Modelling and optimization for palm oil plantation management

Abstract

In this paper, the problem of palm oil plantation management is considered. A non-linear mathematical model is proposed considering two state variables as the density of the young palm oil trees and the part of biomass that can produce oil. In the modelling process, it is assumed that the rate of planting new young trees and the rate of felling inefficient trees can be controlled. It is further assumed that the oil production rate is directly proportional to the biomass of palm oil plantation. A system of delay differential equations is developed to study the behaviour of palm oil plantation. The resulting optimal control problem is also solved to estimate the control variables while the objective is to maintain the biomass at a certain level and maximize the oil palm production in a long period. Numerical simulations are given to illustrate the results.