Raising the effectiveness of strategic management in conditions of high complexity and dynamic change of modern management systems requires the development of an appropriate mathematical toolkit. The task of raising effectiveness of strategic management is especially topical for heat supply enterprises of the Donetsk region, where operations have been complicated by a number of general system problems, and by the presence of substantial external challenges. At the same time, the question of using mathematical apparatus to raise the effectiveness of strategic management of enterprises in the sphere of residential-communal services appears not to have been widely studied. In this regard, the objective of this study is raising the effectiveness of strategic management of heat supply enterprises of the Donetsk region by developing a respective toolkit of mathematical modeling. To achieve the goal we have set, in this work we carried out an analysis of the viability of the system using the methodology proposed by S. Beer; we made an analysis of the elements of the market of heat supply, and also developed system dynamic models based on the approach of J.W. Forrester.
      As a result of our research, we discovered the basic problems influencing the viability of the system at the strategic level. It was established that the problems revealed are the consequence of the imperfections of the methodological base, including absence of timely information on the dynamics of the external environment, forecasting of the key parameters, a toolkit for making decisions, etc. For the purpose of finding a toolkit to improve the methodological base, we performed an analysis and forecast of the heat supply market in the Donetsk region as part of the external environment which exerts a very significant influence on the activity of the heat supply enterprises of the Donetsk region.
      In the course of this market analysis, we established that the offer of heat supply services is not constant and depends on the tariff setting costs. Due to this, we proposed an approach to forecasting tariff setting costs based on the methodology of A.G. Ivakhnenko but distinguished from that by the presence of a training sample and two test samples. In addition, in the course of analyzing the market we discovered new forms of demand for heat supply services – lost demand and unpaid demand. On the basis of the dependencies established, we built a model for forecasting the behavior of consumers of a heat supply company oriented to the level of marketing. With the help of this model, by means of supplements to it and modifications, we built a complex model of strategic management of heat supply enterprises of the Donetsk region allowing us to analyze the effectiveness of using one or another lever of strategic management on the basis of scenario analysis.