Page 151 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Step 6: Requirement 2: By intuition.
Sales girls A1 A2 A3 A4
Sales counters M 41 72 39 52
N 22 29 49 65
O 27 39 60 51
P 45 50 48 52

Step 7: Calculation of total time on optimal assignment.
Sales Counters Sales girls Total sales Time
M A3 39
N A1 22
O A2 39
P A4 52
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Inference
The test of optimality can be confirmed when an assignment is carried out by intuition. As it is
apparent from the above revealed results, that the assignment by intuition would come out with
152 hours. As against hours when Hungarian approach is used.

Example: A project consists of 4 major jobs for which 4 contractors have submitted their
tenders. The tender amount quoted in lakhs of rupees are given in the matrix below:

Jobs A B C D
Contractors 1 10 24 30 15
2 16 22 28 12
3 12 20 32 10
4 9 26 34 16

Find the assignment which minimizes the total project cost [each contractor has to be assigned
at least one job].
Solution:

Using reduction rules

Step 1: Row-wise reduction of the matrix.

Jobs A B C D
Contractors 1 0 14 20 5
2 4 10 16 0
3 2 10 22 0
4 0 17 25 7

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