Agricultural Production Planning under Yield-Dependent Cost and Price

In this study, we examine the relationship between crop yield and the purchasing cost of fruit and the selling price of agricultural good. We coin this relationship as “yield-dependent” cost and price. We use this relationship in determining an agricultural producer’s production planning decisions. Our work is motivated by the applications in the olive oil industry, however, the yield-dependent cost structure can also be observed in other industries such as citrus and wine grapes. Production of olive oil is a particularly challenging business as olives grow every other year making it a riskier investment. Olive oil producers lease farm space from other growers. When the yield of olives is low because of weather and/or diseases, the firm can buy additional olives from other farmers at a cost that varies with the yield. In the same scenario, the sale price of olive oil also increases because of the limited supply. When the yield is high, the company uses some of its olives for olive oil production and the rest of the olives are sold to other oil producers. Upon deriving the olive oil, the company sells its olive oil under demand uncertainty. The paper makes several contributions. It first shows that the objective function is concave in the amount of farm space leased, leading to a unique optimal solution. Next, it determines how the total production of olive oil changes with the yield. The study proves that the optimal amount of leased farm space decreases under the presence of the flexibility pertaining to buying additional olives. Departing from earlier findings, this study shows that higher degrees of yield variance do not necessarily increase the optimal amount of leased farm space in the presence of a secondary purchasing option of olives.