Assignment Problem Algorithm

Assignment Problem Algorithm-73
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 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.

It turns out to be optimal to assign worker 1 to job 3, worker 2 to job 2, worker 3 to job 1 and worker 4 to job 4.

The total time required is then 69 37 11 23 = 140 minutes.

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.

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 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.All other assignments lead to a larger amount of time required.The Hungarian algorithm can be used to find this optimal assignment.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.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.

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