Issues of generation a Petri net based simulation model in solving the task of production planning

Abstract

The presented article presents a description of a systematic approach to solving the task of operational scheduling of production based on simulation modeling with timed Petri nets. The proposed approach is based on the idea of automated synthesis of network models of discrete production systems and the use of an optimization-simulation approach to find the best production plan. Based on the developed theoretical provisions, a test example is presented that characterizes the effect of their application. A typical production system of mechanical processing was chosen as the object of study. The formation of a general simulation model of the production process is carried out from models of the main types of technological processes, which greatly simplifies and speeds up this process. In the practice of using Petri nets, the complexity of developing models, interpreting them, and making changes are factors that significantly limit their use. In the process of solving the task of preliminary production planning, a new way of influencing the optimality criterion is defined and proposed for application by setting various incidence ratios in the Petri net. The optimization procedure is reduced to finding the best structure of the incidence matrix. In the structure of the incidence matrix, an unchanging and a changing part are distinguished. The possibility of parametrization of the variable part has been implemented, which made it possible to formulate the optimization problem. An approach to solving such a problem based on a combination of the method of coordinate-wise descent and enumeration has been tested. He allowed to significantly reduce the search space, as well as to find a production plan for a given value of the objective function. The developed method for solving the problem of optimal production planning develops the theory of Petri nets, makes it more suitable for modeling complex systems with a branched structure and a large number of interconnections, contains a new approach to optimizing processes in operational scheduling. The disadvantage is the dependence of the results of solving the problem on the correct interpretation of the states of the model and, accordingly, the direction of the gradient of the function.