So far we have assumed that the total supply at the origins is equal to the total requirement at the destinations.
Specifically,
S_{i} = D_{j}
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.
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.
S_{i} < D_{j}
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.
Plant | Warehouse | Supply | ||
---|---|---|---|---|
W1 | W2 | W3 | ||
A | 17 | |||
B | 19 | |||
Unsatisfied demand | 0 | 0 | ||
Demand | 1000 |
50 X 28 + 450 X 26 + 250 X 12 + 50 X 16 + 200 X 0 = 16900.