Q1.
Machines
A B C D E
Jobs 1[ 4 3 6 2 7
2[ 10 12 11 14 16
3[ 4 3 2 1 5
4[ 8 7 6 9 6]
Soln:
STEP I:
The given matrix is unbalanced matrix.Hence add a row of "0"
[ 4 3 6 2 7
10 12 11 14 16
4 3 2 1 5
8 7 6 9 6
0 0 0 0 0]
STEP II:
Process row wise.
[2 1 4 0 5
0 2 1 4 6
3 2 1 0 4
2 1 0 3 1
0 0 0 0 0]
Number of straight lines N=4
Order of matrix n=5
N<n
Therefore the smallest value in the previous matrix is "1" subtract from the remaining values and add in the intersecting points.
[ 2 0 3 0 4
0 1 0 4 5
3 1 0 0 3
3 1 0 4 1
1 0 0 1 0]
Number of Straight Lines N =5
Order of Matrix n=5
N=n
Assign the jobs to machines.
A B C D E
1[ 2 0 3 0 4
2[ 0 1 0 4 5
3 [ 3 1 0 0 3
4 [3 1 0 4 1
5[ 10 0 1 0]
1----->B ; 2-->A ; 3-->D; 4---> C ; 5-->E
Cost= 3+10+1+6+0
=Rs.20
Machines
A B C D E
Jobs 1[ 4 3 6 2 7
2[ 10 12 11 14 16
3[ 4 3 2 1 5
4[ 8 7 6 9 6]
Soln:
STEP I:
The given matrix is unbalanced matrix.Hence add a row of "0"
[ 4 3 6 2 7
10 12 11 14 16
4 3 2 1 5
8 7 6 9 6
0 0 0 0 0]
STEP II:
Process row wise.
[
Number of straight lines N=4
Order of matrix n=5
N<n
Therefore the smallest value in the previous matrix is "1" subtract from the remaining values and add in the intersecting points.
[
Number of Straight Lines N =5
Order of Matrix n=5
N=n
Assign the jobs to machines.
A B C D E
1[ 2 0 3
2[ 0 1
3 [ 3 1
4 [3 1 0 4 1
5[ 1
1----->B ; 2-->A ; 3-->D; 4---> C ; 5-->E
Cost= 3+10+1+6+0
=Rs.20
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