Revision:Unbalanced transportation problems

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.