Reviewing the Role of Mathematical Optimization in Operations Research: Algorithms, Applications, and Challenges

This review paper examines the pivotal role of mathematical optimization in operations research, focusing on its algorithms, applications, and challenges. Mathematical optimization, a cornerstone of operations research, offers powerful tools for addressing complex decision-making problems. We discuss a variety of optimization algorithms, from classical methods like linear programming to modern metaheuristic techniques such as genetic algorithms. Through specific case studies, we highlight the diverse applications of mathematical optimization in industries such as logistics, finance, and manufacturing. Additionally, analyze challenges like computational complexity and scalability issues, providing insights into the practical implementation of optimization solutions in real world scenarios. Keywords: Mathematical Optimization, Operations Research, Algorithms, Decision-Making Problems, Challenges, Applications