A mixed-integer linear optimization model for a two-echelon agribusiness supply chain

We formulate and solve a mixed-integer linear program to model an agribusiness two-echelon supply chain between an agro-industrial producer and a wholesaler. The presented model is an equivalent reformulation of a bilevel linear program, using the well known KKT conditions and a disjunction approach on the complementary constraints. It includes a hierarchical decision structure that contemplates an agro-industrial producer in the upper level, who maximizes its profit by delineating the field into management zones and assigning to each one a specific crop rotation plan. In turn, in the lower level is the wholesaler who minimizes the penalization cost of lost sales that could experiment in order to satisfy the demand requirement according to the units provided by the producer. We present a case study to show the relevance of the proposed methodology.