A Novel Linear Programming Framework For Multi-Objective Multi-Commodity Transportation Optimization

The multi-objective multi-commodity transportation problem (MOMCTP) is a complex and significant challenge in modern supply chain management, requiring the simultaneous optimization of multiple conflicting objectives while distributing various products from multiple sources to diverse destinations. This study presents a novel and structured mathematical framework based on linear programming to effectively address this problem. A Multi-Objective Linear Programming (MOLP) model is developed by incorporating three critical performance criteria: minimization of transportation cost, reduction of delivery time, and mitigation of environmental impact through reduced CO₂ emissions. The proposed model integrates realistic operational constraints, including source capacity limitations, destination demand requirements, vehicle capacity restrictions, and multi-commodity allocation policies within a unified optimization framework. To handle the inherent trade-offs among competing objectives, the weighted sum method is employed to generate Pareto-efficient solutions, enabling a systematic analysis of objective interactions and decision priorities. To validate the applicability and effectiveness of the model, a real-world case study based on operational data from a regional distribution system is examined. The problem is solved using WinQSB software to determine optimal shipment plans and routing decisions. Computational results demonstrate that the proposed approach successfully balances multiple objectives, leading to significant improvements in overall system performance, including reductions in transportation cost, delivery time, and carbon emissions. This study contributes to the field of transportation optimization by providing a robust, flexible, and practical decision-support framework for sustainable and efficient multi-commodity logistics planning.