IGNOU MMPO 1 2026 2027 - Solve the following assignment problem to find the optimal solution us

Question

Solve the following assignment problem to find the optimal solution using the Hungarian
Assignment Method (HAM). Four workers are to be assigned to four different jobs (A, B,
C, D) so as to minimize the aggregate time taken (in minutes). Based on previous
experience, he has the information that the time taken by each worker for each job is
given in the table below:
Time Taken (in minutes) by 4 Workers
Worker Job
Job A Job B Job C Job D
1 45 40 51 67
2 57 42 63 55
3 49 52 48 64
4 41 45 60 55

09 Jul 2026

Answer :

Word Count : 666

The assignment problem is solved using the Hungarian Assignment Method to minimize the total time taken by assigning four workers to four different jobs. The given time matrix is: | Worker | Job A | Job B | Job C | Job D | | ------ | ----: | ----: | ----: | ----: | | 1 | 45 | 40 | 51 | 67 | | 2 | 57 | 42 | 63 | 55 | | 3 | 49 | 52 | 48 | 64 | | 4 | 41 | 45 | 60 | 55 | Step 1: Row reduction Subtract the smallest element of each row from all elements of that row. For Worker 1, minimum value = 40: | | A | B | C | D | | - | -: | -: | -: | -: | | 1 | 5 | 0 | 11 | 27 | For Worker 2, minimum value = 42: | | A | B | C | D | | - | -: | -: | -: | -: | | 2 | 15 | 0 | 21 | 13 | For Worker 3, minimum value = 48: | | A | B | C | D | | - | -: | -: | -: | -: | | 3 | 1 | 4 | 0 | 16 | For Worker 4, minimum value = 41: | | A | B | C | D | | - |

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