Hi!

I'd really appreciate a little help with my transportation problem and finding its optimal solution.

Supply and demand werent equal in the initial table (demand > supply by 20 units), so I adjusted demand accordingly for it to match supply (basically by decreasing each of the consumers demand by 5). Then I solved the problem using Vogel's method.

Problem is, when I start checking for optimality (using potentials method u_{1}+ v_{1}= C_{ij }for any filled route), I get that the initial solution is the optimal solution (opportunity cost (= Cij - u_{1}- v_{1}) for nonfilled routes is in all cases non-negative).

I must be doing something wrong, as I know the solution can't be optimal. For example, solving the problem with Vogel's method by creating a fictive supplier to equalize demand and supply results in a much lower transportation cost solution...

Help would be greatly appreciated!