Development of Top-down and Bottom-up Methodology Using Risk Functions for Systems with Multiplicity of Solutions

Zagorodny, A., Bogdanov, V., Ermoliev, Y., & Kulyk, M. (2023). Development of Top-down and Bottom-up Methodology Using Risk Functions for Systems with Multiplicity of Solutions. In: Systems, Decision and Control in Energy IV. Eds. Zaporozhets, A., pp. 3-23 Springer. 10.1007/978-3-031-22464-5_1.

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Abstract

There is a wide and important class of objects and systems with a hierarchical structure, which by their nature should be applied methodology TOP-DOWN–BOTTOM-UP (TD–BU), but in the current state of the most important problems of its study can not be solved existing models TD–BU. This class of tasks, first of all, includes forecasting the production of almost all types of products and services, demand for them in all sectors of the economy, social sphere and in the country as a whole, ensuring unambiguous performance indicators of upper and lower levels of government, banks, trade, transport networks, etc. For these systems, the key problem is the discrepancy between the corresponding indicators for the upper and their sum for the lower hierarchical levels. The problem of discrepancy was solved by developing special analytical dependencies for indicators of both upper and lower levels. However, the solution of the problem of discrepancy led to the problem of ambiguity of solutions, these analytical solutions have n − 1 (n—dimension of the system) modification, each of which provides the necessary equality of indicators of these levels. There was a problem of choosing the best solution from many. The problem of building a mathematical model and a corresponding method that would simultaneously solve the problems of both divergence and ambiguity was overcome in the work by combining the TD–BU methodology with the analytical apparatus of general risk theory. At the same time, using the TD–BU methodology, analytical dependences were obtained that provide a solution to the problem of discrepancy. Based on these dependencies, in combination with the apparatus of risk theory, solutions were determined for both levels that have zero risks. As a function of the risk function, the functionality of the classical least squares method was used, which (method) gives better results (zero risks) for this problem in comparison with others. As a result of combining TD–BU methodology and general risk theory, a comprehensive method of researching a new, important class of problems in the field of TD–BU problems was synthesized.

Item Type:	Book Section
Uncontrolled Keywords:	Bottom-up; Discrepancies; Hierarchy; Risk theory; Risks; TD–BU; Top-down
Research Programs:	Advancing Systems Analysis (ASA) Advancing Systems Analysis (ASA) > Cooperation and Transformative Governance (CAT) Advancing Systems Analysis (ASA) > Exploratory Modeling of Human-natural Systems (EM)
Depositing User:	Luke Kirwan
Date Deposited:	11 Apr 2023 09:27
Last Modified:	11 Apr 2023 09:27
URI:	https://pure.iiasa.ac.at/18711

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