Transportation Models
Autor: goude2017 • April 8, 2018 • 948 Words (4 Pages) • 483 Views
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Vogel's Approximation Method (VAM)
This is the most popular method of developing the initial feasible solution since usually produces an optimal or near- optimal starting solution. One study found that VAM yields an optimum solution in 80 percent of the sample problems tested. The method takes costs into account in allocation. There are five steps that are followed in applying this heuristic:
Step I: Determine the difference between the lowest two cells in all rows and columns, including dummies.
Step II: Allocate as much as possible to the lowest-cost cell in the row or column with the highest difference. If two or more differences are equal, allocate as much as possible to the lowest-cost cell in these rows or columns.
Step III: Adjust supply and demand for the non-crossed rows and columns.
Step IV: Recalculate the differences between the two lowest cells remaining in all rows and columns, then go to Step II. Any row and column with zero supply or demand should not be used in calculating further differences. Repeat step IV until exactly one row or column is left unallocated.
Step V: When exactly one row or column is left, all the remaining variables are basic and are assigned the only feasible and remaining allocation.
Step VI: Deduce the transportation schedule hence calculate the total transportation payoff.
Example
Solve Example I using the Vogel’s Approximation Method VAM method.
Exercises
Question One
The distribution of commodity from warehouses A, B, C, and D is planned to three sources P, Q, and R. The level of availability’s and requirements at various sources are given in the following matrix with related cost of transportation as cells of the matrix.
P
Q
R
Availability
A
2
7
4
5
B
3
3
1
8
C
5
4
7
7
D
1
6
2
14
Requirements
7
9
18
34
Required
Work out the optimal cost of distribution. Use VAM
Question Two
Solve the problem given in the following matrix using;
- North West Corner method,
- Least Cost method and
- Vogel’s Approximation method
D
E
F
Supply
A
6
4
1
50
B
3
8
7
40
C
4
4
2
60
Demand
20
95
35
150
Question Three
Find the solution for the transportation cost and supply/demand matrix given below using;
- North West Corner method,
- Least Cost method and
- Vogel’s Approximation method
Supply Points
Destinations
Supply
D1
D2
D3
D4
P1
19
30
50
12
7
P2
70
30
40
60
10
P3
40
10
60
20
18
Demand
5
8
7
15
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