Growth models with saturation in the problem of parametric programming as applied to agricultural production

Yaroslav M. Ivanyo, Sofia A. Petrova, Valentina V. Tsyrenzhapova

Irkutsk State Agricultural University named after A.A. Ezhevsky

The paper presents the results of applying growth models with saturation to solve prognostic problems and optimize the production of agricultural products based on parametric programming models. The problems of constructing asymptotic and logistic models for medium-term forecasting of agricultural production indicators were solved. The results of modeling by asymptotic and logistic models were compared; Parametric programming problems were created and applied using saturation growth models to optimize the production of agricultural products. At the same time, methods of mathematical modeling, forecasting, probability theory and mathematical statistics and parametric programming were used. As a result, multilevel asymptotic and logistic models are proposed for predicting the production and economic indicators of agricultural production using the example of grain crop yields. The upper level (peak trend) characterizes favorable conditions for the activity of
an agricultural producer, and the lower level (trough trend) describes unfavorable situations for obtaining products. It is shown that growth models with saturation have an advantage in accuracy and significance relative to linear and non-linear trend models that are not limited by an upper bound. In addition, such models are less limited by the amount of data-dependent lead time. When comparing the asymptotic and logistic models, their advantages and disadvantages are highlighted. The developed mathematical models are implemented on real objects. A multilevel model of parametric programming using a logistic function to optimize the production of agricultural products is proposed. Forecasts of crop yields and optimal plans for production until 2024 for favorable, average and unfavorable situations are given. The proposed algorithm for obtaining optimal solutions is aimed at improving the management of agricultural production.

asymptotic model, logistic model, parametric programming, forecasting, agricultural production