Benders Decomposition for Production Planning Optimization in Citriculture

Brazilian citrus growing plays a strategic role in the national and international economy,
highlighting Brazil as the world's largest producer and exporter of orange juice. Nesse
context, the long-term planning of the planting, renovation and eradication of orchards represents
A complex challenge, mainly due to the prolonged production cycle of orange trees,
variations in productivity over the years and uncertainties related to the market and conditions
climatic. This work proposes the application of Benders' Decomposition to the model of
optimization presented by Tavares and Munari (2024), called SPMC (Strategic Planning Model
for Citriculture), with the objective of supporting decision-making in the strategic planning of
citrus production. Benders decomposition is a widely used technique for solving of large optimization problems, in which the original problem is partitioned into < /> Two levels of decision: a strategic level, associated with integer or binary variables, and a level
associated with continuous variables. The Master Problem concentrates strategic decisions
related mainly to planting and eradication operations. These decisions
define the allocation of resources in the long run, determining the overall structure of planning. In
SPMC, the Master Problem is composed of the binary variables, while the Subproblem is responsible
by the treatment of the detailed operational constraints of the model, considering the decisions
fixed by the Master Problem