Basic assumption of transportation model, Managerial Accounting

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.

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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

     
 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

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

 

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.

 

 

 

Posted Date: 12/7/2012 7:25:41 AM | Location : United States







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