Assignment Problem Algorithm

Assignment Problem Algorithm-1
Hopefully, as we go through this, other applications of this strategy will become apparent.The Hungarian Method basically has three steps: Here’s the reasoning behind this method: In each column, we have our individual jobs.The assignment problem is a fundamental problem in the area of combinatorial optimization.

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.

Luckily, there is a great formula for figuring this type of problem out.

And we might naturally just go with Susan, since she’s giving us the best overall price.

However, another solution might be to break down what we need done into individual items.

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.

However, only rows 1, 3 and 4 have zeros, and row 4 has 2 zeros.Now, we will subtract the lowest value, which we’ve converted to zero, from the remaining column values.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.All other assignments lead to a larger amount of time required.The Hungarian algorithm can be used to find this optimal assignment.The rows represent the price we would have to pay the contractors.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.The assignment problem deals with assigning machines to tasks, workers to jobs, soccer players to positions, and so on.The goal is to determine the optimum assignment that, for example, minimizes the total cost or maximizes the team effectiveness.The jobs are denoted by J1, J2, J3, and J4, the workers by W1, W2, W3, and W4.Each worker should perform exactly one job and the objective is to minimize the total time required to perform all jobs.

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    The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual 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.…

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