Transportation Problem - 5 - Vogal's Approximation Method (VAM)-1
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Obtaining Initial Solution of a Transportation Problem by Vogal's Approximation Method (VAM)
Begin by computing for each row and column a penalty equal to the difference between the two smallest costs in the row and column. To be more precise - Penalty means the difference the least cost and the immediate higher cost in a row or column. A penalty here can never be zero or negative, as we subtract the least cost from the immediate higher cost in each row and column. Repetition of the least cost or immediate higher cost in the same row or column does not make any difference.
Next find the row or column with the largest penalty.
Choose as the first basic variable; the variable in this row or column that has the smallest cost.
As described in the earlier method, make this variable as large as possible(i.e. demand or supply, whichever is lower becomes the quantity of allocation). Cross out row or column, and change the supply or demand associated with the basic variable.
Now recompute new penalties (using only cells that do not lie in a crossed out row or column), and repeat the procedure until only one uncrossed cell remains. Set this variable equal to the supply or demand associated with the variable, and cross out the variable’s row and column.
Determine an initial basic feasible solution to the following transportation problem using VAM, if the objective is to minimize the transportation cost:
Source Destination
D1 D2 D3 D4 Supply
S1 1 2 1 4 30
S2 3 3 2 1 50
S3 4 2 5 9 20
D 20 40 30 10 100
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