Problem 2 (25 points) Five workers are available to perform five jobs. The time

Question

Problem 2 (25 points) Five workers are available to perform five jobs. The time it takes each worker to perform each job is given in the table below. The goal is to assign workers to jobs so as to minimize the total time required to perform the five jobs. Use the Hungarian method to solve the problem. Fill out (Hours) Job 3 Job 2 12 Job1 Job 4Job 5 Worker 1 16 Worker 2 12 Worker 3 12 Worker 4 6 Worker 5 10 12 20 16 6 18 4 12 15 18 6 15 10 15 Worker Job Worker 2 Job Worker3 Job Worker 4 Job Worker 5 Job

Explanation / Answer

First we calculate the row mimimum values for each worker

Then subtract each row by the minimum value to get

Then we calculate the column minimum from the above

Then subtract the column minimum from each column

Ttry to fit as minimum number of lines to cover the zero values

Where the values are not covered there we can check for the minimum value and subtract it from the non covered area

Add the value where the column are covered twice

By doing this we get the final result as

So the answer is

Worker 1 = Job 4

Worker 2= Job 2

Worker 3= Job 3

Worker 4 = Job 1

Worker 5= Job 5

Job 1 Job 2 Job 3 Job 4 Job 5 ROW MIN Worker 1 16 12 8 12 4 4 Worker 2 12 8 20 16 6 6 Worker 3 12 9 8 18 4 4 Worker 4 6 12 15 18 6 6 Worker 5 30 15 10 15 5 5

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