Optimized Operational Characteristics and Carbon Reduction Decision Pathways of School Milk Cold-Chain Distribution Network Under an Internal Carbon Pricing Mechanism

Urban short-haul cold-chain distribution operates under strict service constraints while facing increasing pressure to reduce carbon emissions under the dual-carbon goals. Existing emission-aware routing studies often treat carbon emissions as external constraints or ex post evaluation indicators, limiting their influence on operational decision making. This study addresses this gap by developing a cold-chain distribution network optimization model that integrates internal carbon pricing (ICP), enabling carbon emissions to be internalized as economic costs within routing and scheduling decisions. Using the student milk cold-chain distribution system serving 54 primary and secondary schools in Fuzhou as an empirical case, the model incorporates multiple cost components, including energy consumption, warehouse operation, carbon emissions, and low-load penalties, while embedding operational constraints such as vehicle capacity, delivery time windows, and minimum economic loading requirements. An improved genetic algorithm is applied to solve the model. Scenario analyses are conducted across carbon price variation and demand fluctuation. Results show that when the internal carbon price increases from 97.49 RMB/t to 2000 RMB/t, the total distribution cost rises from 3531.2 RMB to 4082.842 RMB, indicating that carbon costs become an increasingly important factor in operational decision making. The distribution network exhibits a core-route-dominated structure, with key routes remaining stable across carbon price scenarios, suggesting that the influence of ICP is primarily reflected through cost internalization rather than route substitution. Demand analysis further shows that a 10% demand reduction reduces costs through route consolidation, while a 20% reduction weakens load efficiency and reduces vehicle utilization without triggering low-load penalty costs. These findings demonstrate that integrating ICP into routing optimization provides an effective pathway for aligning operational decisions with low-carbon transition objectives in rigid-demand cold-chain distribution systems.