Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 22 Issue 4

An Improved Hungarian Algorithm for a Special Case of Unbalanced Assignment Problems Mohammad Shyfur Rahman Chowdhury Abstract- The current Hungarian approach to solving unbalanced assignment issues is based on th e notion that some tasks should be delegated to fictitious or covert components, and those studies should be left unperformed. In real-world scenarios, it may be desirable to carry out all of the tasks on fundamental details. To do this, multiple tasks may be distributed to a single machine. The current research's enhanced Hungarian method for addressing unbalanced assignment challenges results in the ideal work assignment policy. An example using numbers shows how well the suggested strategy works and how effective it is. The acquired result is then likened to other current approaches to demonstrate our algorithm's superiority. I. I ntroduction One of the most significant applications of optimization theory is the Assignment Problem, where various tasks need to be distributed across components to be completed, such as spreding personnel to offices and drivers to buses, among other things. There have been numerous ways of exploring the best policy for assigning jobs to components. The Hungarian approach is the most frequently used method for determining the best assignment policy. The Hungarian Method was named by Kuhn (Kuhn, 1995) and was based in significant part on earlier work by two Hungarian mathematicians, Egervary and D. Konig. When the Hungarian approach is used to address an uneven assignment problem, the technique assigns the jobs to fake components that do not perform them (if the number of jobs is greater than the number of components). It seems impossible to leave jobs unfinished in real-world situations. As a result, rather than assigning extra work to dummy components, it is recommended to do each and every job that may be done by assigning multiple jobs to a single component. To tackle assignment problems, the Hungarian algorithm (Chen., 2011) (W. B. Lee, 1997) and specific heuristic algorithms (e.g., simulated annealing method (B. Li, 2002) ant colony algorithm (Y. Liang, 2005) (R. K. Yin, 2008) particle swarm algorithm (W. F. Tan, 2007) and genetic algorithm (S. Q. Tao, 2004). Heuristic approaches are frequently employed to solve problems with assignments of high complexity. However, because the search is conducted at random, it cannot guarantee that the optimal result will be obtained. The Hungarian algorithm is an algorithm with a mathematical foundation. The Hungarian algorithm is commonly used to tackle assignment problems because of its simplicity and ability to find the best solution without requiring validation 1 Year 2022 29 © 2022 Global Journals Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) Author: Assistant Professor, Department of Business Administration, International Islamic University Chittagong. e-mail: src.dba@iiuc.ac.bd N otes