The document describes Vogel's Approximation Method for solving transportation problems. It involves the following steps: 1) Calculate penalties for each supply row and demand column by taking the difference between the two smallest unit costs. 2) Select the row or column with the highest penalty and allocate to the cell with the minimum unit cost, up to the supply or demand amount. 3) Adjust supplies and demands, eliminate satisfied rows and columns, and set zeros, then repeat until all supply and demand is satisfied.

1. Operation Research
Topic Name :- Vogel’s Approximation
Method

2. Introduction

3.  Step1: Calculate penalty for each row and column by taking the difference between the two smallest unit costs. This penalty or extra cost has to be
paid if one fails to allocate the minimum unit transportation cost.
 Step2: Select the rowor column with the highest penalty and select the minimumunit cost of that row or column. Then, allocate the minimum of supply
or demand values in that cell. If there is a tie, then select the cell where maximum allocation could be made.
 Step1: Calculate penalty for each row and column by taking the difference between the two smallest unit costs. This penalty or extra cost has to be
paid if one fails to allocate the minimum unit transportation cost.
 Step2: Select the rowor column with the highest penalty and select the minimumunit cost of that row or column. Then, allocate the minimum of supply
or demand values in that cell. If there is a tie, then select the cell where maximum allocation could be made.
Vogel’sApproximation Method

4. Step3: Adjust the supply and demand and eliminate the satisfied row or column.
If a row and column are satisfied simultaneously, only of them is eliminated and
the other one is assigned azerovalue.Anyrow or column having zero supply or
demand, can not be used in calculating future penalties.
Step4: Repeat the process until all the supply sources and demand destinations
are satisfied.
Step3: Adjust the supply and demand and eliminate the satisfied row or column.
If a row and column are satisfied simultaneously, only of them is eliminated and
the other one is assigned azerovalue.Anyrow or column having zero supply or
demand, can not be used in calculating future penalties.
Step4: Repeat the process until all the supply sources and demand destinations
are satisfied.

5. S u p p ly R o w D iff.
1 9 3 0 5 0 1 0
7 0 3 0 4 0 6 0
4 0 8 7 0 2 0
8
D e m a n d 3 4
C o l.D iff.
9
1 0
1 2
2 1 2 2 1 0 1 0
D 1 D 2 D 3
S 1
S 2
S 3
5 8 7
D 4
1 4
7
9
1 8
S u p p ly R o w D iff.
1 9 5 0 1 0
5
7 0 4 0 6 0
4 0 7 0 2 0
D e m a n d 3 4
C o l. D iff.
D 1 D 3 D 4
S 1 7
S 2 9
S 3 1 0
5 7 1 4
2 1 1 0 1 0
9
2 0
2 0
S u p p ly R o w D iff.
5 0 1 0
4 0 6 0
7 0 2 0
1 0
D e m a n d 3 4
C o l. D iff. 1 0 1 0
4 0
2 0
5 0
D 3 D 4
S 1 2
S 2 9
S 3 1 0
7 1 4
S u p p ly R o w D iff.
5 0 1 0
2
4 0 6 0
D e m a n d 3 4
C o l.D iff.
2 0
1 0 5 0
4 0
7 4
S 1 2
S 2 9
D 3 D 4
S u p p ly R o w D iff.
4 0 6 0
7 2
D e m a n d 3 4
C o l.D iff.
2 0
7 2
S 2 9
D 3 D 4

7. Advantage

8. Disadvantage

9. ThankYouThankYou

10. ThankYouThankYou