In this paper, we propose a (max,+)-based method for the supervi- sion of discrete event systems subject to tight time constraints. Systems under consideration are those modelled as timed event graphs and repre- sented with linear (max,+) state equations. The supervision is addressed by looking for solutions of constrained state equations associated with timed event graph models. These constrained state equations are derived by reducing duration constraints to elementary constraints whose con- tributions are injected in the system's state equations. An example for supervisor synthesis is given for an industrial manufacturing plant subject to a strict temporal constraint, the thermal treatment of rubber parts for the automotive industries. Supervisors are calculated and classified ac- cording to their performance, considering their impact on the production throughput.