Unbalanced Problems
These notes carry on from Revision Notes: Transportation Problems and Revision Notes: Transportation Algorithm
What is an unbalanced problem
Often, you will get a transportation problem where the total supply does not equal the total demand. For example, in the table below.
| Warehouse 1 | Warehouse 2 | Warehouse 3 | Supply | |
|---|---|---|---|---|
| Bakery 1 | 5 | 8 | 4 | 7 |
| Bakery 2 | 7 | 2 | 8 | 10 |
| Demand | 6 | 8 | 9 |
The total demand exceeds the total supply, so clearly, not all warehouses will get their total order.
'Dummy' Dealers and Suppliers
In cases where you have unbalanced problems, this is solved by introducing a dummy supplier or dealer which can meet the excess. Clearly, they will not really be able to supply or take in loaves of bread, but we can make this adjustment at the end.
| Warehouse 1 | Warehouse 2 | Warehouse 3 | Supply | |
|---|---|---|---|---|
| Bakery 1 | 5 | 8 | 4 | 7 |
| Bakery 2 | 7 | 2 | 8 | 10 |
| Dummy | 0 | 0 | 0 | 6 |
| Demand | 6 | 8 | 9 |
It costs nothing to transport to and from the dummy, because it doesn't really exist. You can now use the algorithms and formulate linear programming problems as you did before.