Complexity of Production Management in a Petri Net Environment

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The objective of this paper is to show that Petri nets facilitate a comprehensive approach to production management and reduce the complexity of the problems involved at the expense of some constraints imposed on the decision making systems.

The first part of the paper focuses on cyclic manufacturing systems. For this type of systems, it is always possible to propose an event graph model which represents both the physical and the decision making systems. We use such a model to propose a near-optimal scheduling algorithm that maximizes productivity while minimizing the work-in-process (WIP) in the deterministic case.

The approach used for non-cyclic manufacturing systems is different in the sense that only the manufacturing processes (i.e. the physical part of the system) and the related constraints are modeled using Petri nets. We use such a Petri net model to propose a short-term planning process which results in a trade- off between the computation burden the level of resource utilization. the short-term planning models is then enhanced to obtain the scheduling model. The latter is used to develop an efficient scheduling algorithm that is able to satisfy the requirements imposed by short-term planning.