Concept explainers
a)
To determine: Thejob sequence, flow time, utilization metric, average number of jobs, and average lateness for EDD, SPT, LPT, and FCFS.
Introduction:
a)
Answer to Problem 18P
The values in the given table have been computed.
Explanation of Solution
Given information:
The following information has been given:
Job | Date order received | Production days needed | Date order due |
BR-02 | 228 | 15 | 300 |
CX-01 | 225 | 25 | 270 |
DE-06 | 230 | 35 | 320 |
RG-05 | 235 | 40 | 360 |
SY-11 | 231 | 30 | 310 |
All the jobs are arrived on day 241.
Table to compute:
Dispatching rule | Job sequence | Flow time | Utilization rating | Average number of jobs | Average lateness |
EDD | |||||
SPT | |||||
LPT | |||||
FCFS |
Computed table:
Dispatching rule | Job sequence | Flow time | Utilization rating | Average number of jobs | Average lateness |
EDD | CX-BR-SY-DE-RG | 385 | 37.60% | 2.66 | 10 |
SPT | BR-CX-SY-DE-RG | 375 | 38.60% | 2.59 | 12 |
LPT | RG-DE-SY-CX-BR | 495 | 29.30% | 3.41 | 44 |
FCFS | CX-BR-DE-SY-RG | 390 | 37.20% | 2.69 | 12 |
Supporting calculation:
Determine the sequence of the job using FCFS:
Processing time | Due date | Flow time | Completion time | Late | |
BR-02 | 15 | 300 | 15 | 265 | 0 |
CX-01 | 25 | 270 | 40 | 280 | 0 |
DE-06 | 35 | 320 | 75 | 315 | 0 |
RG-05 | 40 | 360 | 115 | 345 | 35 |
SY-11 | 30 | 310 | 145 | 385 | 25 |
Total | 390 | 60 |
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 241.
First Come First Served (FCFS):
Completion day of CX-01:
Jobs arrival rate is given as 241. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 265.
Completion day of BR-02:
Start day of BR-02 is the next day of the completion day of CX-01. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 280.
Completion day of DE-06:
Start day of DE-06 is the next day of the completion day of BR-02. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day of DE-06 is 315.
Completion day of SY-11:
Start day of SY-11 is the next day of the completion day of DE-06. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day of SY-11 is 345.
Completion day of RG-05:
Start day of RG-05 is the next day of the completion day of SY-11. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day of RG-05 is 385.
Lateness of CX-01, BR-02, and DE-06:
Completion day of CX-01, BR-02, and DE-06 is less than its respective due date. Hence, there would be no lateness.
Lateness of SY-11:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 35.
Lateness of RG-05:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 25.
Determine the sequence of the job using SPT:
Processing time | Due date | Flow time | Completion time | Late | |
BR-02 | 15 | 300 | 15 | 255 | 0 |
CX-01 | 25 | 270 | 40 | 280 | 10 |
SY-11 | 30 | 310 | 70 | 310 | 0 |
DE-06 | 35 | 320 | 105 | 345 | 25 |
RG-05 | 40 | 360 | 145 | 385 | 25 |
Total | 375 | 60 |
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 241.
Shortest Processing Time (SPT):
Completion day of BR-02:
Jobs arrival rate is given as 241. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 255.
Completion day of CX-01:
Start day of CX-01 is the next day of the completion day of BR-02. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 280.
Completion day of SY-11:
Start day of SY-11 is the next day of the completion day of CX-01. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 310.
Completion day of DE-06:
Start day of DE-06 is the next day of the completion day of SY-11. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 345.
Completion day of RG-05:
Start day of RG-05 is the next day of the completion day of DE-06. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 385.
Lateness of BR-02 and SY-11:
Completion day of BR-02 and SY-11 is less than its respective due date. Hence, there would be no lateness.
Lateness of CX-01:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 10.
Lateness of DE-06:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 25.
Lateness of RG-05:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 25.
Determine the sequence of the job using LPT:
Processing time | Due date | Flow time | Completion time | Late | |
RG-05 | 40 | 360 | 40 | 280 | 0 |
DE-06 | 35 | 320 | 75 | 315 | 0 |
SY-11 | 30 | 310 | 105 | 345 | 35 |
CX-01 | 25 | 270 | 130 | 370 | 100 |
BR-02 | 15 | 300 | 145 | 385 | 85 |
Total | 495 | 220 |
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 241.
