Page 146 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 7: Assignment Problem – Balanced

Notes
Example: A departmental head has 4 subordinates and 4 tasks are to be performed.
Subordinates differ in efficiency and tasks differ in their intrinsic difficulty. Time each man
would take to perform each task is given in the effective matrix. How the tasks should be
allocated to each person so as to minimize the total man hours?
Subordinates I II III IV
Tasks A 8 26 17 11
B 13 28 4 26
C 38 19 18 15
D 19 26 24 10

Solution:
Using Reduction Theorem Rules

Step 1: Row-wise reduction of the matrix.

Subordinates I II III IV
Tasks A 0 18 9 3
B 9 24 0 22
C 23 4 3 0
D 9 16 14 0

Step 2: Column-wise reduction of the matrix.

Subordinates I II III IV
Tasks A 0 14 9 3
B 9 20 0 22
C 23 0 3 0
D 9 12 14 0

Step 3: Assignment of tasks to subordinates.
Subordinates I II III IV
Tasks A 0 14 9 3

B 9 20 0 22
C 23 0 3 0
D 9 12 14 0

Step 4: Calculation of the minimum total man hours associated with the assignment.
Subordinates Tasks Total Man Hours
I A 8
II C 19
III B 4
IV D 10
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