Assignment Problems

1. Travelling Salesman Problem &
Assignment Maximization
Problem
By,
Muhammed Abdulla NC

2. CONTENT
 Introduction about TATA Motors
 Case Briefing
 Introduction to Travelling Salesman
problem
 Introduction to Assignment Problem
 Solution
 Conclusion

3. TATA MOTORS
 Tata Motors Limited (formerly TELCO)
 Is an
Indian multinational automotive manufactur
ing company
 Founded in 1945 as a manufacturer
of locomotives
 Tata Motors entered the passenger vehicle
market in 1991
 Founder : J R D Tata
 Chairman : Cyrus Mistry

4. TATA Motors launch their new SUV.
They want to supply to the major cities of
India.
They face an issue regarding production
cost.
They need to minimize their cost and
maximize their profit.
And also they want to reach their product
to all destinations with minimum
transportation distance.

6. It is a particular case of transportation problem that
is in which no of operations are to be assigned to
an equal no of operators.
No of job = No of machine or operator
Matrix must be in square form,
ie, No of row = No of column
If it is a non square matrix, then add a dummy row
or dummy column to make it a square matrix.

7. Contd.
It is a type of Linear Programming Problem.
We are solving the problem by the help of
Hungarian Algorithm.
Merits.
 Production manager can formulate optimal
maximum product mix.
 It helps manager to improve his decision making
ability
 It increases the profit and decreases the cost.
De Merits.
 There may be cases of infeasibility and
unboundedness.
 It doesn’t consider the effect of time and

8. Profit Maximization
A B C D E F
1 68 120 80 30 45 100
2 21 76 211 66 96 113
3 74 46 118 65 50 165
4 84 27 57 91 59 90
5 68 55 123 43 69 89
6 42 78 113 187 33 48
Amount in Crore. Total Profit=751 Cr

9. Travelling Salesman problem
It is a network problem consisting of finding a route
from one node to another that yield minimum
cost.
Objective Function:
n-1 n
minimize Z= ∑ ∑ Cij xij
i=1 j=1
TSP can be solved by the technique of Assignment
problem

10. SOLUTION
Destinatio A B C D E F
n
A 11 15 16 9 9
∞
B 11 10 15 14 10
∞
C 15 10 8 13 9
∞
D 16 15 8 11 10
∞
E 9 14 13 11 6
∞
F 9 10 9 10 6
∞
Solution is A->B->C->D->E->F-
>A

11. CONCLUSION
 By the help of assignment problem the TATA
Motors can maximize its profit and also minimize
their cost of production.
 As it is a forecasting method some time it will not
give appropriate answer.

12. Thank you