An Algorithm for Optimization of Cereal Output

Authors:
N. Moussouni;M. Aidene
Affiliations:
Labo L2CSP, Faculty of Science, Department of Mathematics, University Mouloud MAMMERI of Tizi-Ouzou, Tizi-Ouzou, Algeria;Labo L2CSP, Faculty of Science, Department of Mathematics, University Mouloud MAMMERI of Tizi-Ouzou, Tizi-Ouzou, Algeria
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2012

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Abstract

Algeria is rich country, it uses fertilizers to improve its cereal production as it is usually known. However, Algerian farmers use fertilizers in a bad manner and in a quite random way. This causes both ground, water pollution, and a loss of output.In the present paper we study a modelization of the evolution of the cereal output production controlled by means of adding fertilizers. We set an optimal control problem where we aim at maximizing the cereal output and meanwhile minimizing pollution effects. We solve theoretically this optimal control problem with the Pontryagin Maximum Principle and then provide different numerical methods to implement it: indirect methods based on the shooting method and direct methods based on a combination of AMPL with IPOPT.