MATHEMATICAL MODELING AND ALLOCATION PROBLEM OF MANUFACTURING SYSTEMS: A REVIEW

ABSTRACT

The majority of firms consider maintenance to be an important component of the overall production environment. As a result of automation advancements, the complexity of the systems involved has raised the necessity of machine reliability. This is especially true in the process industry, which is characterised by high-priced, specialized equipment and stringent environmental standards. As profit margins compress, a solid maintenance planning and management approach is increasingly required, especially for discrete event systems (DES). The DES development is defined by the instantaneous occurrence of events at possibly unknown and/or unexpected time intervals (for example, in communication and transportation systems, computer systems, and industrial systems) (e.g., communication and transport systems, computer systems, and manufacturing systems). These systems are now so complex that traditional techniques of monitoring and scheduling are no longer sufficient to ensure their proper operation. Wonham and Remade came up with the notion of supervising DES. These writers introduced ideas like those employed in the theory of automated control of continuous systems thanks to formal languages and automata. As a result, the fictitious supervisor ensures that the desired legal conduct occurs. In fact, it has been demonstrated that Petri nets (PNs) outperform automata in modelling DES with synchronization and parallelism. Furthermore, PNs are a superior solution to deal with control issues that are defined by system state requirements. They are an excellent tool for analyzing industrial systems since they can be utilized as models and have mathematical qualities.

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