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The majority of studies in General System Theory do not consider any specific configuration of relations between elements. One such configuration is hierarchy which exists in many aspects of reality. A quantitative approach to the representation of hierarchies, as opposed to a qualitative approach, is described. Some properties of the mathematical model of various hierarchies are examined and real‐life examples are presented.

The paper introduces a definition of the resource allocation system (RAS), using the Mesarovic goal‐seeking system description method. A RAS is represented by sets of resources, subjects, results, decisions and values, as well as outcome and performance functions. This concept can be considered as a generalization of existing approaches such as, e.g. “complex‐of‐operations” systems. For single‐objective and multi‐objective cases basic system properties are analysed. For continuous and discrete types of RAS's conditions allowing to decide the questions of their existence and uniqueness are derived. The final part of the paper deals with the mixed and non‐deterministic resource allocation systems. Possible extensions of the obtained results are also outlined.