Page 170 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 8: Assignment Problem – Unbalanced

To Notes
A B C D E
From a  4 7 3 4
b 4  6 3 4
c 7 6  7 5
d 3 3 7  7
e 4 4 5 7 

What should be the sequence of visit of the salesman, so that the total travelled time is minimum.
Solution:
Application of Reduction Theorem Rules

(1) Row-wise Reduced Matrix
To A B C D E
From
a  1 4 0 1
b 1  2 0 1
c 2 1  2 0
d 0 0 4  4
e 0 0 1 3 

(2) Column-wise Reduced Matrix
To A B C D E
From
a  1 3 0 1
b 1  1 0 1
c 2 1  2 0
d 0 0 3  4
e 0 0 0 3 

(i) Modified Matrix – 1
To A B C D E
From
a - 0 1 0 0
b 0 - 0 0 1
c 2 2 - 6 0
d 0 0 2 - 3
e 2 0 0 6 -

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