Application of the Data Envelopment Analysis method to assess the efficiency of social and economic systems

Abstract


 
 
 
 The article deals with the relevant scientific and practical task – assessing the effectiveness of various types of existing systems by methods of mathematical modeling. In particular, the research investigates the efficiency of functioning of social and economic systems using nonparametric methods of mathematical modeling. For the verification of the results, the research uses the Data Envelopment Analysis (DEA), which is a modern method based on the creation of the efficiency limit. The article considers in detail the theoretical foundations of the DEA method, which is based on the problems of mathematical programming, namely, the problems of linear programming. The article presents main theoretical models of this nonparametric method for input and output and analyzes the technique of its application. As an example of the practical use of this method, the research suggests the analysis of the demographic situation in the regions of Ukraine based on the main demographic indicators – mortality and birth rate for a certain estimated period. In the process of analyzing the results of modeling, the research has identified two groups of regions – one with the most effective indicators of the demographic situation, and the second – with the least effective indicators. The selected groups of regions are invariant when using different models of the method. The calculations obtained in the process of modeling confirm the real condition of the demographic situation in the regions of Ukraine, which is characterized by the actual statistical indicators of the population in regions. For each region, the research has established reference regions, which in their structure are similar to the structure of indicators of given regions and are a certain model and reference point for the practical improvement of the demographic situation. The recommended values of indicators that set the direction of improving the demographic situation in each specific region of Ukraine have also been calculated during the research.