# Solve The Following Assignment Problem Term Paper Definition

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.Here, I’ve updated column 1, subtracting the lowest value, 70, from the remaining column values, leaving us with 15, 30, and 80: Now, we’ll notice that each column contains a zero.However, only rows 1, 3 and 4 have a zero, with row for having 2 of them. We cycle through the rows now, and convert the lowest value in each row to a zero, only if the row doesn’t currently have a zero.So by setting that value to zero, we can then subtract that value from the other column values.The rows represent the price we would have to pay the contractors.

Now, we will subtract the lowest value, which we’ve converted to zero, from the remaining column values.Consider the following problem: Due to neglect, your home is in serious need of repair.Naturally, you go out and get quotes on remodeling and repairing what needs to be done.However, another solution might be to break down what we need done into individual items.Then we could get prices from our contractors per repair item.This would be more beneficial in two ways: By using this strategy, we would minimize our time, by spreading the work over 4 contractors, but we also minimize our cost, by hiring contractors per repair item.Despite how simple this may appear, it could get quite difficult to calculate if we had a much larger pool of contractors to choose from, or had many more repairs to consider.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.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.Let’s take a look at how this method could be applied to our current problem: Here, we can see that each column has a zero.

And it feels like time is running out — my dog and I need a home as soon as possible.