Лукацкий А.М., Дубынин Е.В.

ИНФОРМАЦИОННОЕ ПРЕДСТАВЛЕНИЕ АЛГОРИТМОВ БАЛАНСОВЫХ МОДЕЛЕЙ

Резюме: Рассматривается проблема построения структуры на множестве алгоритмов моделей балансового типа. В известных разработках такого типа моделей структуризация применялась только к данным. Для решения этой проблемы используется ранее предложенная табличная форма описания полилинейной модели. Конструкция иллюстрируется на примере модели межотраслевого баланса Леонтьева. Также рассмотрены ее обобщения в аспекте экологических проблем сокращения вредных выбросов, например, выбросов CO2.

Ключевые слова: балансовые модели, полилинейное программирование, мономы, непроцедурное описание алгоритмов, табличная форма описания алгоритмов, матрица удельных затрат, модель Леонтьева, экологическая модель.

A.M. Lukatskii, E.V. Dubynin

INFORMATION REPRESENTATION OF ALGORITMS OF BALANCE MODELS

Summary: The problem of constructing a structure on a set of algorithms of balance-type models is considered. Balance-type models arise in many subject areas. The main tool for their study is multilinear programming. Informatization in these models usually refers to data structuring. An approach was previously proposed that allows describing a multilinear model as a single summary table. This approach makes it possible to structure not only data, but also algorithms for a class of multilinear models. In known developments of this type of models, structuring was applied only to data. To solve this problem, the previously proposed tabular form of describing a multilinear model is used. The form of describing a multilinear model is a summary table in which the rows form the model variables, the multilinear constraints of the model, the criterion of the model, the columns form the monomials of the model and the closing column of the free terms of the model. There is an ambiguity associated with a possible permutation of monomials. To avoid this, ordering is introduced on the set of monomials of a given multilinear model. A standardized representation of the range constraints of the model is also used. The software package that performs the necessary calculations is implemented in the Visual Basic language. EXCEL is used to prepare and edit the table description of the model, directly called from the leading program of the Visual Basic package. The design is illustrated using the example of the Leontiev inter-industry balance model and its various modifications. In particular, a variant of the balance model for environmental problems is considered in the aspect of the task of reducing harmful emissions into the atmosphere, for example, CO2 emissions.

Keywords: balance models, multilinear programming, non-linear optimization, monomials, non-procedural description of algorithms, tabular form of description of algorithms, screen editor, matrix of specific material costs, Leontiev model, ecological model.

DOI: 10.34219/2078-8320-2025-16-3-12-19