Page 159 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Production Cost (` in’ 000s)
Product 1 2 3 4
Plant A 49 60 45 61
B 55 63 45 69
C 52 62 49 68
D 55 64 48 66

Solution:
Step 1: Determination of profit matrix.

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: Conversion of profit matrix into cost matrix.
Product 1 2 3 4
Plant A 7 0 4 7
B 3 1 2 3
C 5 3 4 6
D 5 7 2 5

Using Reduction Rules

Step 3: 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 4: 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 5: 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

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