Optimization of Decision Making when Controlling in a Digitalized System Based on a Multi-Stage Block Programming Procedure

The article discusses the process of formulating optimization models and a multi-stage decision-making procedure when managing the disaggregation of resources and volumes of activity in a digitalized system with a multi-layer structure. A general formulation of the control optimization problem is given within the framework of the theory of potential efficiency of complex systems. The possibility of transforming the optimal condition for the disaggregation of resources and activity volumes into related block linear programming problems is shown. Optimization models are formulated in which the extreme and boundary require­ments of the general formulation of the optimization problem are divided into blocks. In the problem of resource disaggregation, the first block optimization model is based on the requirements of the control environment, supplemented by transfer environments — resource and digital, the second on the requirements of the effective functioning of the activity environment. When disaggregating activity volumes, block optimization models are built in the reverse order. An algorithmic scheme for a multi-stage optimization procedure is proposed that ensures coordination of solutions at two levels: between the blocks of each disaggregation problem, and between tasks. The algorithms of the Dantzig-Wolff and Kornai-Litak methods have been modified by adapting to the peculiarities of decision-making problems when managing a digitalized system with a multilayer structure.