Mathematical modelling of advanced engineering technologies for smart enterprises: an overview of approaches and ways of implementation

The key features of the concept of Industry 4.0 development at the enterprises of machine-building industry were singled out. The analysis of mathematical models on classes of typical tasks for use at the construction of smart enterprises in the machine-building industry were carried out. It was determined, that in the process of ensuring the innovative development of machine-building enterprises within the Industry 4.0 framework it is necessary to use mathematical models, appropriate to machine vision technologies, robotic equipment, automated and intelligent production and control systems within the framework of enterprises’ cyberphysical systems.Such cyberphysical systems should be connected to the outside world through sensors and actuators, receiving data streams from the physical world, establishing and continuously updating the virtual twin of the physical world and including the possibility of interaction in reality according to instructions from the virtual sphere. This will allow ensuring the possibility of joint work, adaptation and development of all enterprise’s systems to improve working conditions, product quality, reduce labour requirements and increase the efficiency of manufacturing process of machine-building enterprises. The introduction of the above classes of mathematical models within the framework of cyberphysical systems must be carried out according to innovations in machine-building enterprises, which will ensure the automation of manual labour, the renewal of the already used innovative technologies and their unification in a single information space. The resulted models demand adaptation and the further development according to those innovative decisions, which will define a management of specific machine-building enterprises, depending on the specificity of the enterprise.Recommendations were given to the heads of machine-building enterprises on the use of mathematical models in the process of introducing the concept of smart-enterprises in the Ukrainian machine-building industry. Prospective directions of research were outlined in the paper.