Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 7.5, Problem 1P

Explanation of Solution

Given:

Five employees are available for performing four jobs. The time taken to perform each job by each of the person is given in the following table:

        Time      (hours) 
PersonJob 1Job 2Job 3Job 4
122183018
218M2722
326202828
41622M14
521M2528

To Determine:

Find an optimal assignment order of jobs to minimize the total time required for performing four jobs using Hungarian method.

Assignment of employees to jobs:

Step 1:

Add another column for Job 5 with zero costs, since the table is not balanced.

        Time      (hours)  
PersonJob 1Job 2Job 3Job 4Job 5
1221830180
218M27220
3262028280
41622M140
521M25280

Step 2:

Take minimum from each row and subtract from the corresponding row. The new resultant table will be as follows:

        Time      (hours)  
PersonJob 1Job 2Job 3Job 4Job 5
1221830180
218M27220
3262028280
41622M140
521M25280
Minimum161825140

Step 3:

Take minimum from each column and subtract from the corresponding column. The new resultant table will be as follows:

        Time      (hours)  
PersonJob 1Job 2Job 3Job 4Job 5
160540
22M280
31023140
404M00
55M0140

Step 4:

Draw minimum number of lines for covering all zeros in the resultant table...

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