Concept explainers
a)
To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).
Introduction: First Come First Served is the
a)
Answer to Problem 17P
The sequence is A-B-C-D.
Explanation of Solution
Given information:
The following information has been given:
Job | Due date | Duration (days) |
A | 212 | 6 |
B | 209 | 3 |
C | 208 | 3 |
D | 210 | 8 |
All the jobs are arrived on day 205.
Determine the sequence of the job using FCFS:
Job | Processing time | Flow time | Due date | Start | End | Lateness |
A | 6 | 6 | 212 | 205 | 210 | 0 |
B | 3 | 9 | 209 | 211 | 213 | 4 |
C | 3 | 12 | 208 | 214 | 216 | 8 |
D | 8 | 20 | 210 | 217 | 224 | 14 |
Working note:
Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205.
End day of Job A:
Jobs arrival rate is given as 205. 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 210.
End day of Job B:
Start day of Job B is the next day of the end day of Job A. 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 213.
End day of Job C:
Start day of Job C is the next day of the end day of Job B. 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 216.
End day of Job D:
Start day of Job D is the next day of the end day of Job C. 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 224.
Lateness of Job A:
End day of Job A is less than its respective due date. Hence, there would be 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 4.
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 8.
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 14.
b)
To determine: The sequence of jobs based on decision rule Shortest Processing Time (SPT).
Introduction: Shortest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the shortest duration would be served first. Then, the process would go on from the shortest to largest duration.
b)
Answer to Problem 17P
The sequence is B-C-A-D.
Explanation of Solution
Given information:
The following information has been given:
Job | Due date | Duration (days) |
A | 212 | 6 |
B | 209 | 3 |
C | 208 | 3 |
D | 210 | 8 |
All the jobs are arrived on day 205.
Determine the sequence of the job using SPT:
Job | Processing time | Flow time | Due date | Start | End | Lateness |
B | 3 | 3 | 209 | 205 | 207 | 0 |
C | 3 | 9 | 208 | 208 | 210 | 2 |
A | 6 | 15 | 212 | 211 | 216 | 4 |
D | 8 | 20 | 210 | 217 | 224 | 14 |
Working note:
Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the ascending order.
End day of Job B:
Jobs arrival rate is given as 205. 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 207.
End day of Job C:
Start day of Job C is the next day of the end day of Job B. 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 210.
End day of Job A:
Start day of Job A is the next day of the end day of Job C. 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 216.
End day of Job D:
Start day of Job D is the next day of the end day of Job A. 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 224.
Lateness of Job B:
End day of Job Bare less than its respective due date. Hence, there would be 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 2.
Lateness of Job A:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 4.
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 14.
c)
To determine: The sequence of jobs based on decision rule Longest Processing Time (LPT).
Introduction: Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the largest duration would be served first. Then, the process would go on from the largest to shortest duration.
c)
Answer to Problem 17P
The sequence is D-A-C-B.
Explanation of Solution
Given information:
The following information has been given:
Job | Due date | Duration (days) |
A | 212 | 6 |
B | 209 | 3 |
C | 208 | 3 |
D | 210 | 8 |
All the jobs are arrived on day 205.
Determine the sequence of the job using LPT:
Job | Processing time | Flow time | Due date | Start | End | Lateness |
D | 8 | 8 | 210 | 205 | 212 | 2 |
A | 6 | 14 | 212 | 213 | 218 | 6 |
C | 3 | 17 | 208 | 219 | 221 | 13 |
B | 3 | 20 | 209 | 222 | 224 | 15 |
Working note:
Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the descending order
End day of Job D:
Jobs arrival rate is given as 205. 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 212.
End day of Job A:
Start day of Job A is the next day of the end day of Job D. 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 218.
End day of Job C:
Start day of Job C is the next day of the end day of Job B. 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 221.
End day of Job B:
Start day of Job B is the next day of the end day of Job C. 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 224.
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 2.
Lateness of Job A:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 6.
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 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 15.
d)
To determine: The sequence of jobs based on decision rule Earliest Due Date (EDD).
