Example: A works manager has to allocate four different jobs to four workmen. Depending on the efficiency
and the capacity of the individual the times taken by each differ as shown in the table 2. How should the tasks be
assigned one jot to a worker so as to minimize the total man-hours?
Table 2
Job
Worker
A B C D
1
10
20
18
14
2
15
25
9
25
3
30
19
17
12
4
19
24
20
10
Solution: The following steps are followed to find an optimal solution.
STEP 1: Consider each row. Select the minimum element in each row. Subtract this smallest element form all the
elements in that row. This results in the table 3.
Table 3
Job
Worker
A B C D
1
0
10
8
4
2
6
16
0
16
3
18
7
5
0
4
9
14
10
0
STEP 2: We subtract the minimum element in each column from all the elements in its column. Thus we obtain
table 4
Table 4
Job
Worker
A B C D
1
0
3
8
4
2
6
9
0
16
3
18
0
5
0
4
9
7
10
0
STEP 3: In this way we make sure that in the matrix each row and each column has atleast one zero element. Having
obtained atleast one zero in each row and each column, we assign starting from first row.
In the first row, we have a zero in (1, A). Hence we assign job 1 to the worker A. This assignment is indicated by a
square. All other zeros in the column are crossed (X) to show that the other jobs cannot be assigned to worker A as
he has already been assigned. In the above problem we do not have other zeros in the first column A.
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