Coordinating harvest planning and scheduling in an agricultural supply chain through a stochastic bilevel programming

This paper addresses a selective harvest planning problem in the context of a hierarchical agricultural supply chain, which integrates the definition of management zones for harvest planning, and the coordination between the producer and the wholesaler. The problem is represented through a stochastic bilevel program that allows the representation of the hierarchy between the producer (leader) and a wholesaler (follower). The producer decides planning and scheduling of the selective harvest for each homogeneous management zone into the resulting partition, and the wholesaler decides the amount to be acquired to satisfy demand requirements. At each decision level, a stochastic optimization model is proposed for representing the uncertainty in future crop yields, prices, and demands, using a finite set of scenarios. A reformulation of the bilevel model into a mixed-integer linear program is provided using Karush-Kuhn-Tucker conditions and replacing the nonlinear complementary constraints allowing for the introduction of auxiliary binary variables and a big-M term. This model was applied in a case study for selective harvesting of grapes with data collected from a farm located in the south central zone of Chile. Our research shows valuable results of the proposed methodology from a set of instances representing the behavior of both decision makers under uncertainty.