An Alternative Row Adaptation technique for Solving Assignment Problems

Assignment problems are a fundamental optimization challenge in operations management, where tasks, resources, or personnel must be assigned efficiently to minimize costs or maximize effectiveness. These problems often arise in various industries, including logistics, manufacturing, and workforce scheduling. The classical assignment problem is modeled as a linear programming problem, typically solved using the Hungarian algorithm, which guarantees an optimal assignment with polynomial-time complexity. This paper explores an alternative time-consuming technique to solve balanced and unbalanced assignment problems which is very effective and straight forward. The traditional technique subtracts the row or column minimum entries from all the entries of assignment matrix whereas technique proposed in this paper subtracts only rows minimum entry from each row of the cost matrix, and for adaptation added unit amount in each row. Finally, the numerical illustrations and comparisons of different real-world problems shows the effectiveness of the proposed technique.