This work is an assignment on the course of 'Mathematics for Decision Making'. I think, it will provide some basic concept about transportation problem in linear programming.

1. Welcome To
Presentation
Khadija Tul Kubra
Id- M1516056
Welcome
To
The Presentation…..
Mirza Tanzida

2. Transportation Problem
In Linear Programming

3. What
Is
Transportation Problem ?

4. An Overview…
Formalized by the French mathematician Gaspard Monge in 1781
In the 1920s A.N. Tolstoi was one of the first to study the transportation problem
mathematically.
In 1930,he published a paper “Methods of Finding the minimal Kilometrage in
cargo Transportation in Space”
Major advances were made in the field during world war second by Leonid
Kantorovich .
Sometimes stated as Monge-Kantorovich transportation.
But the linear programming formulation is known as the Hitchcock-Koopmans
transportation problem.

5.  In mathematics and economics, transportation
theory is given to
- the study of optimal transportation and
- allocation of resources
 Used in operational research.
(continued)
An Overview…

6. Mathematical Calculation

7. Methods of Finding Initial BasicFeasible Solution
• The North-West Corner Method(NWCM)
• The Row-Minima Method (RMM)
• The Column Minima Method (CMM)
• The Matrix Minima Method (MMM)
• The Vogel’s Approximation Method (VAM)

8. Major Considerations of Each Method
 North West Corner Method
The simplest of the procedures used to generate an initial feasible
solution is NWCM. It begins with the North West or upper left corner cell of transportation table.
 Least Cost Method
The allocation according to this method is very useful as it takes into consideration the lowest cost
and therefore, reduce the computation as well as the amount of time necessary to arrive at the
optimal solution.
 Matrix Minima Method
Look for the raw and the column corresponding to which cost is minimum in the entire
transportation table.
 Vogel’s Approximation Method (VAM)
This method is preferred over the others methods because the initial feasible solution obtained is
either optimal or very close to the optimal solution.

9. Transportation Table:
Example

11. Solution of Transportation problemBy NWCM
Factory A B C D Supply
1
4 7 7
1 100
2
12 3 8 8
200
3
8 10 10 5 150
Demand 80 90 120 160 450
80 20
70 120
150
10

12. Feasible solutions
1st allocation is made on cell (1,1);Magnitude being Xıı = min (80,100)
2nd allocation is made on cell (1,2);Magnitude being Xı2 = min (100-80,90)
3rd allocation is made on cell (2,2);Magnitude being X22 = min (90-20,200)
4th allocation is made on cell (2,3);Magnitude being X23 = min (120,200-70)
5th allocation is made on cell (2,4) ;Magnitude being X24 = min (200-70-120,160)
6th allocation is made on cell (3,5);Magnitude being X23 = min (160-10,150)

13. Finding of Total Transportation Cost
Z=
Z= (80 * 4)+ (20*7)+(70*3)+(120*8)+(10*8)+(150*5)
Z= 320+140+210+960+80+750
Z=2460
Note: NWCM does not consider cost factors.