In this method, we start with the first column and allocate as much as possible in the lowest cost cell of column, so that either the demand of the first destination center is satisfied or the capacity of the 2nd is exhausted or both. There are three cases:
a) If the demand of first distribution center is satisfied, cross off the first column and move to the column on the right.
b) If the supply (capacity) of the ith plant is satisfied, cross off the ith row and reconsider, the first column with the remaining demand.
c) If the demand (requirement) of the first distribution center as also the capacity of ith plant are .completely satisfied, make a zero allotment in the second lowest cost cell of the first column. Cross off the column as well as the ith row and move to the second column.
Continue the process for the resulting reduced transportation table till all the conditions are satisfied. The matrix below shows the solution with this method which is similar to Row Minima method.
Distribution centers


X 
Y 
Supply 

A 
Rs.2000
1000 
Rs.=5380 
1000 
Plants 
B 
Rs.2500
1300 
Rs. 2700
200 
1500 

C 
Rs.2500  Rs.1700
1200 
1200 

Demand 
2300 
1400 
3700 
Let us solve the given problem with the help of this method. Lowest cost cell in the column is AX. We allocate minimum i.e., 1000 out of 2300, 1000. With this the capacity of plant A is exhausted and thus row one is crossed off. The next allocation is made in cell BX as it now has the minimum, cost of Rs. 2500 in the first column, We allocate minimum 1300 in this cell. Now the demand of distribution center X is satisfied we can cross the first column.
Now we move to the second column in this minimum cost cell is CY. Allocate 1200 in this cell out of 14,00 and 12,00. Consider the next least cost cell in this column which is BY in which we can allot only Now all the conditions are satisfied.
Transporation cost associated with this solution is
Z = Rs. (2000 × 1000 + 2500 × 1300 + 1700 × 1200 + 2700 × 200)
= Rs. 78.34,000
which is same as obtained with solution by rowminima method.
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