30-06-2012, 01:22 PM
Transportation Models
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Introduction
Today I am going to discuss about Transportation problem.
First question that comes in our mind is what is a transportation problem?
The transportation problem is one of the subclasses of linear programming problem where the objective is to transport various quantities of a single homogeneous product that are initially stored at various origins, to different destinations in such a way that the total transportation is minimum.
F.I. Hitchaxic developed the basic transportation problem in 1941. However it could be solved for optimally as an answer to complex business problem only in 1951, when George B. Dantzig applied the concept of Linear Programming in solving the Transportation models.
Mathematical Model of Transportation Problem
Mathematically a transportation problem is nothing but a special linear programming problem in which the objective function is to minimize the cost of transportation subjected to the demand and supply constraints.
Let ai = quantity of the commodity available at the origin i,
bj = quantity of the commodity needed at destination j,
cij = transportation cost of one unit of a commodity from origin.