PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB
PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB
11th Edition
ISBN: 9780135226742
Author: HEIZER
Publisher: PEARSON
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Question
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Chapter 15, Problem 18P

a)

Summary Introduction

To determine: Thejob sequence, flow time, utilization metric, average number of jobs, and average lateness for EDD, SPT, LPT, and FCFS.

Introduction: Scheduling is the process of controlling and arranging the workloads of the production process using the optimized way. It is used to plan the allocation of  human resources and machinery.

a)

Expert Solution
Check Mark

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=Start day+(Duration 1)=241+(251)=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=Start day+(Duration 1)=266+(151)=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=Start day+(Duration 1)=281+(351)=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=Start day+(Duration 1)=316+(301)=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.

Completion day=Start day+(Duration 1)=346+(401)=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=Completion dayDue date=345310=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.

Lateness=Completion dayDue date=385360=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=Start day+(Duration 1)=241+(151)=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=Start day+(Duration 1)=256+(251)=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=Start day+(Duration 1)=281+(301)=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=Start day+(Duration 1)=311+(351)=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.

Completion day=Start day+(Duration 1)=346+(401)=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=Completion dayDue date=280270=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=Completion dayDue date=345320=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.

Lateness=Completion dayDue date=385360=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=Start day+(Duration 1)=241+(401)=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=Start day+(Duration 1)=281+(351)=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=Start day+(Duration 1)=316+(301)=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=Start day+(Duration 1)=346+(251)=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.

Completion day=Start day+(Duration 1)=371+(151)=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=Completion dayDue date=345310=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=Completion dayDue date=370270=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.

Lateness=Completion dayDue date=385300=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=Start day+(Duration 1)=241+(251)=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=Start day+(Duration 1)=266+(151)=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=Start day+(Duration 1)=281+(301)=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=Start day+(Duration 1)=311+(351)=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.

Completion day=Start day+(Duration 1)=346+(401)=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=Completion dayDue date=345320=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.

Lateness=Completion dayDue date=385360=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 tartiness=Total latenessNumber of jobs=505=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.

Average flow time=Total flow timeTotal duration=385145=2.66

Utilization rating:

It is calculated by dividing total processing time and total flow time. Hence, the utilization rating is 38.6%.

Utilization=Total processing timeTotal flow time×100=145385×100=37.6%

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 tartiness=Total latenessNumber of jobs=605=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.

Average flow time=Total flow timeTotal duration=375145=2.59

Utilization rating:

It is calculated by dividing total processing time and total flow time. Hence, the utilization rating is 38.6%.

Utilization=Total processing timeTotal flow time×100=145375×100=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 tartiness=Total latenessNumber of jobs=2205=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.

Average flow time=Total flow timeTotal duration=495145=3.41

Utilization rating:

It is calculated by dividing total processing time and total flow time. Hence, the utilization rating is 29.3%.

Utilization=Total processing timeTotal flow time×100=145495×100=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 tartiness=Total latenessNumber of jobs=605=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 2.69.

Average flow time=Total flow timeTotal duration=390145=2.69

Utilization rating:

It is calculated by dividing total processing time and total flow time. Hence, the utilization rating is 37.2%.

Utilization=Total processing timeTotal flow time×100=145390×100=37.2%

b)

Summary Introduction

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)

Expert Solution
Check Mark

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)

Summary Introduction

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)

Expert Solution
Check Mark

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)

Summary Introduction

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)

Expert Solution
Check Mark

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)

Summary Introduction

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)

Expert Solution
Check Mark

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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