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In this paper, the expression "production systems" refers to flow-shops, job-shops, assembly systems, Kanban systems and, in general, to any Discrete Event System (DES) which transforms raw material and/or components into products and/or components. Such a system is said to be cyclic if it provides indefinitely the same sequence of products. A schedule of a cyclic production system is defined as soon as the starting time of each operation on the related resource is known. It has been showed that, whatever the feasible schedule applied to the cyclic production system, it is always possible to fully utilize the bottleneck resource. In other words, it is always possible to maximize the productivity of such a system. As a consequence, we aim at finding the schedule which permits to maximize the productivity with a Work-In-Process (WIP) as small as possible. We propose a heuristic approach based on Petri nets to find a near-optimal, if not optimal, solution. We also give a sufficient condition for a solution to be optimal.

An important step when designing a Flexible Manufacturing System (FMS) using Automated Guided Vehicles (AGVs) is the definition of the number of AGVs to be used in order to reach a given productivity. A way to define this number is to consider several scenari, to define the minimal number of AGVs required by each scenario, and to keep the maximal of these numbers. In this paper, we propose a Branch and Bound (B&B) approach to define the minimal number of AGVs require for a scenario. This approach is based on an Event Graph (EG) formulation.

This paper addresses the problem of integration of Petri nets representing manufacturinfg systems. A modular modelling methodology being adopted, we define a class of Petri nets that characterizes a large sort of real-word manufacturing systems. These Petri nets are shown to have the properties of liveness, consistency and reversibility. We also show that the integration of such Petri nets preserves these properties under fairly weak conditions. Moreover the integrated Petri net belongs to the same Petri net class. The results obtained in this paper are expected to shed light on the design, management and control of large scale manufacturing systems where complexity problems are bound to rise and can be dealt with from the point of view of modular modelling and integration.

In this paper, we use event graphs, a paricular type of Petri nets, to evaluate job-shops when manufacturing times are random variables and the control is defined as the sequence of product types at the entrance of each machine. Under very general assumptions, we prove that the cycle time of the system converges in probability to a constant and asymptotically tends in distribution to a normal distribution whose standard deviation tends to zero. We also provide a lower bound of the main cycle time. We finally derive from the previous results a heuristic algorithm which leads to a near optimal solution of the problem (an optimal solution being the minimal work-in-process which allows the maximal productivity, i.e. the minimal cycle time, knowing the control).