Elaboration of an Algorithm for Solving Hierarchical Inverse Problems in Applied Economics

Abstract

One of the key tools in an organization’s performance management is the goal tree, which is used for solving both direct and inverse problems. This research deals with goal setting based on a model of the future by presenting the goal and subgoal in the form of concrete quantitative and qualitative characteristics and stepwise formation of factors. A stepwise solution to a factor generation problem is considered on the basis of mathematical symmetry. This paper displays an algorithm for solving hierarchical inverse problems with constraints, which is based on recursively traversing the vertices that constitute the separate characteristics. Iterative methods, modified for the case of nonlinear models and the calculation of constraints, were used to generate solutions to the subproblems. To realize the algorithm, the object-oriented architecture, which simplifies the creation and modification of software, was elaborated. Computational experiments with five types of models were conducted, and the solution to a problem related to fast-food restaurant profit generation was reviewed. The metrics of remoteness from set values and t-statistics were calculated for the purpose of testing the received results, and solutions to the subproblems, with the help of a mathematical package using optimization models and a method of inverse calculations, were also provided. The results of computational experiments speak to the compliance of the received results with set constraints and the solution of separate subproblems with the usage of the mathematical package. The cases with the highest solution accuracy reached are specified.