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

According to step 8, there is a tie in the 2nd and 3rd rows (containing two zeros). We allocate J 4 to component M 2 (in Table-7) because the cost associated with this position is the lowest in the original cost matrix. Table 7 J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 C 1 30 80 50 40 80 150 0 40 C 2 30 0 120 40 60 0 0 × 90 C 3 0 60 40 50 40 0 100 60 C 4 70 20 0 30 60 60 0 × 80 C 5 0 10 0 × 0 0 10 10 0 Then following step 9, we get the final table -8. Table 8 J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 C 1 30 80 50 40 80 150 0 40 C 2 30 0 120 40 60 0 0 × 90 C 3 0 60 40 50 40 0 × 100 60 C 4 70 20 0 30 60 60 θ 80 C 5 0 × 10 0 × 0 0 10 10 0 VI. R esults and D iscussion Table 9 shows the work assignment policy that reduces the overall cost. Component Job Cost C 1 C 2 C 3 C 4 C 5 J 7 J 2 ,J 6 J 1 J 3 J 4, J 5 , J 8 180 190,180 180 190 140, 210,200 Total Cost1470 We find the total minimum cost in comparison to the other modified Hungarian methods like Kumar [26], Haragopal and Yadaiah [27], and Betts and Vasko [28]. VII. C onclusion The study presents an improved Hungarian algorithm to solve a particular case (when the number of jobs is greater than the number of processing components) of an unbalanced assignment problem. Generally, most of the issues regarding assignments occur in the abovementioned case. The primary premise of our strategy is to allocate all tasks to be completed. If the created assignment plan is invalid, the virtual jobs will be changed, and the procedure will be continued until an actual optimal assignment strategy is discovered. We show that the assignment strategy found by the suggested approach is the best using mathematical analysis. It demonstrates that the revised algorithm is capable of determining the best assignment strategy. R eferences R éférences R eferencias 1. Kuhn, H. W. (1955). The Hungarian method for the assignment problem. Naval research logistics quarterly , 2 (1 ‐ 2), 83-97. 1 Year 2022 33 © 2022 Global Journals Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) An Improved Hungarian Algorithm for a Special Case of Unbalanced Assignment Problems N otes