Theoretical justification of the model of search for optimal solutions in complex resource management systems

Background. The relevance of the article is determined by the complexity and dynamism of resource allocation systems (RR systems), which include numerous time-varying elements, both within the system and in the external environment, and require organization into hierarchical subsystems. The uncertainty of the informational component and influencing factors necessitates the use of effective analytical tools based on decision theory under uncertainty for the objective assessment and management of such systems.

Purpose.  To develop a set of mathematical models for finding optimal solutions in complex resource management systems under uncertainty, required for designing resource allocation structures.

Materials and methods. The study employs a combination of mathematical modeling, decision theory, and optimization techniques to address multicriteria problems in complex systems, particularly in resource allocation systems (RR systems) within transport complexes. The classical decision-making approach involves selecting the optimal solution from a set of alternatives formalized through mathematical models representing the problem situation. For deterministic optimization tasks, the model includes a set of feasible solutions XX and a vector criterion f(x)f(x) to evaluate alternatives. In multicriteria optimization under uncertainty, the lack of a unified mathematical framework requires the use of diverse methods such as combinatorics, graph theory, heuristics, linear and dynamic programming, and search algorithms. The research highlights the challenges of applying these methods in complex systems, where external and internal uncertainties complicate the formulation of constraints and the integration of qualitative and quantitative criteria. The transformation of multicriteria problems into single-criterion formulations with constraints is also explored, emphasizing limitations imposed by unpredictable external factors and the need for experimental validation in complex transport systems.

Results. The main challenge in building effective resource allocation systems (RR systems) lies in the large number of qualitative criteria, which are difficult to formalize and integrate into mathematical models. Qualitative criteria, such as scoring or expert judgments, require the use of ordinal scales, where only monotonic transformations are permissible, limiting quantitative comparison. To address multicriteria problems, methods based on binary relations and value functions are proposed, enabling the formalization of preferences and ranking of alternatives. These approaches, including linear aggregations and utility functions, enhance the objectivity of decisions in complex systems, such as transport complexes, where both quantitative and qualitative criteria are present. However, their application requires careful analysis and adaptation to the specifics of the tasks.