Page 145 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Solve the following assignment problem and find the minimum cost.
Jobs I II III IV
Workers A 10 12 19 11

B 5 10 7 8

C 12 14 13 11
D 8 15 11 9

Solution:
Using Reduction Rules

Step 1: Row-wise Reduction of the matrix.

Jobs I II III IV
Workers A 0 2 9 1

B 0 5 2 3

C 1 3 2 0
D 0 7 3 1

Step 2: Column-wise Reduction of the matrix.
Jobs I II III IV
Workers A 0 0 7 1
B 0 3 0 3

C 1 1 0 0
D 0 5 1 1

Step 3: Assignment of jobs to workers.
Jobs I II III IV
Workers A 0 0 7 1
B 0 3 0 3

C 1 1 0 0
D 0 5 1 1

Step 4: Calculation of the Minimum total job cost associated with the assignment.
Workers Jobs Total Cost (Rs.)
A II 12
B III 7
C IV 11
D I 8
Therefore Total job cost 38

Inference
The minimum total cost required to complete the assignment is ` 38.

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