Optimization Analysis of Deficit Irrigation Systems

Abstract

In the present paper the use of mathematical programming theory is proposed to define optimization criteria for the deficit irrigation of an area. A first application, which was carried out on a sample farm in the Upper Tiber Valley (Central Italy), gave significant results. By using a multiplicative Stewart's formula, it was possible to determine, for various crops, the relationships between crop yield and applied water, which depend on the deterministic component of the process of water exchange soil‐crop‐atmosphere. The stochastic component of the same process is defined by the hypothesis that the functions are variable from year to year. These relationships were introduced as a constraint in a mathematical programming framework, with the aim of optimizing, in economic terms, the application of available irrigation water taking into account the possibility of varying the crop pattern. Finally, since the optimal solution can be found only on an annual basis, due to the stochastic component of the process, an attempt was made to define a method for determining a single, constant and optimal solution.