Abstract
Mixed Integer Linear Programming (MILP) has emerged as a powerful tool for optimizing complex supply chain networks. This paper explores the theoretical foundations of MILP, including the integration of integer variables and advanced solution techniques such as branch-and-bound and branch-and-cut algorithms. Through detailed modeling of production planning, network design, and transportation logistics, MILP enables companies to achieve significant cost reductions and operational efficiencies. We present case studies from retail, manufacturing, and pharmaceutical sectors to illustrate the practical applications of MILP. These examples demonstrate how MILP optimization can lead to reductions in production and inventory costs, improved customer satisfaction, and enhanced service levels. The findings underscore the value of MILP in addressing the multifaceted challenges of modern supply chain management.
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