Page 160 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 8: Assignment Problem – Unbalanced

Step 6: Determination of profit associated with the assignment. Notes
Plant Product Total Profit (Rs.)
A 2 8,000
B 4 5,000
C 1 3,000
D 3 6,000
Total Profit 22,000

When negative signs are used to make the optimal assignment.
Step 1: Profit matrix with (–)ve signs.

Product 1 2 3 4
Plant A –1 –8 –4 –1
B –5 –7 –6 –5
C –3 –5 –4 –2
D –3 –1 –6 –3

Step 2: Row-wise reduction of the matrix.

Product 1 2 3 4
Plant A 7 0 4 7
B 2 0 1 2
C 2 0 1 3
D 3 5 0 3

Step 3: Column-wise reduction of the matrix.
Product 1 2 3 4
Plant A 5 0 4 5
B 0 0 1 0
C 0 0 1 1
D 1 5 0 1

Step 4: Trial assignment.

Product 1 2 3 4
Plant A 5 0 4 5
B 0 0 1 0
C 0 0 1 1
D 1 5 0 1

Step 5: Determine of profit associated with the assignment.
Plant Product Total Profit (`)
A 2 8,000
B 4 5,000
C 1 3,000
D 3 6,000
Total Profit 22,000

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