Integrated optimization of farmland cultivation and fertilizer application: Implications for farm management and crop production

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 yield, crop price, and harvesting cost where the latter two are yield dependent and yield is stochastically increasing in the fertilizer application rate. We develop a two-stage stochastic model of a farmer growing a commodity crop in a single season to maximize the expected profit. We then use the model to evaluate the optimal expected harvest volume (a measure of crop production). Our analytical analysis is complemented with numerical experiments calibrated to data. We characterize how the farmer’s optimal decisions, profitability as well as the optimal expected harvest volume are affected by fertilizer and cultivation costs and yield uncertainty. We find that these effects can be counterintuitive and significantly different from those when only cultivation decision is optimized (as considered in the literature); specifically when these effects induce the farmer to change the two decisions in opposite directions. For example, an increase in fertilizer cost may incent the farmer to cultivate more farmland. Another example is that a reduction in cultivation cost or yield variability may not increase the optimal expected harvest volume. This result is useful for policymakers as it demonstrates that commonly used policies in practice, such as distributing discount vouchers for seed procurement (which reduces the cultivation cost) or increasing seed diversity of the same crop (which reduces yield variability) that have been devised for increasing crop production may not be effective.