Integrated optimization of cultivation and fertilizer application: Implications for farm management and food security
Abstract
Problem definition: Motivated by the fresh produce industry, this paper studies a farmer's joint cultivation and fertilizer (a representative farm-input) application decisions facing uncertainties in both harvesting labor cost and farm yield where yield is stochastically increasing in the fertilizer application rate.Academic/Practical Relevance: This fills the void in the academic literature and it also has important practical implications for farm management and for policy making in increasing crop production to alleviate food insecurity.Methodology: We develop a two-stage stochastic program that captures the trade-offs facing a farmer growing a single crop in a single season to maximize the expected profit. We complement our analytical analysis with numerical experiments calibrated to data.Results: We characterize the optimal decisions and also how these decisions as well as the resulting expected harvest volume (a measure of food security) are affected by (fertilizer and cultivation) costs and (labor cost and farm yield) uncertainties. We find that the effects of costs and uncertainties can be counterintuitive due to joint optimization; specifically when they induce the farmer to change the cultivation volume and fertilizer application rate in opposite directions. For example, an increase in fertilizer cost may incent the farmer to cultivate more farmland. Another example is that a well-intended policy intervention that reduces the cultivation cost or yield variability may backfire and decrease the expected harvest volume.Managerial implications: Our findings provide rules of thumb for a farmer in jointly adapting cultivation and fertilizer application decisions as a response to changes in the business environment and shed light on how policy makers could encourage farmers to increase crop production in order to alleviate food insecurity.