Crop Planning in Sustainable Agriculture: Dynamic Farmland Allocation in the Presence of Crop Rotation Benefits

Abstract

This paper examines crop planning decisions in sustainable agriculture-that is, how to allocate farmland among multiple crops in each growing season when the crops have rotation benefits across growing seasons. We consider a farmer who periodically allocates the farmland between two crops in the presence of revenue uncertainty where revenue is stochastically larger and farming cost is lower when a crop is grown on rotated farmland (where the other crop was grown in the previous season). We characterize the optimal dynamic farmland allocation policy and perform sensitivity analysis to investigate how revenue uncertainty of each crop affects the farmer's optimal allocation decision and profitability. Using a calibration based on a farmer growing corn and soybeans in Iowa, we show that growing only one crop over the entire planning horizon, as employed in industrial agriculture, leads to a considerable profit loss-that is, crop planning based on principles of sustainable agriculture has substantial value. We propose a simple heuristic allocation policy, which we characterize in closed form. Using our model calibration, we show that (i) the proposed policy not only outperforms the commonly suggested heuristic policies in the literature, but also provides a near-optimal performance and (ii) compared with the optimal policy, the proposed policy has a higher allocation of crops to rotated farmland, and thus, it is potentially more environmentally friendly.