A Mixed Integer Linear Programming Framework for Mitigating Enteric Methane Emissions on Dairy Farms Through Optimized Crop and Diet Planning

Abstract

In pursuit of agricultural resilience and sustainability, the European Union (EU) Common Agricultural Policy (CAP) advocates for effective and diverse crop rotations. Yet, dairy farmers face intricate planning challenges due to diet and market complexities. This study introduces a novel mixed integer linear programming (MILP) model that optimizes both crop planning and dairy cow diet formulation within mixed crop-livestock farming systems, considering CAP crop rotation regulations and Greenhouse Gas (GHG) environmental policies. Our approach employs a two-step framework to address enteric methane emissions. First, a multi-objective optimization generates a set of Pareto-efficient solutions, offering policymakers insights into trade-offs between economic returns and methane emissions. Second, the TAX policy (introducing a methane emissions tax) and RED policy (imposing explicit methane reduction targets) can be used to determine the required tax rates or reduction levels to achieve the selected policy goals. These policies also reveal the effects of varying tax rates and reduction levels on crop planning and diet formulation. The proposed approach is illustrated, without loss of generality, on three representative Italian dairy farms – producing milk without Protected Designation of Origin (PDO) rules (STD), or following Grana Padano (GP), or Parmigiano Reggiano (PR) PDO rules. We consider 33 types of crops, allowing double cropping, and 11 animal groups that have distinct nutritional requirements. The multi-objective optimization highlights non-linear trade-offs between economic returns and methane emissions, underscoring the critical role of policymakers in balancing these objectives. RED policy scenarios prove more effective at GHG mitigation than TAX policies. Methane mitigation initiatives prompt dietary adjustments, resulting in higher crude protein percentages and reduced neutral detergent fiber content in cow diets, consequently influencing crop plans. Moreover, under stringent GHG mitigation requirements, dairy farmers lean towards purchasing feed from the market rather than cultivating it on-farm.