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:
At the initial solution
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.
The North-West Corner Rule is a method adopted to compute the initial feasible solution of the transportation problem. The name North-west corner is given to this method because the basic variables are selected from the extreme left corner. The concept of North-West Corner can be well understood through a transportation problem given…
The stepping stone method is an iterative procedure used to improve an initial feasible solution for a transportation problem, in order to find the optimal solution. The method is based on the idea of moving from one feasible solution to another by making small changes in the allocation of goods…
The Vogel’s Approximation Method or VAM is an iterative procedure calculated to find out the initial feasible solution of the transportation problem. Like Least cost Method, here also the shipping cost is taken into consideration, but in a relative sense. The following is the flow chart showing the steps involved in solving the…
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