When the total of allocations of a transportation problem match with supply and demand values the solution is called?

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10 Questions 16 Marks 30 Mins

Concept:

A non-degenerate basic feasible solution

For m × n transportation problem solution is called non-degenerate when the following two conditions are satisfied.

Total number of allocations exactly equal to m + n – 1
This m + n – 1 allocation must be at an independent position.

Calculation:

Given:

Number of supply centers (m) = 4

Number of demand centers (n) = 5

As the case given is unbalanced as demand is less, therefore we have to add extra demand.

Updated number of demand centers (n) = 5 + 1 = 6.

Number of allocations = 4 + 6 – 1 = 9

If the number of allocation is < m + n - 1 it is a case of degeneracy

So, the minimum number of allocations required to avoid degeneracy, in this case, is 9.

Degeneracy

When the number of allocation becomes less than m + n – 1 then an optimality test cannot be performed and such a solution is called degenerate and the condition is known as degeneracy.

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