Design of a multi-objective supply chain and distribution network using robust optimization with interval data mathematical programming and live traffic data

The rapid growth of e-commerce, rising environmental concerns, and increasing urban traffic congestion have placed unprecedented pressure on logistics systems to become more efficient, resilient, and sustainable. Traditional distribution networks often fail to balance cost efficiency with environmental impact and service quality, especially under uncertain and dynamic conditions. Addressing these challenges requires advanced models that integrate economic, environmental, and operational objectives while accounting for real-world uncertainties. Present study introduces and optimizes a multi-objective mathematical programming model for product distribution networks with an outsourcing approach. The proposed model is designed with three primary objectives: minimizing transportation costs, reducing carbon emissions, and maximizing demand coverage. To enhance the precision of transportation times, fuel consumption, and pollutant emissions calculations, live traffic data was utilized for parameter estimation. The model can recommend optimal routes for product transportation across stores, hubs, and customers, thereby optimizing the overall distribution chain, reducing operational costs, and improving transportation system efficiency. This study employs the Robust Optimization with Interval Data (ROID), which provides enhanced flexibility and resilience in managing uncertainty relative to conventional deterministic approaches. This technique enables improved modelling of real-world variability, hence augmenting decision-making in uncertain and dynamic transportation environments. To validate the model’s performance, a case study was simulated using hypothetical data. The results demonstrated that applying the proposed model can significantly reduce logistics costs. Additionally, a sensitivity analysis was conducted on the model’s parameters. The findings revealed that the proposed model is sensitive to variations in input parameters, such as customer demand and transportation capacity, which substantially influence the final outcomes. In conclusion, the development of this model can serve as a practical tool for organizations and industries to achieve economic and environmental objectives. It offers a viable solution for improving the sustainability of logistics systems and mitigating environmental impacts.