Efficient supply chain operations are central to cost minimization, service level improvement, and resilience in modern competitive markets. This study investigates the application of integer programming and convex optimization techniques to address key decision-making problems in supply chain design and operations. A hybrid optimization framework is proposed to integrate strategic decisions such as facility location and capacity planning with tactical and operational decisions including inventory control and transportation allocation. Integer programming is employed to capture discrete choices such as warehouse activation and supplier selection, while convex programming is used to model continuous decisions involving production quantities, inventory levels, and transportation flows under cost and capacity constraints. The proposed framework is evaluated using a multi-echelon supply chain case scenario representing manufacturers, distribution centers, and retail outlets. Results demonstrate significant reductions in total operational cost, improved resource utilization, and enhanced demand fulfillment compared to traditional heuristic-based approaches. The findings confirm that combining integer and convex programming offers a robust, scalable, and analytically sound approach for optimizing complex supply chain systems in uncertain and resource-constrained environments. In addition, the proposed framework demonstrates strong computational stability and scalability, making it suitable for practical implementation in medium to large-scale supply chain networks. The integrated approach provides decision-makers with clear insights into cost–service trade-offs, supporting data-driven strategic planning and efficient operational execution across interconnected supply chain stages.