MODEL OF DYNAMIC CROP ROTATION ON THE BASIS OF THE BELLMAN EQUATION WITH FINAL HORIZON
U.S. Skvortsov, N.A. Ryndin, K.A. Amoa
The problem of the study is to determine the optimal plan for multiple periods, which take into account the economy of the object of study in a dynamic structure. As a result, this article describes a dynamic model based on the Bellman equation with a finite horizon. The object of the study is crop rotation. By maximizing the net present, expected current and future returns, the modified Bellman equation provides optimal crop planting solutions. This model takes into account perennial crop rotations with a different set of crops. The Bellman equation is a partial differential equation with initial conditions given for the last time instant for the Bellman function, which expresses the minimum value of the optimization criterion that can be achieved, provided the system evolves from its current state to some final state. Using the Matlab package, a dynamic model of crop rotation was simulated. MATLAB uses the CompEcon toolkit for solving problems of dynamic programming with discrete time or with a discrete variable. Given the final value of the current and expected profits, the problem is solved by repeatedly applying the Bellman equation.
Keywords: :Markov model, dynamic programming, Bellman equation, crop rotation optimization.