Order-Driven Multi-Objective Optimization of a Three-Echelon Low-Carbon Dairy Cold-Chain Network Considering Demand Variability and Shelf-Life Reliability

Dairy cold-chain network planning requires coordinated decisions under demand variability, product perishability, and environmental constraints. To address these interrelated challenges, this study formulates an order-driven multi-objective mixed-integer nonlinear programming (MINLP) model for the tactical planning of a three-echelon dairy cold-chain network. The model coordinates distribution-center selection, inventory, transportation allocation, vehicle configuration, and refrigeration decisions to minimize total cost, transportation-related carbon emissions, and the quantity- and importance-weighted average freshness-loss rate. Demand variability is represented through service-level-based safe demand, whereas product freshness is evaluated using Weibull-based shelf-life reliability and inventory–transportation exposure. Transportation congestion is further incorporated to capture its effects on travel time, refrigeration emissions, and freshness deterioration. NSGA-II is employed to generate Pareto solutions, with entropy-weighted TOPSIS used for compromise-solution selection and MOEA/D serving as the benchmark algorithm. Numerical results indicate that NSGA-II achieves favorable convergence performance and comparable solution diversity relative to MOEA/D, while small-scale mixed-integer approximation tests support the quality of the obtained solutions. Multi-scale experiments demonstrate stable computational performance as network size increases. Sensitivity and scenario analyses further reveal distinct effects of service levels, shelf-life characteristics, and road capacity on economic, environmental, and freshness performance. The proposed framework provides tactical decision support for coordinating demand-responsive supply, low-carbon operations, and freshness preservation in dairy cold-chain networks.