Largest Processing Time (LPT):
Completion day of RG-05:
Jobs arrival rate is given as 241. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 280.
Completion day of DE-06:
Start day of DE-06 is the next day of the completion day of RG-05. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 315.
Completion day of SY-11:
Start day of SY-11 is the next day of the completion day of DE-06. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 345.
Completion day of CX-01:
Start day of CX-01 is the next day of the completion day of SY-11. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 370.
Completion day of BR-02:
Start day of BR-02 is the next day of the completion day of CX-01. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 385.
Lateness of RG-05 and DE-06:
Completion day of RG-05 and DE-06 is less than its respective due date. Hence, there would be no lateness.
Lateness of SY-11:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 35.
Lateness of CX-01:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 100.
Lateness of BR-02:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 85.
Determine the sequence of the job using EDD:
Processing time | Due date | Flow time | Completion time | Late | |
CX-01 | 25 | 270 | 25 | 265 | 0 |
BR-02 | 15 | 300 | 40 | 280 | 0 |
SY-11 | 30 | 310 | 70 | 310 | 0 |
DE-06 | 35 | 320 | 105 | 345 | 25 |
RG-05 | 40 | 360 | 145 | 385 | 25 |
Total | 385 | 50 |
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 241.
Earliest Due Date (EDD):
Completion day of CX-01:
Jobs arrival rate is given as 241. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 265.
Completion day of BR-02:
Start day of BR-02 is the next day of the completion day of CX-01. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day is 280.
Completion day of SY-11:
Start day of SY-11 is the next day of the completion day of DE-06. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day of SY-11 is 310.
Completion day of DE-06:
Start day of DE-06 is the next day of the completion day of BR-02. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day of DE-06 is 345.
Completion day of RG-05:
Start day of RG-05 is the next day of the completion day of SY-11. Completion day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the completion day of RG-05 is 385.
Lateness of CX-01, BR-02, and SY-11:
Completion day of CX-01, BR-02, and SY-11 is less than its respective due date. Hence, there would be no lateness.
Lateness of DE-06:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 25.
Lateness of RG-05:
It is calculated by subtracting the completion day of the job from the due date of the project. Hence, the lateness is 25.
Summary:
Dispatching rule | Job sequence | Flow time | Utilization rating | Average number of jobs | Average lateness |
EDD | CX-BR-SY-DE-RG | 385 | 37.60% | 2.66 | 10 |
SPT | BR-CX-SY-DE-RG | 375 | 38.60% | 2.59 | 12 |
LPT | RG-DE-SY-CX-BR | 495 | 29.30% | 3.41 | 44 |
FCFS | CX-BR-DE-SY-RG | 390 | 37.20% | 2.69 | 12 |
Working note:
Job sequence and flow time have been calculated in the above segments.
Earliest Due Date (EDD):
Average lateness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 10.
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 2.66.
Utilization rating:
It is calculated by dividing total processing time and total flow time. Hence, the utilization rating is 38.6%.
Shortest Processing Time (SPT):
Average lateness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 12.
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 2.59.
Utilization rating:
It is calculated by dividing total processing time and total flow time. Hence, the utilization rating is 38.6%.
Largest Processing Time (LPT):
Average lateness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 44.
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 3.41.
Utilization rating:
It is calculated by dividing total processing time and total flow time. Hence, the utilization rating is 29.3%.
First Come First Served (FCFS):
Average lateness:
It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 44.
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 2.69.
Utilization rating:
It is calculated by dividing total processing time and total flow time. Hence, the utilization rating is 37.2%.
b)
To determine: The dispatching rule that has the best score in flow time.
Introduction: Scheduling is the process of controlling and arranging the workloads of the production process using the optimized way. It is used to plan on allocating human resources and machinery.
b)
Answer to Problem 18P
Shortest Processing Time has the best flow time.
Explanation of Solution
Given information:
The following information has been given:
Job | Date order received | Production days needed | Date order due |
BR-02 | 228 | 15 | 300 |
CX-01 | 225 | 25 | 270 |
DE-06 | 230 | 35 | 320 |
RG-05 | 235 | 40 | 360 |
SY-11 | 231 | 30 | 310 |
Best score in flow time:
Dispatching rule | Job sequence | Flow time | Utilization rating | Average number of jobs | Average lateness |
EDD | CX-BR-SY-DE-RG | 385 | 37.60% | 2.66 | 10 |
SPT | BR-CX-SY-DE-RG | 375 | 38.60% | 2.59 | 12 |
LPT | RG-DE-SY-CX-BR | 495 | 29.30% | 3.41 | 44 |
FCFS | CX-BR-DE-SY-RG | 390 | 37.20% | 2.69 | 12 |
According to the above table, Shortest Processing Time (SPT) has the best score in flow time. It has less flow time when compare to EDD, LPT, and FCFS.
