Algorithm of realization of ecological-mathematical problems of optimization of agricultural production in conditions of uncertainty

Abstract

The article describes groups of mathematical models for the optimisation of agricultural production which take into account the natural and anthropogenic damage to the environment, depending on the type of reclamation work, the uncertainty of the parameters, the origin of the external influence on the soil and water, and the content of the optimality criterion. An algorithm for solving the mathematical ecology problems of linear programming in a situation of uncertainty is suggested. The article determines mathematical ecology problems for the optimisation of agricultural production with deterministic, interval, and random parameters. To solve these problems we used application software packages together with the Monte-Carlo method. As a result, we obtained a set of optimal solutions for uncertain situations. The parameters were randomly modelled in the given variation intervals. Random variables were modelled based on the probability distribution law. By solving the problem with interval parameters we obtained the lower, upper, and median estimates of the objective function and the corresponding optimum plans. When implementing the models with random parameters, the dependences of the values of the optimality criterion on the probabilities of the parameters were determined. The analytical value of this criterion corresponds to the optimum plan. The suggested algorithm was implemented by an agricultural enterprise which operates on lands, some of which are subject to erosion and soil and water pollution. The results obtained when using the described mathematical models, which take into account the damage caused by the negative impact of natural and anthropogenic factors, namely soil erosion and land pollution, demonstrated that these models can be used to manage the agricultural production while minimizing the environmental damage.