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2 years ago in Mathematical Optimization , Operations Research By Trisha

Are there contradictions in Vogel’s approximation method for transportation problems compared to the minimum cost method?

While teaching operations research, students frequently point out that Vogel's method, designed for a better initial solution, sometimes yields a higher initial cost than the simple Minimum Cost method. This seems counter-intuitive given its advanced heuristic. I'm seeking a principled explanation for when and why this can occur.

 

Algorithms VogelsApproximation

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By Kirti Answered 1 year ago

I've seen this confusion arise many times in the classroom. There's no true contradiction; it's a misunderstanding of the heuristics. Vogel's method penalizes the next best choice, aiming for a solution closer to optimal overall. The Minimum Cost method is myopically greedy. In specific problem structures, this myopia can accidentally align better for the initial cost, but Vogel's solution typically requires fewer iterations to reach the true optimum. I would recommend presenting them as complementary lenses, not competitors.

 

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