• M. Karpenko O.M. Beketov National University of Urban Economy in Kharkiv
  • O. Stelma O.M. Beketov National University of Urban Economy in Kharkiv
Keywords: management, resources, processes, model, resource allocation, aggregation, disaggregation, mathematical programming, optimization


The article proposes a mathematical model of the hierarchical system of volume-dynamic resource allocation. The model describes resource consumption processes in multi-layered systems and allows us to view the management of such systems from a single perspective, to reflect the interrelationship of decisions formed at different levels of the hierarchy.

According to the proposed model, a production (or business) system is considered as a large dynamic resource allocation system that is characterized by the interaction of three components: processes, resources, and time (R, P, and T.). Each of these components is represented by many lower-level elements with a defined ratio of a partial order, which sets the structure of the corresponding systems. The article proposes the way of description and features of the system of resources, processes and time, rules of aggregation, and disaggregation taking into account the structure of R, P, and T systems.

On the basis of the described models, a description of the production system at the lower level in the form of a binary function  π0 , as well as procedures for the formation of appropriate descriptions for arbitrary levels of the hierarchy in the form of a set of tetra relations πi. An algorithm for the formation of the solution π0 , as well as procedures for its transformation to the model of an arbitrary level, is proposed.

The use of formal methods to describe the procedures of resource allocation at different levels of the hierarchy allows building a single database, to develop a structured and compact system of requests for information in the formation of management decisions.

In such a system, data for processing queries are represented by a tuple of three elements Kin (levels of input aggregation by process and time resources), the basic solution πб, a set of elements R, P, T of the corresponding level, a tuple Kout (three levels of output aggregation).

Depending on the Kin and Kout, values, the system handles the πб base solution using either aggregation or disaggregation procedures, resulting in a final result.

Author Biographies

M. Karpenko, O.M. Beketov National University of Urban Economy in Kharkiv

Associate Professor Departament

O. Stelma, O.M. Beketov National University of Urban Economy in Kharkiv

senior lecturer Departament


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How to Cite
KarpenkoM., & StelmaO. (2020). RESOURCE ALLOCATION MODELS IN HIERARCHICAL MANAGEMENT SYSTEMS. Municipal Economy of Cities, 1(154), 120-125. Retrieved from