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

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

1Sonia,2Sikander Hans, ,3Balwinder Kumar, 4Deepam, Priyanka, Savita

1Assistant Professor, Department of Applied Science, KC group of Research & professional institute, Pandoga, Una

2Principal, Department of Electrical Engineering, KC group of Research & professional institute, Pandoga, Una

3Principal, Department of Electrical Engineering, KC Polytechnic, Pandoga, Una

4Department of Computer Science, KC group of Research & professional institute, Pandoga, Una

Soniajairath42@gmail.com

Abstract: 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