The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.

1. TOPIC: ASSIGNMENT MODEL
OPERATION RESEARCH

2. ASSIGNMENT MODEL

3. ASSIGNMENT MODEL
• Assigning of jobs to factors (men or machine) to
get most optimum output or get least cost.
• Hungarian method is the mostly used method of
solving assignment problems.
• Types of Assignment problems:
(i) Balanced
(ii) Unbalanced

4. OBJECTIVES
(i) No workers is more than one job.
(ii) No job is allotted to more than one worker.
(iii)Total time taken to complete a job is
minimum.
(iv)The work done is cost effective.

5. BALANCED ASSIGNMENT
• An assignment is called balanced assignment problem if
the number of persons (factors) is same as the number
of jobs.
J1 J2 J3 _ _ _ _ _ _ _ _ _ _ _ _ Jn
P1 T11 T12 T13 _ _ _ _ _ _ _ _ _ _ _ _ T1n
P2 T21 T22 T23 _ _ _ _ _ _ _ _ _ _ _ _ T2n
P3 T31 T32 T33 _ _ _ _ _ _ _ _ _ _ _ _ T3n
I I I I _ _ _ _ _ _ _ _ _ _ _ _ I
I I I I _ _ _ _ _ _ _ _ _ _ _ _ I
Pn Tn1 Tn2 Tn3 _ _ _ _ _ _ _ _ _ _ _ _ Tnn

6. EXAMPLE OF BALANCED PROBLEM
1 2 3 4
A 1 8 4 1
B 5 7 6 5
C 3 5 4 12
D 3 1 6 3
PROFITS (IN 1000’s)
PLANTS
Solve the following assignment problem to get
maximum profit:

7. METHOD
STEP 1
• Subtract all the element of
each row from the largest
elements of respective
rows.
STEP 2
• Subtract the least element of
each column from other
elements of respective
column and allot jobs.
1 2 3 4
A 7 0 4 7
B 2 0 1 2
C 9 7 8 0
D 3 5 0 3
PROFIT
S
PLANTS
PROFITS
PLANTS
1 2 3 4
A 5 0 4 7
B 0 0 1 2
C 7 7 8 0
D 1 5 0 3
0

8. METHOD
• Hence the optimum solution is:
(i) A2
(ii) B1
(iii) C4
(iv) D3
Hence the total profit will be
8000+ 5000+ 12000 +6000 = 31000
8000
8000
12000
6000

9. UNBALANCED ASSIGNMENT
• An assignment is called unbalanced assignment problem
if the number of persons (factors) is not same as the
number of jobs.
J1 J2 J3 _ _ _ _ _ _ _ _ _ _ _ _ Jn-1
P1 T11 T12 T13 _ _ _ _ _ _ _ _ _ _ _ _ T1(n-1)
P2 T21 T22 T23 _ _ _ _ _ _ _ _ _ _ _ _ T2(n-1)
P3 T31 T32 T33 _ _ _ _ _ _ _ _ _ _ _ _ T3(n-1)
I I I I _ _ _ _ _ _ _ _ _ _ _ _ I
I I I I _ _ _ _ _ _ _ _ _ _ _ _ I
Pn Tn1 Tn2 Tn3 _ _ _ _ _ _ _ _ _ _ _ _ Tn(n-1)

10. EXAMPLE OF UNBALANCED PROBLEM
Solve the following assignment problem to get it
completed in least time:
A B C D E
1 62 78 50 101 82
2 71 84 61 73 59
3 87 92 111 71 81
4 48 64 87 77 80
JOBS
MACHINES
5 0 0 0 0 0

11. METHOD
Subtract all the element of each row from
the largest elements of respective rows.
•STEP 1
A B C D E
1 39 23 51 0 19
2 13 0 23 11 25
3 24 19 0 40 30
4 39 23 0 10 7
5 0 0 0 0 0
JOBS
MACHINES

12. METHOD
Subtract the least element of each column
from other elements of respective column
and allot jobs.
•STEP 2
V A B C D E
1 39 23 51 0 19
2 13 0 23 11 25
3 24 19 0 40 30
4 39 23 0 10 7
5 0 0 0 0 0
JOBS
MACHINES
0
0 0 0 0

13. METHOD
Cancel all zeros by drawing lines less than
the number of rows or columns.
•STEP 3
A B C D E
1 39 23 51 0 19
2 13 0 23 11 25
3 24 19 0 40 30
4 39 23 0 10 7
5 0 0 0 0 0
JOBS
MACHINES

14. METHOD
Choose the least uncovered element and
add it to all intersection points and subtract
it from all uncovered elements.
•STEP 4
A B C D E
1 32 23 51 0 12
2 6 0 23 11 18
3 17 19 0 40 23
4 32 23 0 10 0
5 0 7 7 7 0
JOBS
MACHINES
0
0

15. METHOD
• Hence the optimum solution is:
(i) A5 0
(ii) B2 84
(iii) C3 111
(iv) D1 101
(v) E4 80
Hence the total profit will be
0+ 84+ 111 +101+ 80 = 376

16. THANK YOU