Multi-stage farm management optimization under environmental and crop rotation constraints

This paper presents a novel multi-stage optimization model for farm management during a certain planning time horizon. The salient features of this optimization model are the proper incorporation of crop rotation schemes and the consideration of crop impacts on the environment via linear environmental constraints. This decision support tool produces an optimal crop rotation plan (i.e. which crop to cultivate each year and their area) which maximizes farmer' profit while satisfying specified environmental constraints and crop rotation schemes requirements. The optimization model is formulated as a mixed-integer linear programming (MILP) problem for which sound and powerful solvers exist. The paper thoroughly investigates the impact of various types of environmental constraints, which aim at maintaining the environmental impacts of farm activities below specified levels either overall, i.e. over the entire planning horizon, or tight, i.e. after each crop rotation. The environmental constraints are derived by adopting a Life Cycle Assessment (LCA) approach. The proposed approach is illustrated, without loss of generality, using agriculture system data specific to Luxembourg. The impact of a variety of environmental constraints, including greenhouse gas emissions and European Union (EU) common agricultural policy (CAP), is discussed.