Linear programming model to optimize the water resource use in irrigation projects: an application to the Senator Nilo Coelho Project

Abstract

The main objective of this paper was to develop a separable linear programming model, considering a set of technical factors which may influence the profit of an irrigation project The model presents an objective function that maximizes the net income and specifies the range of water availability. It is assumed that yield functions in response to water application are available for differents crops and describe very well the water-yield relationships. The linear programming model was developed genetically, so that, the rational use of the available water resource could be included in an irrigation project Specific equations were developed and applied in the irrigation project "Senator Nilo Coelho" (SNCP), located in Petrolina - Brazil Based on the water-yield functions considered, cultivated land constraints, production costs and products prices, it was concluded that: (a) the model was suitable for the management of the SNCP, resulting in optimal cropping patterns and showing the water requirements; (b) for 7,424 ha of land and 66, 644,500 m³ of water available on a year basis, the shadow price of these resources were respectively, US$ 1,115.20/ha e USS 281.60/1000 m³; (c) for the total monthly water availability of 9,861,040 m³, the total annual water availability of 66,644,500 m³ became an effective restriction to the increase of the net income of the production system in the SNCP; (d) maintaining the total monthly water availability of 9,861,040 m³, annual volumes lower than 88,338,983 m³ were used fully to reach the optimal solution, and that higher volumes than this limit, did not increase the net return; (e) the optimization model presented, estimated a net return of 5234 % higher than the traditional cropping pattern used hi the SNCP, considering the agricultural year of 1992.