Green Supply Chain Modeling for Carbon Emission and Logistics Cost Minimization Using Multi-Objective Optimization

Abstract

Balancing economic efficiency and environmental sustainability remains a critical challenge in green supply chain network design, particularly when transportation decisions simultaneously influence logistics costs and carbon emissions. This study develops a multi-objective mixed-integer linear programming model for a four-echelon green supply chain comprising suppliers, production plants, warehouses, and customers. The model simultaneously minimizes total logistics cost and transportation-related carbon emissions while incorporating sourcing, production, distribution, facility utilization, vehicle capacity, and operational constraints. The optimization is evaluated using weighted-sum and epsilon-constraint approaches to represent alternative managerial priorities and identify the cost–emission trade-off, followed by sensitivity analysis of customer demand, vehicle emission factors, and vehicle capacity. The results demonstrate a pronounced economic–environmental trade-off. The cost-oriented configuration yields a minimum logistics cost of 165,348.68 currency units but generates 7,402.25 kg CO₂, whereas the carbon-oriented configuration reduces emissions to 4,770.83 kg CO₂ at a cost of 177,887.17 currency units. Notably, the balanced configuration reduces emissions by 35.5% relative to the cost-oriented solution while increasing logistics cost by only 0.27%. The epsilon-constraint analysis confirms a distinct knee-point region, indicating that most low-cost emission reductions can be achieved before additional reductions require disproportionate expenditure. Sensitivity results further show robustness across demand, emission-factor, and vehicle-capacity variations. The findings establish the balanced configuration as a practical decision benchmark for achieving substantial environmental improvement without materially compromising economic performance and provide a transparent framework for sustainable supply chain planning.