Construction of Algorithms For Solving the Inverse Problem When Using Indicators in Several Calculation Functions

This paper reports a solution to the inverse problem when using indicators in several calculation functions. Such problems arise during the formation of a multi-level scorecard; solving them makes it possible to determine the value of arguments in order to achieve the specified value of the resulting indicator of each level. Thus, the characteristics of an economic object can be defined in order to achieve the specified indicators of its functioning. Optimization models are given in the presence of various types of conditions for achieving the result. In contrast to existing methods, the approach based on building nonlinear programming models makes it possible to solve the inverse problem for the case where several indicators are used in different calculation functions. Algorithms for solving the inverse problem have been constructed, involving the transformation of constraints and the use of an iterative procedure based on inverse calculations. For the case of using coefficients of relative importance, two techniques of solving the problem have been considered: the formation of a single model for subtasks and the adjustment of the solution to subtasks while minimizing the sum of squares of argument changes. In comparison with the existing method, the proposed algorithms have made it possible to derive a solution with a greater correspondence of the changes in the arguments to the coefficients of relative importance. A solution to the inverse problem has been considered related to the formation of marginal profit of an enterprise in the presence of two points of sale and three types of products, as well as the joint formation of revenue and cost. The results of this study could prove useful to specialists in the field of decision-making in the economy and to developers of software decision support systems that include functions for solving inverse and optimization problems