Using PDE Model and System Dynamics Model for Describing Multi-Operation Production Lines

Two classes of models for describing production flow lines are analyzed. The use of models of these classes for the design of highly efficient control systems of production lines, the technological route of which consists of a large number of technological operations, is analyzed. The division of the technological route into a large number of operations is caused by the development trend of modern production lines. Synchronization of production line equipment performance is provided by an accumulating buffer. A formalized description of the production line was used as a foundation for constructing equations for each models class. The common features of using each models class in the description of production systems, as well as the conditions for their application, are shown. The form of the system dynamics model and PDE model equations is substantiated. The assumption about a deterministic rate of processing parts and the absence of a time delay and feedback between the parameters of technological operations was made when deriving the equations. The use of generalized technological operations in the system dynamics model as a way to reduce the number of model equations is discussed. Two limiting transitions from the PDE model equations to the system dynamics equations are demonstrated. It is shown that the system dynamics equations are a special case of the PDE model equations, the result of the aggregation of production line parameters within the technological operation. The method for constructing level equations for the system dynamics model is substantiated. For production lines with a different number of operations, the solution to the problem of processing parts along a production line is presented. The comparative analysis of the solutions obtained using the system dynamics and PDE model equations is obtained