In a transportation problem if the total supply equals the total demand, it is said to be balanced transportation problem. Otherwise it is said to be unbalanced transportation problem.

**Summary**

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In a transportation problem if the
total supply equals the total demand, it is** **said to be balanced transportation problem. Otherwise it is said
to be unbalanced transportation problem

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

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

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

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**Non
degenerate basic feasible Solution**: If a basic feasible solution to
a** **transportation problem contains
exactly m+n-1 allocations in independent positions, it is called a Non
degenerate basic feasible solution.

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**Degeneracy
: If **: If a basic feasible solution to a transportation problem contains** **less than m+n-1 allocations , it is
called a degenerate basic feasible solution.

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In an assignment problems number of rows
and columns must be equal

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The optimum assignment schedule remains
unaltered if we add or subtract a constant from all the elements of the row or
column of the assignment cost matrix.

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If for an assignment problem all Cij >
0 then an assignment schedule (x_{ij}) which satisfies âˆ‘C_{ij}
x_{ij} = 0 must be optimal.

Tags : Operations Research , 12th Business Maths and Statistics : Chapter 10 : Operations Research

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12th Business Maths and Statistics : Chapter 10 : Operations Research : Summary | Operations Research

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