Abstract
This paper presents a comprehensive model of an organization and formalizing it mathematically, shows theoretical results. Due to the space limit the proofs of the results are not included. The comprehensive model is given by specialization of the hierarchical complex model of the mathematical general systems theory. In particular, an organization is defined as a contrived system with a goal called organizational goal and is modelled consisting of three management layers, operational, organizational and institutional. The theoretical results are derived for three aspects of the model. First, the hierarchical structure is formalized as a tree of the graph theory so that a mathematical theory of an organization chart is presented. Second, the coordination function of the organizational layer is investigated so that a condition when harmonization of the operational layer implies realization of the organizational goal is given. Finally, the adaptive function of the institutional layer is studied in terms of the variety concept of Ashby and showed in a formal way that a sustaining organization should satisfy the variety matching principle against the environmental change.
