Sale-Manrubia model with fuzzy characteristics for logistics companies

The article analyzes the stages of the life cycle of logistics systems, defines the basic principles of population ecology as one of the modern concepts of the formation of logistics organizations. To study the system, which is a set of logistics companies, a modification of the evolutionary model of the Sale-Manrubia of interspecific interaction with a cooperative matrix, dynamically changing during the model time, has been developed. This system is complex, stochastic. To consider these factors of the model, the use of fuzzy sets defining fuzzy relationships with their membership functions for simulation modeling of system dynamics is proposed. When forming a vector for assessing the economic state of a system consisting of elements representing a set of logistics companies, it is proposed to use fuzzy numbers with a piecewise defined membership function. A simulation model of the life cycle of a set of logistics systems was built, which determines the number of companies that continue to operate, as well as the number of organizations that have ceased their activities in each unit of the model time. In the work, using the Python programming language, an experiment was carried out to analyze the evolution of a system whose activity is determined only by a set of natural factors, as well as an experiment with the imposition of additional external conditions, the analysis of the results obtained is carried out.