Optimization of Sustainable Supply Chains with Carbon Footprint Constraints

The urgent need to align economic objectives with environmental sustainability has brought carbon-constrained supply chain design to the forefront of industrial and academic research.This paper develops a novel mixed-integer linear programming (MILP) model that simultaneously minimises transportation costs and internalised carbon penalties within a single integrated framework.A synthetic but realistic dataset, based on publicly available EPA emission factors and transportation cost standards, was generated to simulate a freight network comprising five distribution facilities and twenty customer zones.The model was tested across multiple scenarios, including pure cost minimisation, carbon pricing at $50 and $100 per metric tonne of CO, and emission cap regimes with 10% and 25% tighter targets compared to baseline emissions.Results demonstrate that introducing a moderate carbon price ($50 t) achieves an 18% reduction in emissions with only a 6% increase in total cost, while a higher price ($100 t) secures a 43% emission cut at a 17% cost premium.Cap-based scenarios offered similar emission reductions at slightly lower cost increments.Sensitivity analysis revealed a concave elasticity between cost and emission reduction, indicating diminishing returns beyond moderate carbon price levels.The study offers actionable insights for policymakers and logistics managers aiming to operationalise sustainable freight strategies under emerging carbon regulatory regimes.