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This could be especially handy if, as in our example above, we decided to add more repairs, or get more contractor quotes.Hopefully, as we go through this, other applications of this strategy will become apparent.The minimum row value represents the minimum price we will have to pay each contractor, and similarly, setting it to zero allows us to subtract it from the other values in the row.
Now, this is originally what we had decided anyway, and with only a 4x4 matrix, it wasn’t that difficult. Trying to allocate jobs in this way, in order to minimize both time and expense would be incredibly difficult.
This method allows make those calculations much more easily.
Let’s assume the four quotes you received look like this: This would seem pretty reasonable, all things considered.
And we might naturally just go with Susan, since she’s giving us the best overall price.
Now, let’s look at how we might create a program that would solve this problem for us.
My goal here is to not simply write a program to solve this exact problem, but to write code that will solve this problem for any size matrix, allowing me to re-use the code for multiple applications.
The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual methods.
It was developed and published in 1955 by Harold Kuhn, who gave the name “Hungarian method” because the algorithm was largely based on the earlier works of two Hungarian mathematicians: Dénes Kőnig and Jenő Egerváry.
In row 4, we could select Susan for either Painting or Flooring.
We could select either Diego or Susan for flooring.