(untitled) (International Journal of Latest Technology in Engineering Management & Applied Science, 2026)
The assignment problem is one of the most fundamental optimization models in operations research, focusing on the efficient allocation of limited resources to specific tasks while minimizing total cost or maximizing overall effectiveness. Because of its mathematical simplicity and computational efficiency, the model has become an essential decision – support tool across manufacturing, logistics, healthcare, education, transportation and many other industries. This paper presents a comprehensive examination of the assignment problem through a practical case study approach. It begins with an overview of the historical evolution of the assignment problem, followed by a review of relevant literature and a discussion of its theoretical foundations. The paper further distinguishes the assignment problem from other optimization techniques, including transportation and linear programming models. To illustrate its practical applicability, a real-world-inspired machine-to-job allocation problem is formulated and solved systematically using the Hungarian Method. Each stage of the solution process is explained with appropriate tables and interpretations to enhance conceptual understanding. The study also highlights the diverse applications of assignment models across multiple industries and discusses emerging research directions involving artificial intelligence, machine learning, fuzzy optimization, and dynamic decision-making. The findings demonstrate that the assignment problem remains a powerful analytical tool for improving operational efficiency and supporting evidence-based managerial decisions in increasingly complex organizational environments.