Mathematical modeling and optimization of complexly structured objects

This work is devoted to the formalized description of mathematical models and optimization problems of complex-structured objects. As an object of modeling, we consider production systems with a complex structure, including the interaction of subsystems of two main types: "processing" and "assembly". An analysis of the specifics of the functioning of complex-structured production systems is presented. A method is proposed for the formalized description of mathematical models of technological processes of processing and assembly based on the theory of queuing using the apparatus of simulation. The fundamental difference between the mathematical description of a subsystem of the "assembly" type and a subsystem of the "processing" type is that to complete the assembly process, a given number of applications from different streams must be received at the input of the device, which means that all the necessary components are available. This feature limits the use of standard methods of queuing theory, since there are no functional dependencies for the analytical description of processes of the "assembly" type. For this reason, it becomes necessary to develop simulation models of complexly structured objects. At the same time, the mathematical model of the production system takes into account the random nature of the distribution of the parameters of objects and the probability of refusals in servicing applications due to overflow of the waiting queue. The optimization problem of finding the optimal structure of the system is considered under restrictions on a given number of parts obtained within a certain period of time, as well as on the maximum capacity of the input storage and the volume of production resources.

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