Modeling of Transport and Logistics Systems and the Study of the Structural Stability

Abstract

The structural stability of the system to external influences is an important parameter of the transport and logistics task. In modern literature, the concept of structural stability is defined as applied to each individual problem, as a result of which there are difficulties in applying the developed methods to new problems. The paper describes assessing the stability of the functioning of transport and logistics systems. The methodological base of the research includes the theory of optimal control and multicriteria optimization; elements of graph theory are used as modeling tools, as well as numerical analysis to evaluate stability coefficients. A list of actions on the system in the form of elementary events over graphs, including their superposition, is proposed. There was proposed the concept of structural destruction of a graph that implies a partition of the graph into disconnected components. The formulation of the combined transport and logistics problem —  the search for flows and routes. The authors propose an efficiency coefficient for comparing the obtained solutions, as well as a stability coefficient for assessing the influence of structural changes in the graph on the solution of the problem. A computer simulation of structural destruction on test data sets was carried out. As a result of experiments series, the distribution of a special coefficient for elementary fracture processes was established, as well as an interval of permissible values   corresponding to a stable state of the system. The theoretical significance of the study lies in the possibility of using the results obtained at the stage of designing transport and logistics networks. From a practical point of view, the proposed tools can be used to assess the stability of the functioning of existing transport and logistics systems.