Principles Of Operations Management
11th Edition
ISBN: 9780135173930
Author: RENDER, Barry, HEIZER, Jay, Munson, Chuck
Publisher: Pearson,
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Question
Chapter 15, Problem 7P
a)
Summary Introduction
To solve: The given information by using the assignment method.
Introduction: The assignment method is one of the methods available in the process of optimization. Here, the jobs are assigned to every available resource.
a)
Expert Solution
Answer to Problem 7P
The problem has been solved by using the assignment method.
Explanation of Solution
Given information:
| Squad | Case | ||||
| A | B | C | D | E | |
| 1 | 14 | 7 | 3 | 7 | 27 |
| 2 | 20 | 7 | 12 | 6 | 30 |
| 3 | 10 | 3 | 4 | 5 | 21 |
| 4 | 8 | 12 | 7 | 12 | 21 |
| 5 | 13 | 25 | 24 | 26 | 8 |
Assign cases to respective squads:
Row minimum:
| Squad | Case | Row minimum | ||||
| A | B | C | D | E | ||
| 1 | 14 | 7 | 3 | 7 | 27 | 3 |
| 2 | 20 | 7 | 12 | 6 | 30 | 6 |
| 3 | 10 | 3 | 4 | 5 | 21 | 3 |
| 4 | 8 | 12 | 7 | 12 | 21 | 7 |
| 5 | 13 | 25 | 24 | 26 | 8 | 8 |
Table after the row subtraction is given below:
The row minimum value mentioned in the above table should be subtracted from each value of the row.
| Squad | Case | ||||
| A | B | C | D | E | |
| 1 | 11 | 4 | 0 | 4 | 24 |
| 2 | 14 | 1 | 6 | 0 | 24 |
| 3 | 7 | 0 | 1 | 2 | 18 |
| 4 | 1 | 5 | 0 | 5 | 14 |
| 5 | 5 | 17 | 16 | 18 | 0 |
Column minimum:
| Squad | Case | ||||
| A | B | C | D | E | |
| 1 | 11 | 4 | 0 | 4 | 24 |
| 2 | 14 | 1 | 6 | 0 | 24 |
| 3 | 7 | 0 | 1 | 2 | 18 |
| 4 | 1 | 5 | 0 | 5 | 14 |
| 5 | 5 | 17 | 16 | 18 | 0 |
| Column minimum | 1 | 0 | 0 | 0 | 0 |
Table after the column subtraction is given below:
The column minimum value mentioned in the above table should be subtracted from each value of the column.
| Squad | Case | ||||
| A | B | C | D | E | |
| 1 | 10 | 4 | 0 | 4 | 24 |
| 2 | 13 | 1 | 6 | 0 | 24 |
| 3 | 6 | 0 | 1 | 2 | 18 |
| 4 | 0 | 5 | 0 | 5 | 14 |
| 5 | 4 | 17 | 16 | 18 | 0 |
Assigning squads to the cases:
Step 1: The first row must be checked for the zero. As there is only one zero in the first row, it must be marked and the entire column should be striked out.
Step 2: As only one zero is available in the second row, it must be marked and the entire column should be striked out.
Step 3: As only one zero is available in the third row, it must be marked and the entire column should be striked out.
Step 4: As only one zero is available in the fourth row, it must be marked and the entire column should be striked out.
Step 5: As only one zero is available in the fourth row, it must be marked and the entire column should be striked out.
Step 5: All the zeroes in the table have been striked out. The marked zeroes help to assign the cases to the squads.
Calculate the total person-days that are projected by using the assignment method:
The value has been taken in the given information where, the zeroes have been marked in the final answer.
| Squad | Case | Value |
| 1 | C | 3 |
| 2 | D | 6 |
| 3 | B | 3 |
| 4 | A | 8 |
| 5 | E | 8 |
| Total | 28 | |
Conclusion
According to the table, Squad 1 should be assigned to Case C, Squad 2 should be assigned to Case D, Squad 3 should be assigned to Case B, Squad 4 should be assigned to Case A, and Squad 5 should be assigned to Case E. The total person days are 28 days.
b)
Summary Introduction
To solve: The given information by using assignment method.
Introduction: The assignment method is one of the methods available in the process of optimization. Here, the jobs are assigned to every available resource.
b)
Expert Solution
Answer to Problem 7P
The problem has been solved by using the assignment method.
Explanation of Solution
Given information:
| Squad | Case | ||||
| A | B | C | D | E | |
| 1 | 14 | 7 | 3 | 7 | 27 |
| 2 | 20 | 7 | 12 | 6 | 30 |
| 3 | 10 | 3 | 4 | 5 | 21 |
| 4 | 8 | 12 | 7 | 12 | 21 |
| 5 | 13 | 25 | 24 | 26 | 8 |
It is given that the squad 5 cannot work on Case 5 because of the conflict.
