Page 150 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 7: Assignment Problem – Balanced

Solution: Notes
Using Reduction Rules

Step 1: Row-wise reduction of the matrix.
Sales girls A1 A2 A3 A4
Sales counters M 2 33 0 13
N 0 7 27 43
O 0 12 33 24
P 0 5 3 7

Step 2: Column-wise reduction of the matrix.
Sales girls A1 A2 A3 A4
Sales counters M 2 28 0 6
N 0 2 27 36
O 0 7 33 17
P 0 0 3 0
L 1 L 2

Step 3: Hungarian Approach used.
Sales girls A1 A2 A3 A4
Sales counters M 4 28 0 6
N 0 0 25 34
O 0 5 31 15
P 2 0 3 0

Step 4: Trial assignment.

Sales girls A1 A2 A3 A4
Sales counters M 4 28 0 6
N 0 0 25 34
O 0 5 31 15
P 2 0 3 0

Step 5: Calculation of total time on optimal assignment.

Sales Counters Sales girls Total sales Time
M A3 39
N A2 29
O A1 27
P A4 52
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