The ε- Constrained Method to Solve a Bi-Objective Problem of Sustainable Cultivation

Abstract

This study presents a nonlinear bi-objective 0-1 optimization model for sustainable cultivation and proposes an exact method to solve it. In this formulation, among a set of cultures, a predefined number of cultivable plots and planning horizon, it is intended to decide which crops, periods and plots should be cultivated. Two conflicting objectives are considered: (i) minimize the proliferation of pests and (ii) maximize the profit of the planting schedule in all planning horizon. The mathematical formulation was solved by the classical ε- constrained method. We linearized the original model and obtained an alternative linear version of our problem. Then, we compare the performance of ε- constrained method in this two formulation to determine some Pareto optimal solutions in 27 instances generated by a semi-random procedure of real dimension. The experiments showed that mathematical models along with the proposed method may be powerful tools in the complex decision-making in this field.