Overview of the Problems of Combinatory Optimization of Determination of Profitability of Agricultural Production and Methods of Their Solution

• Datum: 2021
• Hauptverfasser: Ємець, Олег, Черненко, Оксана, Чілікіна, Тетяна, Ольховська, Олена
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Кам'янець-Подільський національний університет імені Івана Огієнка 2021
• Online Zugang: http://mcm-math.kpnu.edu.ua/article/view/251165
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

The paper presents an overview of the works of Poltava researchers devoted to mathematical modeling of problems on Euclidean combinatorial sets. Statements of practical tasks of agricultural production are stated, namely: tasks on maintenance of the maximum profitability of production; tasks on the procedure for sowing plots to obtain maximum profitability; tasks on the procedure for sowing part of the plots for maximum profit, taking into account the application of fertilizers; the task of finding the optimal amount of crops grown by two farms (various modifications). Models of these problems in the form of Euclidean combinatorial optimization problems are constructed. The mathematical model of the problem of ensuring maximum profitability of production is reduced to a conditional problem with a fractional-linear objective function on a set of placements. The problem of the order of sowing plots to obtain maximum profitability is interpreted as a completely combinatorial problem on a set of permutations. For the problem of the order of sowing part of the plots for maximum profit, taking into account the application of fertilizers, a model was built in the form of a partially combinatorial problem on the permutable set. Problems for finding the optimal amount of cultivation of crops by two farms are considered as problems of combinatorial optimization of the game type with constraints that specify the set of permutations. Methods for solving them have been developed for the considered classes of problems. For a conditional problem with a fractional-linear objective function on a combinatorial set of placements, the linearization of the function and further application of the combinatorial clipping method are proposed. For conditional problems on vertex-set sets, a combinatorial clipping algorithm is constructed, both for fully and partially combinatorial problems, and a modified method of branches and boundaries is constructed. Game-type problems on permutable sets are solved by various iterative methods. Numerical experiments were performed for all types of problems, which confirmed the efficiency of algorithms and speed.