Concept explainers
a)
To determine: Thesequence of jobs based on the decision rule, i.e, First Come First Served (FCFS).
Introduction: The First Come First Served is the
a)
Answer to Problem 15P
The sequence is A-B-C-D-E.
Explanation of Solution
Given information:
The following information has been given below:
Job | Due date | Duration (days) |
A | 313 | 8 |
B | 312 | 16 |
C | 325 | 40 |
D | 314 | 5 |
E | 314 | 3 |
All the jobs have arrived on day 275.
Determine the sequence of the job by using FCFS:
Job | Due date | Duration (days) | Flow time | Start | End | Lateness |
A | 313 | 8 | 8 | 275 | 282 | |
B | 312 | 16 | 24 | 283 | 298 | |
C | 325 | 40 | 64 | 299 | 338 | 13 |
D | 314 | 5 | 69 | 339 | 343 | 29 |
E | 314 | 3 | 72 | 344 | 346 | 32 |
Total | 72 | 237 | 74 |
Working note:
The duration and due date for the jobs has been given. The flow time is the cumulative value of the duration. The jobs arrival rate is given as 275.
End day of Job A:
The jobs arrival rate is given as 275. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 282.
End day of Job B:
The start day of Job B is the next day of the end day of Job A. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 298.
End day of Job C:
The start day of Job C is the next day of the end day of Job B. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 338.
End day of Job D:
The start day of Job D is the next day of the end day of Job C. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 343.
End day of Job E:
The start day of Job E is the next day of the end day of Job D. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job E is 346.
Lateness of Job A and Job B:
The end day of Job A and Job B is less than its respective due date. Hence, there is no lateness.
Lateness of Job C:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 13.
Lateness of Job D:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 29.
Lateness of Job E:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job E is 32.
b)
To determine: The sequence of jobs based on the decision rule, i.e, Earliest Due Date (EDD).
Introduction: The Earliest Due Date is the scheduling rule, which helps to arrange the sequence in the order. Here, the job with the earliest due date would be served first. Then, the process would be go on from the earliest due date to the latest due date.
b)
Answer to Problem 15P
The sequence is B-A-D-E-C.
Explanation of Solution
Given information:
The following information has been given below:
Job | Due date | Duration (days) |
A | 313 | 8 |
B | 312 | 16 |
C | 325 | 40 |
D | 314 | 5 |
E | 314 | 3 |
All the jobs have arrived on day 275.
Determine the sequence of the job by using EDD:
Job | Due date | Duration (days) | Flow time | Start | End | Lateness |
B | 312 | 16 | 16 | 275 | 290 | |
A | 313 | 8 | 24 | 291 | 298 | |
D | 314 | 5 | 29 | 299 | 303 | |
E | 314 | 3 | 32 | 304 | 306 | |
C | 325 | 40 | 72 | 307 | 346 | 21 |
Total | 72 | 173 | 21 |
Working note:
The duration and due date for the jobs have been given. The flow time is the cumulative value of the duration. The jobs arrival rate is given as 275. The job should be arranged based on the due date. The due date should be assembled in the ascending order.
End day of Job A:
The jobs arrival rate is given as 275. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 290.
End day of Job B:
The start day of Job B is the next day of the end day of Job A. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 298.
End day of Job C:
The start day of Job C is the next day of the end day of Job B. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 303.
End day of Job D:
The start day of Job D is the next day of the end day of Job C. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 306.
End day of Job E:
The start day of Job E is the next day of the end day of Job D. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job E is 346.
Lateness of Job A, Job B, Job C, and Job D is given below:
The end day of Job A, Job B, Job C, and Job dare less than its respective due date. Hence, there is no lateness.
Lateness of Job E:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job E is 21.
c)
To determine: The sequence of jobs based on the decision rule, i.e, Shortest Processing Time (SPT).
Introduction: The Shortest Processing Time is the scheduling rule, which helps to arrange the sequence in the order. Here, the job with the shortest duration is served first. Then, the process would be go on from the shortest to the largest duration.
c)
Answer to Problem 15P
The sequence is E-D-A-B-C.
Explanation of Solution
Given information:
The following information has been given below:
Job | Due date | Duration (days) |
A | 313 | 8 |
B | 312 | 16 |
C | 325 | 40 |
D | 314 | 5 |
E | 314 | 3 |
All the jobs are arrived on day 275.
