Fertilizer application management under uncertainty using approximate dynamic programming

Finding the right amount of fertilizer for the plants in different maturity levels is a dynamic and stochastic problem due to the uncertainties in the weather conditions and yields. Besides, two conflicting objectives of multiple stakeholders, maximizing the yield and minimizing the environmental impact should be considered together. This paper proposes a mathematical model based on stochastic dynamic programming to find the fertilization levels in a citrus orchard for a finite planning period. Due to the size of the problem, we develop an Approximate Dynamic Programming (ADP) algorithm to obtain the best policy. The data for the case study is collected through literature sources and from farmers in southern Turkey where the income from orchards are unstable and groundwater pollution is observed. We find that ADP performs better than static and dynamic heuristics in a wide range of parameters. Extensive sensitivity analysis indicates that if the penalty for the leaching is computed per acre of orchard, this may lead to excessive fertilizer use in large orchards. Finally, the increase in the standard deviation of rainfall due to the global warming is expected to cause up to 22% drop in the yield.