Basic Assumption of Transportation Model
The basic assumption of the model is that the transportation cost on a given route is directly proportional to the number of units transported. The "unit of transportation" will differ based on the "commodity" transported i.e. a truck load may be a better unit than single product units.
![559_diagram1.jpg](https://www.expertsmind.com/CMSImages/559_diagram1.jpg)
m = Source
n = Destination
A source or destination is represented by a node. The line joining a source with a destination represents the route through which the commodity is transported.
The quantity of supply at source i is ai and the demand at destination j is bj. The "unit" transportation cost between source i and destination j is cij
Let xij represent the amount transported from i to destination j.
The LP Model symbolizing the transportation problem is given usually as:
![1127_diagram2.jpg](https://www.expertsmind.com/CMSImages/1127_diagram2.jpg)
xij > 0 for all i and j
(1) It stipulates that the sum of the shipments from a source cannot exceed its supply.
(2) It requires that the sum of the shipments to a destination must satisfy its demand.
![529_diagram3.jpg](https://www.expertsmind.com/CMSImages/529_diagram3.jpg)
The model explained above implies that the total supply
must at least equal the total demand if the total supply equal the total demand then it is called a balanced transportation model. It differs from the above model in the fact that all constraints are equations.
![1529_diagram5.jpg](https://www.expertsmind.com/CMSImages/1529_diagram5.jpg)
In actual life, this is not essentially true. Though, a transportation model can always be balanced. The balancing, in addition to its usefulness in modeling certain practical situations is important for the development of a solution method that fully exploits the special structure of the transportation model.