A Mathematical Modeling Approach for Analyzing Dairy Supply Chains Under Heterogeneous Conditions

Dairy supply chains are characterized by high structural complexity due to the interaction of multiple actors, stringent quality requirements, and the perishable nature of milk and its derivatives. These systems operate under heterogeneous conditions, where variability in production capacity, logistics infrastructure, and market dynamics significantly affects overall performance. Despite the growing body of literature on optimization, sustainability, and logistics in dairy supply chains, existing mathematical models often rely on simplified or homogeneous assumptions that limit their ability to represent real-world conditions. This study proposes a mathematical modeling framework to analyze the behavior of dairy supply chains under heterogeneous operating conditions. The model integrates production, processing, and distribution decisions within a unified structure, capturing the interdependencies between key components of the system. Scenario-based parameters are incorporated to represent variability in supply and logistics, allowing the evaluation of system performance under different operating conditions. The objective function is formulated to maximize the expected net profit of the system, considering revenues and multiple cost components, including raw material, processing, inventory, transportation, and fixed costs. The proposed formulation enables the analysis of trade-offs between cost efficiency and demand fulfillment, while providing insights into how variability in system conditions affects overall performance. Rather than focusing on isolated optimization problems, the model offers a structured approach to represent the combined effects of operational constraints and system heterogeneity. The results support the use of mathematical modeling as a tool for understanding supply chain behavior in complex agri-food systems and for informing decision-making under non-ideal conditions.