what is assignment problem method ,type and exampled with numerical and live example is presented

1. Assignment model
By :-
Rishika Gupta
Pallavi Singh
Ekta Kumari
Ankita Kumari
Manshi Singh.
Khusboo Singh

2. Assignment problem
To assign the job to the right operator.
Assignment problem arises in diverse situations,
where one needs to determine an optimal way to
assign subjects to subjects in the best way.
Objective of Assignment problem

3. Application of assignment problem
•Assignment of
workers of machines.
•Salesmen to different
sales area.
•Contract to bidders.

4. Assumption of assignment problem
•Number of jobs is equal to the number of machines or persons.
•Each man or machine is assigned only one job.
•Assigning criteria is clearly specified (minimizing cost or maximizing
profit).

5. Methods of solving assignment problem
•Hungarian Method
•Travelling salesman
problem
•Simplex methods of
solving assignment
problem

6. Hungarian method of solving
assignment problem
Types of Assignment problem
•Balanced assignment problem (m*n)
•Unbalanced assignment problem (m is not equal to n)

7. Steps of Hungarian methods
Subtract the minimum element from each element of a row
Subtract the minimum element from each element of the column
Assign zero to each row one by one
Assign zero to each column one by one
Draw the minimum no of lines to cover all zero of matrix

8. Add minimum no. at intersected point
Assign zero to each row and cut all the of belonging column.
Put the original value of assigned zero
Subtract uncovered Zero from minimum no.

9. Balanced assignment problem
Row min reduction Column min reduction

10. Draw min line to cut the zero
Assign zero to each row
and cut other zero of the
same column
1
2
3
4
Put the original value of
assigned zero

11. Unbalanced assignment
problem
Add dummy column
Row reduction

12. Draw lines to cut zero
Subtract uncovered element with
min element
Again draw the line Subtract uncovered element
5

13. Assign the Zero of each row and
cut other zero
Draw lines to cut zero
Put original value of assigned Zero

14. •The traveling salesman problem consists of a salesman and a set of
cities .
•Traveling salesman method minimize the total length of the trip.
•The problem was first formulated as a mathematical problem by
Manger (1930) and is one of the most intensively studied problems in
optimization.
•To find the shortest route of trip.
•To find the minimum cost .

15. TSP though Hungarian method
1 E A

16. SIMPLEX METHOD OF SOLVING
ASSIGNMENT PROBLEM
Since each assignment problem can be formulated as
a 0 or 1 which becomes integer linear programming
problem.
Such a problem can also be solved by the simplex
method

17. conclusion
• An assignment problem is considered as a
particular case of a transportation problem
because the no. of row equals to columns.
• Hungarian method is used to obtained
optimal solution of assignment problem.