Optimization Model for Alternative Use of Different Quality Irrigation Waters

Abstract

A linear programming model was developed to optimize the use of different quality waters by alternative irrigations rather than by blending. In a situation of poor‐quality ground water and limited good‐quality canal water, the model decides how much land to put under each crop and how much ground water to abstract and apply to each crop in each time period. The irrigation system, based on an area in Pakistan, was modeled to maximize the net returns. These are the product of the area under each crop and the crop gross margin. The latter is a function of crop yield, which is itself a function of the irrigation water applied, i.e., the sum of canal water and ground water. Maximization of the net return therefore involves maximizing a function including the product of two variables, crop area and amount of ground water applied. To overcome the difficulties of nonlinearity and therefore greatly reducing computation time, a number of irrigation strategies were identified for each crop. Each strategy has a corresponding yield level, which becomes a coefficient in the objective function rather than a variable. The model developed presents a solution procedure wherever low rainfall and limited and different quality waters are the basic parameters governing the irrigation system. An example is given to illustrate the use of model.