Determine the sequence of the job by using SPT:
Job | Due date | Duration (days) | Flow time | Start | End | Lateness |
E | 314 | 3 | 3 | 275 | 277 | |
D | 314 | 5 | 8 | 278 | 282 | |
A | 313 | 8 | 16 | 283 | 290 | |
B | 312 | 16 | 32 | 291 | 306 | |
C | 325 | 40 | 72 | 307 | 346 | 21 |
Total | 72 | 131 | 21 |
Working note:
The duration and due date for the jobs have been given. The flow time is the cumulative value of the duration. The jobs arrival rate is given as 275. The job should be arranged based on the duration (processing time). The duration should be assembled in the ascending order.
End day of Job A:
The jobs arrival rate is given as 275. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 277.
End day of Job B:
The start day of Job B is the next day of the end day of Job A. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 282.
End day of Job C:
The start day of Job C is the next day of the end day of Job B. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 290.
End day of Job D:
The start day of Job D is the next day of the end day of Job C. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 306.
End day of Job E:
The start day of Job E is the next day of the end day of Job D. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job E is 346.
Lateness of Job A, Job B, Job C, and Job D is as follows:
The end day of Job A, Job B, Job C, and Job D are less than its respective due date. Hence, there is no lateness.
Lateness of Job E:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job E is 21.
d)
To determine: The sequence of jobs based on the decision rule, i.e, Longest Processing Time (LPT).
Introduction: The Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, the job with the largest duration is served first. Then, the process would go on from the largest to the shortest duration.
d)
Answer to Problem 15P
The sequence is C-B-A-D-E.
Explanation of Solution
Given information:
The following information has been given below:
Job | Due date | Duration (days) |
A | 313 | 8 |
B | 312 | 16 |
C | 325 | 40 |
D | 314 | 5 |
E | 314 | 3 |
All the jobs have arrived on day 275.
Determine the sequence of the job by using LPT:
Job | Due date | Duration (days) | Flow time | Start | End | Lateness |
C | 325 | 40 | 40 | 275 | 314 | |
B | 312 | 16 | 56 | 315 | 330 | 18 |
A | 313 | 8 | 64 | 331 | 338 | 25 |
D | 314 | 5 | 69 | 339 | 343 | 29 |
E | 314 | 3 | 72 | 344 | 346 | 32 |
Total | 72 | 301 | 104 |
Working note:
The duration and due date for the jobs have been given. The flow time is the cumulative value of the duration. The jobs arrival rate is given as 275. The job is arranged based on the duration (processing time). The duration should be assembled in the descending order
End day of Job A:
The jobs arrival rate is given as 275. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 314.
End day of Job B:
The start day of Job B is the next day of the end day of Job A. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 330.
End day of Job C:
The start day of Job C is the next day of the end day of Job B. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 338.
End day of Job D:
The start day of Job D is the next day of the end day of Job C. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 343.
End day of Job E:
The start day of Job E is the next day of the end day of Job D. The end day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job E is 346.
Lateness of Job A:
The end day of Job A is less than its respective due date. Hence, there is no lateness.
Lateness of Job B:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 18.
Lateness of Job C:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 25.
Lateness of Job D:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 29.
Lateness of Job E:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job E is 32.
Summary:
Decision rule | Average tardiness | Average flow time | Average number of jobs in system |
FCFS | 14.8 | 47.4 | 3.3 |
EDD | 4.2 | 34.6 | 2.4 |
SPT | 4.2 | 26.2 | 1.8 |
LPT | 20.8 | 60.2 | 4.2 |
First Come First Served (FCFS):
Average tardiness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 14.8.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 47.4.
Average number of jobs in the system:
It is calculated by dividing the total flow time with the total duration of all the jobs. Hence, the average number of jobs in the system is 3.3.
Earliest Due Date (EDD):
Average tardiness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 4.2.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 34.6.
Average number of jobs in the system:
It is calculated by dividing the total flow time with the total duration of all the jobs. Hence, the average number of jobs in the system is 2.4.
Shortest processing time (SPT):
Average tardiness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 4.2.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 26.2.
Average number of jobs in the system:
It is calculated by dividing the total flow time with the total duration of all the jobs. Hence, the average number of jobs in the system is 1.8.
Largest processing time (LPT):
Average tardiness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 20.8.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 60.2.
Average number of jobs in the system:
It is calculated by dividing the total flow time with the total duration of all the jobs. Hence, the average number of jobs in the system is 4.2.
Shortest processing time has the minimum average tardiness, average flow time, and the average number of jobs in systems. Hence, SPT is the best decision rule.
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Chapter 15 Solutions
Principles Of Operations Management
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