Assignment Problem Algorithm Essay On Importance Of School
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.
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.
After solving this problem using pseudo code, I’ll look at how we can use Python to create a function to solve it using the same method.
The steps of the Hungarian algorithm can be found here, and an explanation of the Hungarian algorithm based on the example above can be found here.
After completing step 2 we can see that each row and each column have a zero, which leaves us with the challenge of allocating the appropriate jobs to each contractor.The assignment problem is a fundamental problem in the area of combinatorial optimization.Assume for example that we have four jobs that need to be executed by four workers.The advantage to using Python, is that we can create a dynamic function that would solve our equation, no matter the grid size.This could be especially handy if, as in our example above, we decided to add more repairs, or get more contractor quotes.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.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.