AMPL-Implementation for Models of Structural and Technological Changes

Introduction. In the 1920s and 1930s, economically developed countries were engulfed in a period of global economic instability characterized by declining industrial production, widespread unemployment, overproduction, falling prices, and other challenges. This turmoil underscored the urgent need for state regulation of economic processes occurring within their territories. During this period, various mechanisms of influence – both administrative and economic – were devised and implemented to steer economic activity. Among these regulatory models was W. Leontief's pioneering “input-output” model, which provided a comprehensive description of the economy of an entire country or individual regions. For this groundbreaking work, Leontief was awarded the Nobel Prize in Economics in 1973. Our scientists, including those affiliated with the Institute of Cybernetics, made significant contributions to advancing and applying the theory of inter-industry balance. Notably, M.V. Mikhalevich focused extensively on studying and developing Leontief’s inverse models. These inverse models play a crucial role in production planning by determining the necessary gross output to meet a specified aggregated demand. They also facilitate the analysis of how changes in production technology affect output volumes. Overall, the inverse models serve as a key instrument in inter-sectoral balance by linking final demand to gross production through the inverse matrix of the total cost coefficients. The purpose of the research is to study the modification of Leontief’s classical “input-output” model through its optimization-based extension developed by M.V. Mikhalevich, incorporating structural and technological shifts, institutional changes, wage levels, and profit shares across various industries. This study seeks to justify the applicability of the modified model for strategic planning of inter-sectoral proportions within an economic policy framework focused on growth without cost inflation. Additionally, it involves the development of AMPL implementations to solve optimization problems related to structural and technological changes in the inter-sectoral balance, utilizing the AMPL (A Modeling Language for Mathematical Programming) through solver SNOPT and BARON on server NEOS. Results. The AMPL implementation has been developed to solve optimization problems of structural and technological changes in the inter-industry balance. The effectiveness of solving test problems using modern versions of solvers on the NEOS server has been investigated. Conclusions. The inter-industry models for planning structural and technological changes discussed in the article give rise to complex optimization problems characterized by non-convex objective functions and nonlinear constraints. In order to address these challenges an AMPL implementation of the optimization models for structural and technological changes in the inter-industry balance was developed. Computational results obtained with the SNOPT and BARON solvers on the NEOS server demonstrated the effectiveness of this approach in solving specialized problems. Keywords: modified ‘input-output’ models, modelling of inter-industry balance, aggregated demand, optimization, AMPL-implementation, NEOS.