Optimizing Resource Allocation with the Hungarian Method

Abstract

This study explores the assignment problem, a critical optimization challenge in operations research, which focuses on the optimal allocation of tasks to agents to minimize costs or maximize efficiency. As businesses face increasingly complex operational demands, effective resource management becomes essential. The study begins with an overview of the characteristics and significance of the assignment problem, followed by a detailed mathematical formulation that includes decision variables, objective functions, and constraints. The Hungarian Method is presented as a systematic approach to solving the assignment problem. It is illustrated through practical examples demonstrating its applicability in real-world scenarios such as workforce allocation and logistics. The results confirm the method's effectiveness in achieving optimal assignments while minimizing costs. This study underscores the importance of mathematical modeling in operations research and its potential to enhance decision-making processes across various industries, ensuring efficient resource utilization and improved operational performance.