Solving transient scheduling problem for cyclic production using timed Petri nets and constraint programming

We are interested in Discrete Event Dynamic Systems and especially in Flexible Manufacturing Systems (FMS) and their production management. In order to master both the complexity and combinatory of the problem, we adopt steady, repetitive and deterministic command. We have already determined a progressive and structured approach to compute this cyclic command (which corresponds to the steady state) while optimizing quantitative and qualitative performance criteria : cycle time (throughput), Work In Process, simplicity of the command. In order to apply this command we consider and compute the transient periods to start and end the production. In a previous paper, see [kor9], we gave a preliminary study of the transient states. We computed upper and lower bounds for the transient state, the steady state and the makespan then we established a method to optimize the makespan. In this paper, we recall some necessary assumptions and definitions for the study of the transient states then we give the exact method and a heuristic for a computation and optimization of the makespan.