Operational research problem(Vogel Approximation)

[prashant_ora]

Sir,
Suppose we are asked to find the basic feasible solution for maximizing transportation cost using Vogel approximation method (VAM). We then write the row penalty and column penalty. Suppose there is tie between 2 penalty values, which should be taken first? I have this doubt because I get 2 different solutions in each case.
If there is a tie we would take that penalty corresponding to which there is minimum cost. If there is a tie again in the minimum cost then we would allocate in the cell where maximum can be allocated, and again if there is a tie, then what?
If I choose randamoly then the ansawer would be different . So tell me what should I do.

 

[eachus]

I think you meant to find the minimum transportation cost (or maximize profit). In any case, you should not be surprised that a heuristic method for allocating an initial feasible solution can result in different solutions.

If you iterate to get an optimal solution, these optimal solutions should have the same cost (or benefit). But it is possible that the optimal solution set includes a polyhedral face of the feasible solution space, or just an edge. If so there are multiple optimal solutions.

It is hard to know how to explain to you the underlying reality without knowing what tools (and/or textbooks) you are using. Just remember that the Kuhn-Tucker conditions will be satisfied for any optimal solution, which means that an optimal solution is also a feasible solution for both the problem and its dual.

 

[zuriat2244]

If two costs in the same row or column are the same will the penalty of that row or column be zero? or will it be calculated using the regular method i.e. by subtracting the smallest unit cost from the next smallest cost?

 

[jane43]

The Vogel's approximation method (VAM) usually produces an optimal or near- optimal starting solution. One study found that VAM yields an optimum solution in 80 percent of the sample problems tested.