Analyzing the value of the residue of crops grown on arable land with stochastic optimization

Abstract

A B S T R A C TDetermining the value of the residues of crops grown on arable land is a non-trivial task, depending much on how it is defined. In this paper the value of residues is considered to be the savings achieved on the total expense of artificial fertilizer distribution by returning the residues into the soil. A general linear programming approach is presented to obtain optimal artificial fertilizer allocation. Since the amount of artificial fertilizers required depends on uncertain inputs Monte Carlo simulation is applied in conjunction with linear programming to solve the arising stochastic optimization problem. The input data, such as the national average yield, specific amounts of nutrients required by crops to achieve the national average yield and publicly available details of different artificial fertilizer products are specific to Hungary, but the mathematical model presented is general in nature. Simulations are executed for some of the major crops, including wheat, corn, sunflower and rape. The distribution of savings achieved on returning their residues to the soil is provided at the end of the paper for further use.