Concept explainers
a)
To determine: Sequence of jobs based on decision rule First Come First Served (FCFS).
Introduction: First Come First Served is the
a)
Answer to Problem 19P
The sequence is A-B-C-D-E.
Explanation of Solution
Given information:
The following information has been given:
Job | Date order received | Production days needed | Due date |
A | 110 | 20 | 180 |
B | 120 | 30 | 200 |
C | 122 | 10 | 175 |
D | 125 | 16 | 230 |
E | 130 | 18 | 210 |
All the jobs are arrived on day 130.
Determine the sequence of the job using FCFS:
Job sequence | Processing time | Flow time | Due date | Start day | End day | Lateness |
A | 20 | 20 | 180 | 130 | 149 | |
B | 30 | 50 | 200 | 150 | 179 | |
C | 10 | 60 | 175 | 180 | 189 | 14 |
D | 16 | 76 | 230 | 190 | 205 | |
E | 18 | 94 | 210 | 206 | 223 | 13 |
Total | 94 | 300 | 27 |
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 130.
End day of Job A:
Jobs arrival rate is given as 130. 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 149.
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 179.
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 189.
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 205.
End day of Job E:
Start day of Job E 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 E is 223.
Lateness of Job A, Job B, and Job D:
End day of Job A, Job B, and Job D is 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 14.
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 13.
b)
To determine: 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, the job with the earliest due date would be served first. Then, the process would be going on from the earliest due date to the latest due date.
b)
Answer to Problem 19P
The sequence is C-A-B-E-D.
Explanation of Solution
Given information:
The following information has been given:
Job | Date order received | Production days needed | Due date |
A | 110 | 20 | 180 |
B | 120 | 30 | 200 |
C | 122 | 10 | 175 |
D | 125 | 16 | 230 |
E | 130 | 18 | 210 |
All the jobs are arrived on day 130.
Determine the sequence of the job using EDD:
Job sequence | Processing time | Flow time | Due date | Start day | End day | Lateness |
C | 10 | 10 | 175 | 130 | 139 | |
A | 20 | 30 | 180 | 140 | 159 | |
B | 30 | 60 | 200 | 160 | 189 | |
E | 18 | 78 | 210 | 190 | 207 | |
D | 16 | 94 | 230 | 208 | 223 | |
Total | 94 | 272 |
Working note:
Duration and due date for the jobs have been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 130. 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 130. 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 139.
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 159.
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 189.
End day of Job E:
Start day of Job E 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 E is 207.
End day of Job D:
Start day of Job D is the next day of the end day of Job E. 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 223.
Lateness of Job A, Job B, Job C, Job D, and Job E:
End day of all the jobs is less than its respective due date. Hence, there would be no lateness.
c)
To determine: 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, the job with the shortest duration would be served first. Then, the process would be going on from shortest to largest duration.
c)
Answer to Problem 19P
The sequence is C-D-E-A-B.
Explanation of Solution
Given information:
The following information has been given:
Job | Date order received | Production days needed | Due date |
A | 110 | 20 | 180 |
B | 120 | 30 | 200 |
C | 122 | 10 | 175 |
D | 125 | 16 | 230 |
E | 130 | 18 | 210 |
All the jobs are arrived on day 130.
Determine the sequence of the job using SPT:
Job sequence | Processing time | Flow time | Due date | Start day | End day | Lateness |
C | 10 | 10 | 175 | 130 | 139 | |
D | 16 | 26 | 230 | 140 | 155 | |
E | 18 | 44 | 210 | 156 | 173 | |
A | 20 | 64 | 180 | 174 | 193 | 13 |
B | 30 | 94 | 200 | 194 | 223 | 23 |
Total | 94 | 238 | 36 |
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 130. The job should be arranged based on the duration (processing time). The duration should be assembled in the ascending order.
End day of Job C:
Jobs arrival rate is given as 130. 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 139.
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 155.
End day of Job E:
Start day of Job E 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 E is 173.
End day of Job A:
Start day of Job A is the next day of the end day of Job E. 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 193.
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 223.
Lateness of Job C, Job D, and Job E:
End day of Job C, Job D, and Job E are less than its respective due date. Hence, there would be no lateness.
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 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 23.
d)
To determine: 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, the job with the largest duration would be served first. Then, the process would be going on from largest to shortest duration.
d)
Answer to Problem 19P
The sequence is B-A-E-D-C.
Explanation of Solution
Given information:
The following information has been given:
Job | Date order received | Production days needed | Due date |
A | 110 | 20 | 180 |
B | 120 | 30 | 200 |
C | 122 | 10 | 175 |
D | 125 | 16 | 230 |
E | 130 | 18 | 210 |
All the jobs are arrived on day 130.
Determine the sequence of the job using LPT:
Job sequence | Processing time | Flow time | Due date | Start day | End day | Lateness |
B | 30 | 30 | 200 | 130 | 159 | |
A | 20 | 50 | 180 | 160 | 179 | |
E | 18 | 68 | 210 | 180 | 197 | |
D | 16 | 84 | 230 | 198 | 213 | |
C | 10 | 94 | 175 | 214 | 223 | 48 |
Total | 94 | 326 | 48 |
Working note:
Duration and due date for the jobs have been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 130. The job should be arranged based on the duration (processing time). The duration should be assembled in the descending order
End day of Job B:
Jobs arrival rate is given as 130. 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 159.
End day of Job A:
Start day of Job A 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 A is 179.
End day of Job E:
Start day of Job E 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 E is 197.
End day of Job D:
Start day of Job D is the next day of the end day of Job E. 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 213.
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 223.
Lateness of Job B, Job A, Job E, and Job D:
End day of Job B, Job A, Job E, and Job D are 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 48.
Summary:
Scheduling rule | Average lateness | Average flow time | Average number of jobs in system |
FCFS | 5.4 | 60.0 | 3.2 |
EDD | 0.0 | 54.4 | 2.9 |
SPT | 7.2 | 47.6 | 2.5 |
LPT | 9.6 | 65.2 | 3.5 |
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 5.4.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 60.
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 3.2.
Earliest Due Date (EDD):
Average tardiness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 0.0.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 54.4.
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 2.9.
Shortest Processing Time (SPT):
Average tardiness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 7.2.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 47.6.
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 2.5.
Longest Processing Time (LPT):
Average tardiness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 9.6.
Average flow time:
It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 65.2.
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 3.55.
Hence, Earliest Due Date is the best method for the average lateness. Shortest processing time has the minimum average flow time and average number of jobs in systems.
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Chapter 15 Solutions
Principles Of Operations Management
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