________________________________________ ++ Professor; *Corresponding author; J. Adv. Math. Com. Sci., vol. 38, no. 8, pp. 6-15, 2023 Journal of Advances in Mathematics and Computer Science Volume 38, Issue 8, Page 6-15, 2023; Article no.JAMCS.94246 ISSN: 2456-9968 (Past name: British Journal of Mathematics & Computer Science, Past ISSN: 2231-0851) _______________________________________________________________________________________________________________________________________ Alternate Approach (Penalty Approach) to Assignment Problem Solving and Comparison to Existing Approaches Hudu Mohammed a* , F. T. Oduro b++ and S. K. Appiah b++ a Department of Mathematical Sciences, Kumasi Technical University, Kumasi, Ghana. b Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana. Authors’ contributions This work was carried out in collaboration among all authors. All authors read and approved the final manuscript. Article Information DOI: 10.9734/JAMCS/2023/v38i81785 Open Peer Review History: This journal follows the Advanced Open Peer Review policy. Identity of the Reviewers, Editor(s) and additional Reviewers, peer review comments, different versions of the manuscript, comments of the editors, etc are available here: https://www.sdiarticle5.com/review-history/94246 Received: 13/12/2022 Accepted: 16/02/2023 Published: 07/06/2023 __________________________________________________________________________________ Abstract Assignment problem is an important area in Operation Research and is also discussed in real physical world. In this paper an attempt has been made to solve the assignment problem using a new Method called the Penalty method. We discuss a numerical example by using the new Method and compare it with standard existing method which is the Hungarian method. We compare the optimal solution of the new Method and the Hungarian method. The new method is a simple procedure, easy to apply for solving assignment problem. Keywords: Assignment problem; Hungarian method; alternative method; operation research. Original Research Article