The job shop problem is particularly important among the scheduling problems found in production systems, being characterized by N parts which are processed by M machines or work stations. If the processing times in each machine are determined and known a-priori and the parts are produced repetitively, then the problem is called deterministic cyclic job shop scheduling. In this case a steady state solution, corresponding to a set point for the production system can be calculated. However, real systems are subjected to perturbations like machine failures, lack of raw material etc., that can affect the steady state solution. In this context, this work is concerned with the determination of a control law i.e. a law for the determination of the starting time of each operation in the subsequent cycles such that the set point (reference solution) be reestablished and maintained. The proposed control law is based in max-plus algebra concepts. The starting times of the operations are calculated from the starting times of the preceding operations and from a set of matrices defined in max-plus algebra.
Discrete event systems; cyclic job shop; max-plus algebra; control laws; manufacturing systems
