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

III. P roposed A lgorithm Think about the issue of distributing a group of "n" jobs. J = J 1 , J 2 ,... J n to an execution set with "m" components. C = (C 1 , C 2 , ..., Cm). X ij , i = 1, 2,..., m; j = 1, 2,..., n (n > m), indicating that there are more tasks than components. In this case, n stands for columns and m for rows. Step-01: Enter the following values: m, n Step-02: Each column's lowest cost should be subtracted from the column it belongs. This process results in each column reducing the cost column by having at least a single zero. Step-03: Determine each row's lowest cost and then deduct it from the associated row. Step-04: Analyze the feasibility of doing an ideal task so that the smallest number of lines needed to cover each zero is calculated. If the number of lines and rows equals one, proceed to Step 7; if not, proceed to Step 5. Choose the minimum uncovered cost if the number of lines exceeds the number of rows. 1. Take the least exposed cost in the table and subtract it from each exposed cost. 2. The cost at each intersection point is added by those minimum cost. Step 06: If the case (the total number of lines and rows is equal) fails, then continue steps 04 and 05. To assign the work, look for a row with only one zero. Choose that zero and block the other zeros in the relevant columns (the same component can be performed on more than one job, but the same job cannot be assigned more than one component). Step-08: Assign the value with the lowest cost in the initial problem if there is a tie, that is, if any rows have two or more zeros. Step-09: Repeat steps 7 and 8 until all positions have been filled, that is, all jobs have been assigned to one or more processing components. Step-10: End IV. P arallelism between P roposed A lgorithm and H ungarian A lgorithm Table 1 Proposed Hungarian • This tactic is employed to address issues with unbalanced assignments. • If the number of jobs exceeds the number of processing components, all jobs must be completed using the available components.\ • There are no unfinished projects. • Related to at least one job that can be performed by a single component. • A single component can only be assigned to a single job. • This tactic is employed to address issues with unbalanced assignments. • If the number of jobs exceeds the number of components, the remaining jobs are performed by dummy components. • Some jobs aren't being completed. • A single component can only do one thing. • Only one component can be allocated to a single job. 1 Year 2022 3 © 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