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Linear programming: transportation problem

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...(Headbang)

Help would be greatly appreciated!

Re: Linear programming: transportation problem

Yeah, I'm clueless, to be honest.