Considering Time Interval Models, which can de-scribe a large class of models including Timed Event Graphsand P-time Event Graphs, a general aim is to control the systemsuch that it follows a 1-periodic behavior starting from an initialstate with a minimal or maximal cycle time. The aim of thispaper is the optimization of the time durations in order toachieve a given rate of production when the quantity of resources(number of pallets, machines,...), usually represented by the initialmarking, is assumed to be a fixed datum. A prior step is thedetermination of the critical subsystems, whose variations caninfluence these optimal values and affect the obtainment of therelevant trajectories, and the non-critical subsystems leading totime margins. Two approaches are proposed in that aim. A firsttechnique is based on an adaptation of the classical Mart ́ınez andSilva’s algorithm, where each solution gives a critical subsystem,while a second approach checks each inequality of the system byan optimality verification. Using this partition of the subsystemsand particularly exploiting the time margins corresponding toidle times of machines, the approach allows an optimization ofthe non-critical time durations when the extremum cycle timesand the resources are the constant parameters of the problem. Inthis paper, the definition of P-time Event Graphs is generalizedby introducing the model ofTime Supervisor Placewhich restrictsthe time behavior of a set of places. The approach is applied toa plant bakery composed of two production lines.