Analytical management models in the transport complex resource allocation system

Background. The management of resource allocation in a transport complex is significantly complicated by the presence of uncertain informational states, a characteristic feature of such complex, multi-level systems. Traditional management models often prove inadequate as they fail to fully account for this stochastic uncertainty and the ergatic nature of the system, which involves interaction between heterogeneous technical elements and human collectives with potentially conflicting goals. This necessitates the development of specialized analytical models based on robust mathematical apparatuses, such as entropy theory, to formalize decision-making processes and increase the efficiency of resource distribution under conditions of incomplete information.

Purpose. To develop analytical models for managing the resource allocation system in a transport complex, based on the principles of entropy measurement and the theory of decision-making under uncertainty, aimed at formalizing the procedures for evaluating efficiency and selecting optimal solutions.

Materials and methods. The study employs the theoretical foundations of K. Shannon’s entropy to quantify uncertainty within the system. The core methodological tool is the model for researching second-order uncertainty functions, designed for systems with discrete states, such as resource allocation systems. To form a system of probability distributions for informational states, a model based on Fishburn’s estimates is used. The mathematical apparatus includes constructing matrices of evaluation functionals (2) for various decision options and criteria. The analysis of solution efficiency is conducted using a graphical model for a set of mutually exclusive options, particularly for, and for a priori probability distributions.

Results. A graphical model for determining efficiency within the system was developed and presented, illustrating the solution space for a given preference of a priori probabilities. The application of the model based on Fishburn’s estimates was shown to solve the primary task of reducing uncertainty. However, it was established that this model alone does not identify the probability characteristics corresponding to the maximum of the evaluation functional across the entire set of external environment states. To address this, the model was supplemented with a targeted condition (4). Furthermore, the fundamental differences between the method of Fishburn’s estimates and alternative methods – the zoning method by the principle of dominance of probabilities of possible states of the external environment (DPPSE) and the zoning method by the principle of maintaining the hierarchical ratio of probabilities of possible states of the external environment (MHRPSE) – were demonstrated. A comparative analysis of these methods was conducted using a hypothetical example.