# Unbalanced Transportation Problem

So far we have assumed that the total supply at the origins is equal to the total requirement at the destinations.

Specifically,

Si = Dj

But in certain situations, the total supply is not equal to the total demand. Thus, the transportation problem with unequal supply and demand is said to be unbalanced transportation problem.

How to solve?

If the total supply is more than the total demand, we introduce an additional column, which will indicate the surplus supply with transportation cost zero. Similarly, if the total demand is more than the total supply, an additional row is introduced in the table, which represents unsatisfied demand with transportation cost zero. The balancing of an unbalanced transportation problem is illustrated in the following example.

## Example of Unbalanced Transportation Problem

Plant Warehouse Supply
W1 W2 W3
A 28 17 26 500
B 19 12 16 300
Demand 250 250 500

Solution:

The total demand is 1000, whereas the total supply is 800.

Si < Dj

Total supply < total demand.

To solve the problem, we introduce an additional row with transportation cost zero indicating the unsatisfied demand.

Plant Warehouse Supply
W1 W2 W3
A 28 17 26 500
B 19 12 16 300
Unsatisfied demand 0 0 0 200
Demand 250 250 500 1000

Using matrix minimum method, we get the following allocations.

Use Horizontal Scrollbar to View Full Table Calculation.

Plant Warehouse Supply
W1 W2 W3
A 17 500
B 19 300
Unsatisfied demand 0 0 200
Demand 250 250 500 1000
##### Initial basic feasible solution

50 X 28 + 450 X 26 + 250 X 12 + 50 X 16 + 200 X 0 = 16900.