Digital Transformation of Optimal Decision-making in Economic and Engineering Systems Based on the Theory and Methods of Vector Optimization

Abstract

Objective: The purpose of the work is to analyze, study the processes of digital transformation and make optimal decisions in economic and engineering systems based on the theories and methods of vector optimization. Methods: Methods for studying the processes of digital transformation of economic and engineering systems are based on the author's theory of vector optimization, which is represented by: axiomatics and optimality principles that show how one solution is better than another. On the basis of the principles of optimality, constructive methods for solving vector problems have been built, firstly, with equivalent criteria, and, secondly, with a given priority of the criterion: https://rdcu.be/bhZ8i (Springer Nature's "Vector optimization with equivalent and priority criteria" is distributed free of charge.) The paper presents that the problem of accepting the optimal process is carried out as a result of the digital transformation of the initial (statistical, experimental) data into vector problems in optimization, which represents a mathematical model of economic and engineering systems. Depending on the number and type of criteria, we solve problems with a vector of criteria, each component of which is directed to the maximum, and with a vector of criteria, each component of which is aimed at a minimum, in aggregate. Results: The result of the study is the practical orientation of digital transformation, which is shown in the computer-aided design of economic and engineering systems based on vector optimization. For this purpose, software for solving vector problems of linear and nonlinear programming has been developed. Linear vector problems are used in economic systems (forecasting, planning). Software for solving vector problems of nonlinear programming are used digital transformation of optimal decision-making in engineering problems. Conclusion: In conclusion, numerical examples in the field of economic systems are presented by the digital transformation of optimal decision-making in the development of the company. When making optimal decisions in engineering systems, the following has been developed: the construction of initial data (technical task) for modeling; transformation of a mathematical model under uncertainty into a model under conditions of certainty; making an optimal decision with equivalent criteria; making the optimal decision with a given priority criterion