The objective of transportation problem is to determine the amount to be transported from each origin to each destinations such that the total transportation cost is minimized.

**Transportation
Problem**

The objective of
transportation problem is to determine the amount to be transported from each
origin to each destinations such that the total transportation cost is
minimized.

Let there be m origins
and n destinations. Let the amount of supply at the *i th* origin is *a _{i}*.
Let the demand at

The cost of transporting
one unit of an item from origin *i* to destination j is *c _{ij }*and
is known for all combinations

The objective is to
determine the quantity *x _{ij}* to be transported over all routes
(

The above transportation
problem can be written in the following tabular form:

Now the linear
programming model representing the transportation problem is given by

**Feasible Solution**:** **A feasible solution to a
transportation problem is a set of non-negative** **values *x _{ij}*(

**Basic Feasible
Solution**:**
**A feasible solution is
called a basic feasible solution if it contains** **not more than *m*+*n*â€“1
allocations, where m is the number of rows and n is the number of columns in a
transportation problem.

**Optimal Solution**:** **Optimal Solution is a
feasible solution (not necessarily basic) which** **optimizes(minimize) the
total transportation cost.

**Non degenerate basic
feasible Solution**:** **If a basic feasible solution to a transportation** **problem contains exactly
*m*+*n*â€“1 allocations in independent positions, it is called a Non degenerate
basic feasible solution. Here *m* is the number of rows and *n* is
the number of columns in a transportation problem.

**Degeneracy :**If a basic feasible
solution to a transportation problem contains less than** ***m*+*n*â€“1 allocations
, it is called a degenerate basic feasible solution. Here m is the number of*
*rows and n is the number of columns in a transportation problem.

Tags : Definition and formulation, Structure | Operations Research , 12th Business Maths and Statistics : Chapter 10 : Operations Research

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12th Business Maths and Statistics : Chapter 10 : Operations Research : Transportation Problem | Definition and formulation, Structure | Operations Research

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