he Freezer Fresh Company freezes fresh vegetables at three p

he Freezer Fresh Company freezes fresh vegetables at three plants and then ships them to four warehouses from which grocery stores are supplied. The following information is known about the company.

                                

Plant

Capacity

Warehouse

Demand

1

100

A

60

2

100

B

85

3

100

C

90

D

65

                                         

Costs

To

A

B

C

D

From

1

7

10

9

4

2

3

5

10

3

3

2

6

9

4

Using the SHORT-CUT method, find the OPTIMAL solution and  TOTAL COST. Must use Short-cut and show steps.

Plant	Capacity	Warehouse	Demand
1	100	A	60
2	100	B	85
3	100	C	90
		D	65

Solution

Solution:

A short-cut approach to solving the transportation problem is the Vogel Approximation Method (VAM), which is a very simple means of performing step 1 of the Transportation Method. Application of VAM to a given problem does not guarantee that an optimal solution will result. However, a very good solution is invariably obtained, and is obtained with comparatively little effort. For many purposes, using VAM to carry out step 1 of the Transportation Method eliminates (or all but eliminates) the need for performing steps 2 and 3.

The VAM method uses the difference between minimum and the next minimum costs of each row and column.

This is the penalty or opportunity cost of not utilising the next best alternative. The highest penalty is given the 1st preference This need not be lowest cost.

For example if a row has minimum cost as 3, and the next minimum as 2 then penalt is 1;   

The given problem is balanced minimization transportation problem. The objective of the company is to minimise the cost let us find the initial feasible solution using Vogel\'s Approximation method (VAM).

Plant/Warehouse	A	B	C	D	Capacity		Difference
1	7	10	9	4	100/90/0	1
2	3	5	10	3	100/35/0	2
3	2	6	9	4	100/40/0	2
Demand	60/0	85/50/10/0	90/0	65/0	300
Difference	1	1		1
		4		-
		0		0