Improved Crop Productivity Through Optimized Planting Schedules

Abstract

Problem definition: We study the optimal seeding policy under rainfall uncertainty in rain-fed agriculture and explore its advantage over commonly used heuristics in practice. Academic/practical relevance: Our work is in the area of agriculture operations, and we focus on the improvement of farmer’s expected total profit by optimizing planting schedules. Methodology: We model a farmer’s planting problem under limited planting capacity in a finite-horizon stochastic dynamic program. Results: We show that the optimal planting policy is a time-dependent, threshold-type policy, and the optimal threshold is dependent on the soil water content and planting capacity. In our computational study, we use the well-known Decision Support System for Agrotechnology Transfer simulator used in agriculture to obtain the expected yield when planting in any given period. Utilizing field weather data from Southern Africa, in a real-size, large-scale problem, we demonstrate a significant relative profit advantage of the optimal planting schedule over commonly used heuristics in practice. We show that the relative advantage of the optimal policy increases as the climate condition becomes more severe for planting. We also develop a heuristic based on the secretary problem and demonstrate the increased efficacy of the secretary heuristic. Managerial implications: We show that the farmer should plant down to the optimal threshold of seed amount. However, in practice, farmers start to plant each year after observing enough cumulative rainfall. Utilizing field weather data, in a real-size, large-scale problem, we show significant improvement of the expected total profit if the farmer could adopt the optimal policy.