Hungarian Assignment Method

Hungarian Assignment Method-46
The Hungarian algorithm consists of the four steps below.

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Step 3: Cover all zeros with a minimum number of lines Again, We determine the minimum number of lines required to cover all zeros in the matrix.If n lines are required, an optimal assignment exists among the zeros. If less than n lines are required, continue with Step 4.Step 4: Create additional zeros Find the smallest element (call it k) that is not covered by a line in Step 3.The resulting matrix is: Step 3: Cover all zeros with a minimum number of lines We will now determine the minimum number of lines (horizontal or vertical) that are required to cover all zeros in the matrix.All zeros can be covered using 3 lines: Because the number of lines required (3) is lower than the size of the matrix (n=4), we continue with Step 4.This lesson will go over the steps of this algorithm and we will also see this algorithm in action by applying it to a real-world example.This table is also called a matrix, which is an array of elements in rows and columns.Step 4: Create additional zeros First, we find that the smallest uncovered number is 6.We subtract this number from all uncovered elements and add it to all elements that are covered twice.We consider an example where four jobs (J1, J2, J3, and J4) need to be executed by four workers (W1, W2, W3, and W4), one job per worker.The matrix below shows the cost of assigning a certain worker to a certain job.

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