Modified given information:
It is given that the squad 5 cannot work on Case 5 because of the conflict. Thus, the value should be modified from 8 to any other higher values. It is taken as 50 here.
| Squad | Case | ||||
| A | B | C | D | E | |
| 1 | 14 | 7 | 3 | 7 | 27 |
| 2 | 20 | 7 | 12 | 6 | 30 |
| 3 | 10 | 3 | 4 | 5 | 21 |
| 4 | 8 | 12 | 7 | 12 | 21 |
| 5 | 13 | 25 | 24 | 26 | 50 |
Assign cases to respective squads:
Row minimum:
| Squad | Case | Row minimum | ||||
| A | B | C | D | E | ||
| 1 | 14 | 7 | 3 | 7 | 27 | 3 |
| 2 | 20 | 7 | 12 | 6 | 30 | 6 |
| 3 | 10 | 3 | 4 | 5 | 21 | 3 |
| 4 | 8 | 12 | 7 | 12 | 21 | 7 |
| 5 | 13 | 25 | 24 | 26 | 50 | 13 |
Table after the row subtraction is given below:
The row minimum value mentioned in the above table should be subtracted from each value of the row.
| Squad | Case | ||||
| A | B | C | D | E | |
| 1 | 11 | 4 | 0 | 4 | 24 |
| 2 | 14 | 1 | 6 | 0 | 24 |
| 3 | 7 | 0 | 1 | 2 | 18 |
| 4 | 1 | 5 | 0 | 5 | 14 |
| 5 | 0 | 12 | 11 | 13 | 37 |
Column minimum:
| Squad | Case | ||||
| A | B | C | D | E | |
| 1 | 11 | 4 | 0 | 4 | 24 |
| 2 | 14 | 1 | 6 | 0 | 24 |
| 3 | 7 | 0 | 1 | 2 | 18 |
| 4 | 1 | 5 | 0 | 5 | 14 |
| 5 | 0 | 12 | 11 | 13 | 37 |
| Column minimum | 0 | 0 | 0 | 0 | 14 |
Table after the column subtraction is given below:
The column minimum value mentioned in the above table should be subtracted from each value of the column.
| Squad | Case | ||||
| A | B | C | D | E | |
| 1 | 11 | 4 | 0 | 4 | 10 |
| 2 | 14 | 1 | 6 | 0 | 10 |
| 3 | 7 | 0 | 1 | 2 | 4 |
| 4 | 1 | 5 | 0 | 5 | 0 |
| 5 | 0 | 12 | 11 | 13 | 23 |
Assigning squads to the cases:
Step 1: The first row must be checked for the zero. As there is only one zero in the first row, it must be marked and the entire column should be striked out.
Step 2: As only one zero is available in the second row, it must be marked, and the entire column should be striked out.
Step 3: As only one zero is available in the third row, it must be marked, and the entire column should be striked out.
Step 4: As only one zero is available in the fourth row, it must be marked, and the entire column should be striked out.
Step 5: As only one zero is available in the fifth row, it must be marked, and the entire column should be striked out.
Step 5: All the zeroes in the table have been strikedout. The marked zeroes help to assign the cases to the squads.
Calculate the total person days that are projected by using the assignment method:
The value has been taken in the given information where, the zeroes have been marked in the final answer.
| Squad | Case | Value |
| 1 | C | 3 |
| 2 | D | 6 |
| 3 | B | 3 |
| 4 | E | 21 |
| 5 | A | 13 |
| Total | 46 | |
Conclusion
According to the table, Squad 1should be assigned to Case C, Squad 2 should be assigned to Case D, Squad 3 should be assigned to Case B, Squad 4 should be assigned to Case E, and Squad 5 should be assigned to Case A. The total person days are 46 days.
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Chapter 15 Solutions
Principles Of Operations Management
Ch. 15 - Prob. 1EDCh. 15 - Prob. 1DQCh. 15 - Prob. 2DQCh. 15 - Prob. 3DQCh. 15 - Prob. 4DQCh. 15 - Prob. 5DQCh. 15 - Prob. 6DQCh. 15 - Prob. 7DQCh. 15 - Prob. 8DQCh. 15 - Prob. 9DQ
Ch. 15 - Prob. 10DQCh. 15 - Prob. 11DQCh. 15 - Prob. 12DQCh. 15 - Prob. 13DQCh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Prob. 11PCh. 15 - Prob. 12PCh. 15 - Prob. 13PCh. 15 - Prob. 14PCh. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Prob. 24PCh. 15 - Prob. 25PCh. 15 - Prob. 26PCh. 15 - Prob. 27PCh. 15 - Prob. 28PCh. 15 - Daniels Barber Shop at Newark Airport is open 7...Ch. 15 - Given the following demand for waiters and...Ch. 15 - Prob. 1CSCh. 15 - Prob. 2CSCh. 15 - Prob. 3CSCh. 15 - Prob. 4CSCh. 15 - Prob. 1.1VCCh. 15 - Prob. 1.2VCCh. 15 - Prob. 1.3VCCh. 15 - Prob. 2.1VCCh. 15 - Prob. 2.2VCCh. 15 - Why is seniority important in scheduling servers?Ch. 15 - Prob. 2.4VC
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