Optimisation of crop rotations: A case study for corn growing practices in forest-steppe of Ukraine

Abstract

The formation of optimal crop rotations is virtually unsolvable from the standpoint of the classical methodology of experimental research. Here, we deal with a mathematical model based on expert estimates of “predecessor-crop” pairs’ efficiency created for the conditions of irrigation in the forest-steppe of Ukraine. Solving the problem of incorporating uncertainty assessments into this model, we present new models of crop rotations’ economic efficiency taking into account irrigation, application of fertilisers, and the negative environmental effect of nitrogen fertilisers’ introduction into the soil. For the considered models we pose an optimisation problem and present an algorithm for its solution that combines a gradient method and a genetic algorithm. Using the proposed mathematical tools, for several possible scenarios of water, fertilisers, and purchase price variability, the efficiency of growing corn as a monoculture in Ukraine is simulated. The proposed models show a reduction of the profitability of such a practice when the purchase price of corn decreases below 0.81 EUR∙kg –1 and the price of irrigation water increases above 0.32 EUR∙m –3 and propose more flexible crop rotations. Mathematical tools developed in the paper can form a basis for the creation of decision support systems that recommend optimal crop rotation variations to farmers and help to achieve sustainable, profitable, and ecologically safe agricultural production. However, future works on the actualisation of the values of its parameters need to be performed to increase the accuracy.

Keywords

• combinatorial optimisation
• corn
• crop rotation
• genetic algorithms