Hence, SPT has the best score in flow time.
c)
To determine: The dispatching rule that has the best score in utilization metric.
Introduction: Scheduling is the process of controlling and arranging the workloads of the production process using the optimized way. It is used to plan on allocating human resources and machinery.
c)
Answer to Problem 18P
Shortest Processing Time has the best utilization metric.
Explanation of Solution
Given information:
The following information has been given:
Job | Date order received | Production days needed | Date order due |
BR-02 | 228 | 15 | 300 |
CX-01 | 225 | 25 | 270 |
DE-06 | 230 | 35 | 320 |
RG-05 | 235 | 40 | 360 |
SY-11 | 231 | 30 | 310 |
Best score in utilization metric:
Dispatching rule | Job sequence | Flow time | Utilization rating | Average number of jobs | Average lateness |
EDD | CX-BR-SY-DE-RG | 385 | 37.60% | 2.66 | 10 |
SPT | BR-CX-SY-DE-RG | 375 | 38.60% | 2.59 | 12 |
LPT | RG-DE-SY-CX-BR | 495 | 29.30% | 3.41 | 44 |
FCFS | CX-BR-DE-SY-RG | 390 | 37.20% | 2.69 | 12 |
According to the above table, Shortest Processing Time (SPT) has the best score in utilization metric. It has maximum utilization metric when compare to EDD, LPT, and FCFS.
Hence, SPT has the best score in utilization metric.
d)
To determine: The dispatching rule that has the best score in average lateness.
Introduction: Scheduling is the process of controlling and arranging the workloads of the production process using the optimized way. It is used to plan allocating human resources and machinery.
d)
Answer to Problem 18P
Earliest Due Date has the best utilization metric.
Explanation of Solution
Given information:
The following information has been given:
Job | Date order received | Production days needed | Date order due |
BR-02 | 228 | 15 | 300 |
CX-01 | 225 | 25 | 270 |
DE-06 | 230 | 35 | 320 |
RG-05 | 235 | 40 | 360 |
SY-11 | 231 | 30 | 310 |
Best score in average lateness:
Dispatching rule | Job sequence | Flow time | Utilization rating | Average number of jobs | Average lateness |
EDD | CX-BR-SY-DE-RG | 385 | 37.60% | 2.66 | 10 |
SPT | BR-CX-SY-DE-RG | 375 | 38.60% | 2.59 | 12 |
LPT | RG-DE-SY-CX-BR | 495 | 29.30% | 3.41 | 44 |
FCFS | CX-BR-DE-SY-RG | 390 | 37.20% | 2.69 | 12 |
According to the above table, Earliest Due Date (EDD) has the best score in average lateness. It has less average lateness when compare to SPT, LPT, and FCFS.
Hence, EDD has the best score in average lateness.
e)
To determine: The dispatching rule that would be selected by Person X.
Introduction: Scheduling is the process of controlling and arranging the workloads of the production process using the optimized way. It is used to plan allocating human resources and machinery.
e)
Answer to Problem 18P
Person X would select Earliest Due Date.
Explanation of Solution
Given information:
The following information has been given:
Job | Date order received | Production days needed | Date order due |
BR-02 | 228 | 15 | 300 |
CX-01 | 225 | 25 | 270 |
DE-06 | 230 | 35 | 320 |
RG-05 | 235 | 40 | 360 |
SY-11 | 231 | 30 | 310 |
Best score in average lateness:
Dispatching rule | Job sequence | Flow time | Utilization rating | Average number of jobs | Average lateness |
EDD | CX-BR-SY-DE-RG | 385 | 37.60% | 2.66 | 10 |
SPT | BR-CX-SY-DE-RG | 375 | 38.60% | 2.59 | 12 |
LPT | RG-DE-SY-CX-BR | 495 | 29.30% | 3.41 | 44 |
FCFS | CX-BR-DE-SY-RG | 390 | 37.20% | 2.69 | 12 |
According to the above table, EDD has the less average lateness and other values are also having a slight difference when compared with SPT. Thus, EDD should be selected.
Hence, Person X would choose Earliest Due Date (EDD).
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Chapter 15 Solutions
Principles Of Operations Management
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