Transient state study for cyclic schedules: bounds and optimization

We are interested in discrete event dynamic systems and especially the manufacturing systems and their production management. To reduce the complexity of the problem, we consider only steady, repetitive and deterministic command. We have previously (1996) developed a structured and progressive method to elaborate the cyclic behavior of the production while optimizing quantitative and qualitative performance criteria: cycle time (throughput), work-in-process, simplicity of the command...but we have only optimized the steady period. To apply this command we may at first consider and compute the transient periods. In this paper, we will recall our method to establish a cyclic scheduling and study the transient times to begin and end this cyclic production in order to optimize the makespan of the real production. We will establish upper and lower bounds for the makespan of this production and lay down an approach to compute the optimal one which is a function of the beginning date of the periodic loading.