Spatio-temporal combinatorics of resource flows conservation and reduction of risks in conditions of uncertainty of the external environment
Authors: Petrushenko N. 
Published: August 2022

Management of non-structured and weakly structured systems for the impacts of the dy-namic changes is not have a developed methodological basis. Management decisions are made on the basis of stochastic recommendations based on the results of existing experience with ex-trapolation to future trends without taking into account risks and possible faults. It is not neces-sary to introduce a great lack of value and inadequacy of acceptance of solutions, related to a wide range of criteria for assessments, without a wide range of factors, and highly direct indicators. When modeling management in the conditions of uncertainties of the environment, which are constantly changing, a large variety of source data is possible. The development of methods and models to support decision-making in terms of geo-graphically distributed processes is a very complex and non-trivial task. All interactions take place within a territorially distributed system. Such model can be built on a continuous basis, but it cannot be used to analyze spatial areas in real time. To reduce the level of risk and the results of possible losses, it is necessary to carefully study the possible carriers of risk, taking into account their individual characteristics, as well as market participants with the development of their original methods of risk management. The initial information on identifying problems of unstable market development is contained in the ratio of internal and external destabilizing factors. Information as an integral part of doing business plays a key role in reducing the risks that ensure the commercialization of proposals. Decision-making in a complex system is that from the available set of acceptable con-trols, it is necessary to identify several options that are the best. The rule that establishes the advantage in many solutions is the principle of optimality. When solving problems of optimal control as a set of valid alternatives use the combinatorics of acceptable management. An important difference between the construction of mathematical models of complex systems is that the modeling is not above the global function and the allocation of the main parts, and below, with the construction of models of individual processes and lower hierar-chical levels. Larger modules and the system as a whole are modeled on the basis of reasona-ble complexity. Combinatorics is directly related to simulation modeling, when it is impossible to apply mathematical solutions to problems in conditions of uncertainty. A perspective area of analysis and management of development under conditions of un-certainty and ambiguity of the external environment is graph theory using the Ford-Falkerson algorithm. Control under the action of constantly changing environments with the onset of change is solved using the Ford-Falkerson algorithm. The network of possible movements is considered as a connected digraph. In the conditions of global risks it is not necessary to count only on one direction of de-velopment. The sudden emergence of restrictions forces to move to another branch of the network, for which the network provides additional vertical edges with their probabilities and bandwidth. As the change of the situation is unpredictable, the transition from one branch to another can occur spontaneously, which is reflected in the presence in the source network of inclined edges that have their own direction and their own weights. The introduction of the method of transition from one branch of the oriented network to another at the time of termination of its implementation due to the unpredictable influence of environmental factors ensures the distribution of risks between the components. The use of combinatorics of the proposed options for interactions in the state space, their implementation at different moments of iterations, their application with the synchronization of flow throughput can reduce the risks arising from the functioning of systems.