Development of a direct-solution algorithm for determining the optimal crop planning of farms using deficit irrigation

The irrigation farms placed in areas of scare water demand methodologies that can increase their profitability via more efficient use of their resources. Determining the combination of factors that maximizes the profitability of any productive process requires the use of optimization methodologies. Traditionally, these types of problems were solved using heuristic methods. However, a direct-solution algorithm would produce faster and more accurate solutions. The aim of this work was to develop a direct-solution algorithm capable of determining the crop planning (area and volume of water per crop) that maximizes the profitability of an irrigation farm. The data required by the algorithm include the total cultivable area of the farm and the amount of available irrigation water as well as the “gross margin vs. irrigation depth” functions of the considered crops. Cultivating one or two crops is the way to reach higher profitability, but this strategy is not suitable from an agricultural point of view (i.e., crop rotation, diseases, weather risks, regulations of agricultural policies, etc.). Due to this algorithm must be compatible with the MOPECO model, a methodology has been developed to allow its implementation in this model. The objective of this software is to maximize the profitability of irrigation farms by incorporating a more efficient use of irrigation water using regulated deficit irrigation techniques. The current version of this model uses genetic algorithms for determining optimal crop planning, which are time consuming. For a hypothetical 100 ha farm, considering 10 different crops and 11 scenarios of water availability, the developed algorithm adapted to MOPECO achieved gross margins around 0.5% lower than LINGO, and 1.1% higher than genetic algorithms, decreasing the calculation time requirements by between 50 and 100 and approximately 2000 times, respectively. Another relevant result is the fact that the algorithm may be used manually, by drawing the tangent lines between the gross margin curves, for reaching the optimal combinations of irrigation depth and, indirectly, the cultivable area of each crop. Moreover, the algorithm allows to understand the relationships among crops, which may advise users in the determination of the optimal solution under real conditions. This methodology also highlights the importance of using regulated deficit irrigation techniques when managing irrigation farms with a low supply of irrigation water. The developed algorithm may also be useful in the optimization of other production processes.