just-in-time supervisor, as well as the synthesis of minimally permissive and just-after-time supervisor, are proposed. Results are also specialised to non-decreasing solutions, because only such supervisors can be realised in practice. The inherent issue of rationality raised recently is discussed. An illustration of concepts and results is presented through an example of a flexible manufacturing system.