Introduction: Earliest Due Date is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the earliest due date would be served first. Then, the process would go on from the earliest due date to latest due date.
d)
Answer to Problem 17P
The sequence is C-B-D-A.
Explanation of Solution
Given information:
The following information has been given:
Job | Due date | Duration (days) |
A | 212 | 6 |
B | 209 | 3 |
C | 208 | 3 |
D | 210 | 8 |
All the jobs are arrived on day 205.
Determine the sequence of the job using EDD:
Job | Processing time | Flow time | Due date | Start | End | Lateness |
C | 3 | 3 | 208 | 205 | 207 | 0 |
B | 3 | 6 | 209 | 208 | 210 | 1 |
D | 8 | 14 | 210 | 211 | 218 | 8 |
A | 6 | 20 | 212 | 219 | 224 | 12 |
Working note:
Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.
End day of Job C:
Jobs arrival rate is given as 205. 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 207.
End day of Job B:
Start day of Job B is the next day of the end day of Job C. 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 210.
End day of Job D:
Start day of Job D is the next day of the end day of Job B. 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 218.
End day of Job A:
Start day of Job A is the next day of the end day of Job D. 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 224.
Lateness of Job C:
End day of Job Care less than its respective due date. Hence, there would be 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 1.
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 8.
Lateness of Job A:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 12.
e)
To determine: The sequence of jobs based on critical ratio.
Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.
e)
Answer to Problem 17P
The sequence is D-C-A-B.
Explanation of Solution
Given information:
The following information has been given:
Job | Due date | Duration (days) |
A | 212 | 6 |
B | 209 | 3 |
C | 208 | 3 |
D | 210 | 8 |
All the jobs are arrived on day 205.
Calculate the critical ratio:
Job | Due date | Processing time | Critical ratio |
A | 212 | 6 | 1.17 |
B | 209 | 3 | 1.33 |
C | 208 | 3 | 1 |
D | 210 | 8 | 0.63 |
Calculate the critical ratio of Job A:
It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.17.
Calculate the critical ratio of Job B:
It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.33.
Calculate the critical ratio of Job C:
It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.00.
Calculate the critical ratio of Job D:
It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 0.63.
Sequence based on critical ratio:
Job | Critical ratio |
D | 0.63 |
C | 1 |
A | 1.17 |
B | 1.33 |
Determine the sequence of the job using EDD:
Job | Processing time | Flow time | Due date | Start | End | Lateness |
D | 8 | 8 | 210 | 205 | 212 | 2 |
C | 3 | 11 | 208 | 213 | 215 | 7 |
A | 6 | 17 | 212 | 216 | 221 | 9 |
B | 3 | 20 | 209 | 222 | 224 | 15 |
Working note:
Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.
End day of Job D:
Jobs arrival rate is given as 205. 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 212.
End day of Job C:
Start day of Job C is the next day of the end day of Job D. 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 215.
End day of Job A:
Start day of Job A is the next day of the end day of Job C. 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 221.
End day of Job B:
Start day of Job B is the next day of the end day of Job A. 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 224.
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 2.
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 7.
Lateness of Job A:
It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 9.
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 15.
Summary:
Scheduling rule | Average lateness | Average flow time | Average number of jobs in system |
FCFS | 6.5 | 11.8 | 2.4 |
SPT | 5 | 10.25 | 2.1 |
LPT | 9 | 14.8 | 3 |
EDD | 5.25 | 10.8 | 2.2 |
Critical ratio | 8.3 | 14 | 2.8 |
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 6.5.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 11.8.
Average number of jobs in the system:
It is calculated by dividing the total flow time with 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 5.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.25.
Average number of jobs in the system:
It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.1.
Largest Processing Time (LPT):
Average tardiness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 9.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.8.
Average number of jobs in the system:
It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 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 5.25.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.8.
Average number of jobs in the system:
It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.2.
Critical ratio:
Average tardiness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 8.3.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.
Average number of jobs in the system:
It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.8.
Shortest processing time has the minimum average tardiness, average flow time, and 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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