This paper proposes an optimal solution to large-scale Flexible Manufacturing System (FMS) scheduling problems under availability constraints based on Timed Petri Nets (TPNs). First a decomposition method of TPNs is proposed, then a mathematical model is derived based on their properties. The mathematical model is built to determine the optimal firing sequence of TPN transitions to minimize the total manufacturing time. The resulting firing sequence of TPN transitions is used to generate the manufacturing system supervisor operated by TPN and digital controllers. Several numerical examples and comparative studies are provided in this paper in order to prove the new approach’s efficiency.

This paper proposes an optimal scheduling model under production and maintenance constraints for a real case of a discrete event system. The intent was to use the rich mathematical theory and algorithms of optimization in the study of this important class of systems. The current study detailed firstly a new approach for mapping a simulation event relationship graph into a mixed-integer program, with a flexible workshop real case. Several other potential applications of the mathematical model are examined, thanks to the model constraints flexibility characteristics, including a general case of a manufacturing system for optimal resource scheduling, an application on the case of hospital beds’ management. The model extension could be also interesting for other applications like museum systems or the case of big data in complex and social networks.

The k-out-of-N system is widely applied in several industrial systems. This structure is a part of fault-tolerant systems for which both parallel and series systems are special cases. Because of the importance of industrial systems reliability determination for production and maintenance management purposes, a number of techniques and methods are incorporated to formulate and estimate its analytic expression. In this paper, an algorithm is put forward for a k-out-of-N system with identical components under information about the influence factors that affect the system efficiency. The developed approach is applied in the case of the Pitot sensors system. However, the algorithm application could be generalized for any device which during a mission is subject to environmental and operational factors that affect its degradation process.