Some Approaches for Solving Multicriterial Problems in the Agricultural Sector - Tonoyan, Gagik; Buniatyan, Marine (Bulletin of Yerevan University G: Economics, 2022)
The article proposes new methods for solving multicriteria problems in the agricultural sector. Four optimization tasks are formulated: maximizing the total yield of all benefits, maximizing the total profit, minimizing the total volume of irrigation water and minimizing the total risks of crop cultivation (hail, frost, drought, etc.). In addition, additional restrictions are also formulated: uniform distribution of the crop, ensuring food security, and export opportunities are also discussed. According to the above conditions (or part of them), 60 tasks arise, 44 of which are multicriteria (with two, three or four objective functions). To solve these problems, three methods are proposed: the method of combining objective functions and combinations of weight coefficients, the dynamic programming method, the method of cuts and exclusions, which are mostly new. All these methods, with some simple transformations, can be applied to solve problems both in the field of economics and in various areas of public life. The algorithms of the methods are described, their complexity is estimated. The algorithms of all proposed methods are efficient (with polynomial complexity). Some suggestions and comments are given that will expand the range of problems under consideration, or, by narrowing this range; improve the efficiency of the proposed methods.
Keywords: multicriterial problems; Pareto equilibrium principle; efficient algorithms and their complexity; simplex method; transportation problem; dynamic programming