Degenerating in Transportation Problem

If the basic feasible solution of a transportation problem with m origins and n destinations has fewer than m + n – 1 positive xij (occupied cells), the problem is said to be a degenerate transportation problem. Degeneracy can occur at two stages:

1. At the initial solution
2. During the testing of the optimal solution

If modified distribution method (MODI) is applied to test for optimality, it will not be possible to find all the variables ui and vj since the number of allocated cells and their corresponding cij values is not enough.

Consider the following example:

The initial basic feasible solution (by north-west rule) is:

No. of factories (origins) m = 3, no. of dealers (destinations) n = 4

So m + n – 1 = 3 + 4 – 1 = 6. But no. of allocations = 5.

So the solution is degenerate.