Simulation Petri Net Model in the Tasks of Operational Control of Discrete Production

Abstract

The presented article describes the approach to solving the task of discrete production control based on the reference imitation model. A discrete production system, represented by typical technological equipment, was chosen as the object of research. The  simulation  model uses the mathematical apparatus of temporary Petri nets. A method  for automated  synthesis of ready-to-use production models has been formed and tested. The  method  is based on the idea of synthesizing a production process model  from models  of typical  technological  processes. In the practice of applying Petri nets, the complexity  of developing, subsequent  interpretation  of models, and,  consequently, making  changes are factors that  significantly  hinder  their practical use. A new way of influencing the criterion is proposed by setting different incidence  ratios in the Petri net. In the structure of the incidence matrix, the invariable and variable parts are distinguished.  A method for specifying the structure of the variable part through the vector of parameters is described, which made it possible to use a metaheuristic  algorithm for finding its best structure. The problem of optimal production planning defined for the approach described above is formulated.  The bioinspired algorithm of jumping frogs is adapted  to the search for the best network structure for a given optimality criterion. Changes in the specified algorithm made  it possible to reduce the number  of search steps, as well as work with discrete type parameters. In the  process of solving,  the  most  popular  optimality  criterion  was used.  The  obtained  theoretical  results are  within  the framework  of the optimization-simulation approach  and  are its logical development.  The  developed  approach to solving the problem of optimal production control develops the theory of Petri nets, makes  it more suitable for modeling complex systems with a branched  structure and a large number of interconnections.  On the basis of the developed theoretical provisions, a test example  is presented that characterizes  the effect of their application.  Recommendations for the practical use of the proposed approach in the sense of minimizing  the time for making  managerial  decisions with the required accuracy  are determined.