Assignment # 2 (Article - 2)

Article Reference:

J.A. Frizzone, R.D Coelho, D. Dourado-Neto, R. Soliani, June 1997, Linear Programming model to optimize the water resource use in irrigation projects – An application to the senator Nilo Coelho Project

Summary:

Objective of the paper is to develop a linear programming model using all the factors effecting and influencing the profit of the irrigation project. Linear programming model was considered to optimize the cropping patterns and the water requirements based on the constraints like – water availability, water-yield relationship, land constraints, production cost, and product price. Vital goal while planning an irrigation project is to explore how to combine the existing resources so as to maximize the profit and minimize the cost. Mathematical model quantifies the optimum solution using the scare resource and meeting the proposed goals.

Linear programming model was developed based on maximizing the net income subjected to restrictions of cropping area and water availability. Gross income was considered as proportional to the production and variable component is dependent on seasonal irrigation depth. Objective function was to maximize the net income which resulted in the following restrictions - seasonal water requirement of the crop should be less than or equal to the annual volume of available water, crop irrigated area should be less than the crop restricted area, total planted area restriction of each month and irrigated depth at any interval should not exceed the irrigated depth corresponding to maximum production. Considering all these constraints, objective and functions of the problem, linear programming model is used to optimize a solution for the cropping pattern in the region.

Case study: Model was applied to Senator “Nilo Coelho” irrigation project in Petrolina - Brazil

The aim of the model was to generate a optimal crop pattern suitable for the area and which maximizes the net income. The functions used in model area – water, seeding season, production cost (excluding the cost fo water) and product price. Crop water requirement was estimated based on the total irrigation depth in relation to the maximum Evapo-Transpiration of the crop. Monthly available water considered is Annual available water considered for the model is 66644500 (m³). Using these constraints and considering the crop area requirements, the linear programming model resulted in optimized crop planning. Though all the crops are irrigated with a deficit, recommended irrigation level of each crop satisfy the objective of maximizing the net income. Optimization model (LP) estimated net income of 53$ higher than the traditional crop pattern.

Sensitivity analysis was carried to see how the marginal cost, water availability, marginal net income and water misuse affects the optimum solution proposed. As the misuse of water will eventually effect the net income generated, It was recommended that when the resource is becoming scare, there should be a differential amount associated to the excess amount of water used by the users, this will improve the strategies involved in water management.

Discussions

Paper was interesting as it dealt with the basis of how the linear programming is carried out in planning a irrigation project. With the considered case study it gives a practical insight of how optimization modeling can be used in estimating an optimum crop pattern considering the maximum net income. The paper insights about various sensitivity analysis, which could be carried out to check the optimum solution, thereby looking into the problem in a broader approach.

If I was carrying out my research in the same field then my future work for this topic would be to analyze more on the sensitivity of water availability and the irrigation methods. How the net income be affected using different methods of irrigation would be interesting topic to explore.