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Shvoong Home>Science>Mathematics>Transportation Problem With Vogel’S Approximation Method. Summary

# Transportation Problem With Vogel’S Approximation Method.

Academic Paper Summary   by:Ashraful     Original Author: Md. Ashraful Babu

# Transportation problem with Vogel’s approximation method.

Factory Warehouse Availability

A B C D
F1 3 2 5 2 15

F2 2 1 4 4 24

F3 2 3 4 3 21

Requirement 13 12 16 19 60

Vogel’s approximation method is more systematic and orderly than other two methods.

Following steps are given below
1. Identify the smallest unit cost and second smallest unit cost of each row or column for determining the penalties. To calculate penalty of each row or column we use the formula Penalty = (Second lowest – lowest) costs of that row/column
2. Identify the row or column with maximum of the penalties. Also find the cell with lowest cost in the selected row or column. Allocate the maximum possible units to this cell by comparing the demand and supply associated with that cell.
3. Delete the row or column whose demand or supply in exhausted
4. Continue the process till demand and supply is exhausted.

Transportation model

Factory Warehouse Availability
Penalty
A B C D
F1 3 2 5 2 15
3-2=1

F2 2 1
12 4 4 24-12=12
2-1=1
F3 2 3 4 3 21
3-2=1
Requirement 13 12-12=0 16 19 48

Penalty 3-2=1 2-1=1 5-4=1 3-2=1

1. The penalty of all column and rows are same. So we select x22 with lowest unit cost of tk 1. Here the maximum possible allocation of 12 units to x22 and remaining supply 24 – 12 = 12 units. Hence the column for warehouse B is deleted.

The shrunken matrix is

Factory Warehouse Availability
Penalty
A B C D
F1 3 2 5 2 15
3-2=1

F2 2
12 1
12 4 4 12-12=0

4-2=2
F3 2 3 4 3 21
3-2=1
Requirement 13-12=1 0 16 19 36

Penalty 3-2=1 2-1=1 5-4=1 3-2=1

2. The maximum penalty occurs of row 2 (F2) is 2. So we select with lowest unit cost of tk 2. Here the maximum possible allocation of 12 units to x21 and remaining demand 13 – 12 = 1 units. Hence the row for F2 is deleted.

The shrunken matrix is

Factory Warehouse Availability
Penalty
A B C D
F1 3 2 5 2
15 15-15=0
3-2=1

F2 2
12 1
12 4 4 0

4-2=2
F3 2 3 4 3 21
3-2=1
Requirement 1 0 16 19-15=4 21

Penalty 3-2=1 2-1=1 5-4=1 3-2=1

3. The penalty of all column and rows are same. So we select x14 and x31 with lowest unit cost of tk 2. Here the maximum possible allocation of 15 units to x14 and remaining demand 19 – 15 = 4 units. Hence the row for F1 is deleted.

Thus the final allocation matrix is

Factory Warehouse Availability

A B C D
F1 3 2 5 2
15 15

F2 2
12 1
12 4 4 12

F3 2
1 3 4
16 3
4 21

Requirement 13 12 16 19 60

So, it can be observed that the number of occupied cells in the solution is (m + n - 1) = (3 + 4 – 1) = 6. Hence the initial solution is feasible.

The total transportation cost is
z = x14 × c14 + x21 × c21 + x22 × c22 + x31 × c31 + x33 × c33 + x34 × c34
=15 × 2 + 12 × 2 + 12 ×1 + 1 × 2 + 16 × 4 + 4 × 3
= 144
Published: May 29, 2010
 Please Rate this Summary : 1 2 3 4 5
1. Answer   Question  :    how do u use vogels approximation for maximisation
1. Answer  :    Convert the Maximization problem into Minimization problem by identifying the largest profit element in the matrix and subtracting each of the profit elements from the largest profit element Then solve it as a normal transportation problem. Regards Linesh Chungath 17.07.13 8800125336 Sunday, March 17, 2013
1. Answer   Question  :    tie occure ho jaya to kis terhan arbitrarily keya jata hi
1. Answer  :    If a tie occurs in the penalties, select the one which has the minimum cost. If there is a tie in the minimum cost also,select that row/column which will have maximum possible allocation Regards Linesh Chungath 17.03.2013 8800125336 Sunday, March 17, 2013
1. Answer   Question  :    1.how can we find the penalty if a row or column contains two similar costs.(10,20,10,60) what will be the penalty.
1. Answer  :    The Penalty will be Zero in such cases Regards Linesh Chungath 17.03.13 Sunday, March 17, 2013
1. Answer   Question  :    HOW CAN YOU SOLVE A PROBLEM HAVING DIFFERENT AMOUNT IN SUPPLIER AND DEMAND?
1. Answer  :    When Total Supply exceeds Total Demand, an additional column (a dummy demand centre)should be added to the transportation table to absorb the excess supply and the transportation cost for the cells in this column shall be set equal to zero. Vice Versa when Total Demand exceeds Total Supply Regards Linesh Chungath 17.03.2013 8800125336 Sunday, March 17, 2013
1. Answer  :    what step of vogils Saturday, June 04, 2011
1. Answer   Question  :    sample paper on vogel,s approximation method
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