Optimal specialty crop planning policies with yield learning and forward contract

Hops are the flowers of a specialty crop that provide unique flavors to craft beer. We study a multi‐year crop planning problem for a farmer who seeks to add hops production to the current production of a conventional crop. The farmer must dynamically determine the number of acres to allocate to each crop and design the terms of the forward contract under which brewers purchase the hops, considering the uncertainty of weather conditions, hops yield, hops spot market price, and conventional crop price. We formulate a multi‐period stochastic dynamic programming framework that incorporates statistical learning methods that depend on exogenous factors. We also develop an easy‐to‐implement learning‐based marginal total profit heuristic which can potentially be used as a decision support tool. Our numerical analyses suggest that yield learning is particularly important for a farmer who is considering investing in a high margin, but potentially risky, new crop such as hops. We also characterize the conditions under which yield learning is most beneficial for farmers. This paper contributes to the literature on specialty crop planning by introducing a multi‐year planning framework that incorporates unique characteristics of specialty crop production. We fill a gap in the crop planning literature by considering how farmers can learn about crop yields based on realized yields and exogenous factors such as weather conditions. Our paper is also of practical importance for farmers who seek to diversify their crop portfolio to hedge against risks associated with trade tensions and potential price drops for conventional crops.