Optimizing sustainable supplier selection and order allocation using an integrated mathematical programming and machine learning approach

This study presents a novel three-phase hybrid approach for sustainable supplier selection and order allocation, integrating Multi-Criteria Decision-Making (MCDM), machine learning, and mathematical programming techniques. In the first phase, the Grey-TOPSIS method is employed to evaluate suppliers based on economic, environmental, and social criteria, effectively handling uncertainty in expert judgments. In the second phase, a machine learning model based on Support Vector Regression (SVR) is developed to calculate suppliers' final sustainability scores. This model enhances consistency and scalability by leveraging the initial evaluations and learning from historical data. In the third phase, the predicted scores are incorporated into a multi-objective mixed-integer programming model to determine the optimal supplier selection and order allocation. The model considers practical constraints such as supplier capacity, transportation modes, and risk mitigation through order splitting. The key innovation of this study is the sequential integration of these three important techniques for the first time. With the SVR method, once new suppliers are introduced, it is not necessary to re-apply the MCDM method, as the SVR model learned can predict sustainability scores. Additional innovations include the application of uncertainty through grey number theory in the initial phase and the possibility of obtaining financial support, as well as the need to limit the supply of each good from each supplier to reduce risk in the mathematical model during the third phase. To validate the proposed approach, two evaluations were conducted. First, the impact of the SVR model was assessed by comparing the results with a scenario using only Grey-TOPSIS scores. Incorporating SVR led to a 1.76% improvement in the weighted goal programming objective. Second, the proposed model was compared with four company-specific policies reflecting current operational practices. The results showed average improvements of 0.67% in sustainable procurement, 5.57% in operational cost, and 2.9% in environmental cost, resulting in an overall 5.61% enhancement in the weighted objective function. These findings demonstrate the practical effectiveness of the proposed framework in delivering balanced sustainability outcomes in real-world supply chain decision-making.