1. Unbalanced Assignment Model
Lecture 24 By
Dr. Arshad Zaheer

2. RECAP Assignment Model (Maximization) Hungarian Method Steps Involved
Illustrations
Optimal Assignment

3. Unbalanced Assignment Problem
Case 1 This is the case when the total number of machines exceeds total number of jobs. In this case, introduce required number of fictitious or dummy jobs at ‘0’ cost or at the cost stated in the problem to get the balanced assignment problem. Then use the assignment technique to obtain the optimal assignment. The fictitious or dummy jobs assigned to the machines mean that the corresponding machine will not be assigned any job.

4. Unbalanced Assignment Problem
Case 2 This is the case when the total number of jobs exceeds total number of machines. In this case, introduce required number of fictitious or dummy machines at ‘0’ cost or at the cost stated in the problem to get the balanced assignment problem. Then use the assignment technique to obtain the optimal assignment. The jobs which are assigned fictitious or dummy machines will be left over.

5. Illustration Machines exceeds Jobs

6. Problem J1 J2 J3 J4 M1 2 4 3 5 M2 8 9 12 M3 11 10 M4 18 15 M5 22 20 M6 25
In this given problem, there are only four jobs while six machines. In an ideal condition there should be equal no of jobs so we need to make them equal. For this purpose we will introduce two fictitious jobs at zero cost.
Requirement: Which job is to assign which machine to get the minimum cost

7. Balanced Problem J1 J2 J3 J4 J5 J6 M1 2 4 3 5 M2 8 9 12 M3 11 10 M4 18M2 8 9 12 M3 11 10 M4 18 15 M5 22 20 M6 25

8. Step 1. Identify minimum of each rowJ1 J2 J3 J4 J5 J6
Min. Row M1 2 4 3 5 M2 8 9 12 M3 11 10 M4 18 15 M5 22 20 M6 25

9. Subtract identified no from each and every entry of corresponding rowJ1 J2 J3 J4 J5 J6
Min. Row M1 2 4 3 5 M2 8 9 12 M3 11 10 M4 18 15 M5 22 20 M6 25

10. Step 2. identify minimum of columnJ1 J2 J3 J4 J5 J6 M1 2 4 3 5 M2 8 9 12 M3 11 10 M4 18 15 M5 22 20 M6 25
Min. column

11. Subtract identified no from each and every entry of corresponding columnJ1 J2 J3 J4 J5 J6 M1 M2 1 4 6 7 M3 2 8 5 M4 14 12 M5 18 17 13 M6 21 15
Min. column 3

12. J1 J2 J3 J4 J5 J6 M1 M2 1 4 6 7 M3 2 8 5 M4 14 12 M5 18 17 13 M6 21 15

13. J1 J2 J3 J4 J5 J6 M1 M2 M3 M4 M5 M6

14. J1 J2 J3 J4 J5 J6 M1 M2 M3 M4 M5 M6

15. J1 J2 J3 J4 J5 J6 M1 M2 M3 M4 M5 M6

16. Original Tableau J1 J2 J3 J4 J5 J6 M1 2 4 3* 5 M2 3 8* 9 12 M3 11 10*M2 3 8* 9 12 M3 11
10* M4 18 15 0* M5 2* 22 20 M6 25

17. Optimal Distribution M1 ------- J3=3 M2 ------- J2=8
TOTAL =23

18. Illustration Jobs exceeds Machines

19. Problem J1 J2 J3 J4 J5 J6 M1 2 4 3 5 M2 8 9 12 15 M3 11 10 18 16 M4 20
In this given problem, there are only four machines but six jobs. In an ideal condition there should be equal no of jobs so we need to make them equal. For this purpose we will introduce two fictitious Machines at zero cost.
Requirement:
Which job is to assign which machine to get the minimum cost

20. Balanced Problem J1 J2 J3 J4 J5 J6 M1 2 4 3 5 M2 8 9 12 15 M3 11 10 1816 M4 20 M5 M6

21. Step 1. Identify minimum of each rowJ1 J2 J3 J4 J5 J6
Min.
Row M1 2 4 3 5 M2 8 9 12 15 M3 11 10 18 16 M4 20 M5 M6

22. Subtract identified no from each and every entry of corresponding rowJ1 J2 J3 J4 J5 J6
Min.
Row M1 2 1 3 M2 5 6 9 12 M3 8 7 14 4 M4 15 17 M5 M6

23. Step 2. identify minimum of columnJ1 J2 J3 J4 J5 J6 M1 2 1 3 M2 5 6 9 12 M3 8 7 14 M4 15 17 M5 M6
Min.
Column

24. J1 J2 J3 J4 J5 J6 M1 2 1 3 M2 5 6 9 12 M3 8 7 14 M4 15 17 M5 M6

25. J1 J2 J3 J4 J5 J6 M1 M2 M3 M4 M5 M6

26. J1 J2 J3 J4 J5 J6 M1 M2 M3 M4 M5 M6

27. Original Tableau J1 J2 J3 J4 J5 J6 M1 2 4 3 5 2* M2 8* 9 12 15 M3 11
10* 18 16 M4 3* 20 M5 0* M6

28. Optimal Distribution M1 ------- J5=2 M2 ------- J2=8
TOTAL =23

29. Thank You