A model of centralized supply chains with independent behavior of separate nodes

This paper proposes a model of supply chains combining a centralized structure with independent behavior of individual nodes. The peculiarity of this model is that it finds application in the modeling of decentralized big data systems, which have become widespread recently. To build the model, existing architectures and approaches, in particular from the theory of automatic control, were considered. These approaches made possible to choose the most appropriate approach to represent the big data network dynamics and, accordingly, its behavior in time. In the proposed model, this is achieved by using a centralized approach to the construction of network architecture and modeling the behavior of network nodes and individual chains with a model predictive control. As part of the study, the problem of the three-dimensional forecasting horizon is posed, which consists in the need to describe the dynamics in three coordinates, which are responsible for the spread of the solution in depth, width and time, which clearly affects the complexity and the possibility of its solution in an acceptable time. In order to solve this problem, we propose to split the model into separate coordinates, which allows solving the spatio-temporal representation of nodes and, accordingly, the state space model by separate systems of dynamics equations - in space and time. To test the model, an experimental implementation was created, which implements the tasks of modeling network dynamics of the model with the involvement of neuro-optimal regulators, based on Pontryagin’s principal of maximum - for temporal dynamics and a predictive control model for spatial network dynamics, respectively. As a result of the experimental tests of the model, an assessment of the adequacy of the model was given and general recommendations for the development of supply chain models were given, as well as possible potential advantages of using neuro-optimal regulators compared to the predictive control model were indicated.