EBK PRINCIPLES OF OPERATIONS MANAGEMENT
EBK PRINCIPLES OF OPERATIONS MANAGEMENT
11th Edition
ISBN: 9780135175859
Author: Munson
Publisher: VST
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Chapter 15, Problem 17P

a)

Summary Introduction

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

a)

Expert Solution
Check Mark

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 A=Start day+(Duration 1)=205+(61)=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 B=Start day+(Duration 1)=211+(31)=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 C=Start day+(Duration 1)=214+(31)=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.

End day of Job D=Start day+(Duration 1)=217+(81)=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 B=End dayDue date=213209=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 C=End dayDue date=216208=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.

Lateness of Job D=End dayDue date=224210=14

b)

Summary Introduction

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)

Expert Solution
Check Mark

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 B=Start day+(Duration 1)=205+(31)=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 C=Start day+(Duration 1)=208+(31)=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 A=Start day+(Duration 1)=211+(61)=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.

End day of Job D=Start day+(Duration 1)=217+(81)=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 C=End dayDue date=210208=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 A=End dayDue date=216212=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.

Lateness of Job D=End dayDue date=224210=14

c)

Summary Introduction

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)

Expert Solution
Check Mark

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 D=Start day+(Duration 1)=205+(81)=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 A=Start day+(Duration 1)=213+(61)=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 C=Start day+(Duration 1)=219+(31)=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.

End day of Job B=Start day+(Duration 1)=222+(31)=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 D=End dayDue date=212210=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 A=End dayDue date=218212=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 C=End dayDue date=221208=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.

Lateness of Job B=End dayDue date=224209=15

d)

Summary Introduction

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)

Expert Solution
Check Mark

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 C=Start day+(Duration 1)=205+(31)=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 B=Start day+(Duration 1)=208+(31)=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 D=Start day+(Duration 1)=211+(81)=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.

End day of Job A=Start day+(Duration 1)=219+(61)=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 B=End dayDue date=210209=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 D=End dayDue date=218210=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.

Lateness of Job A=End dayDue date=224212=12

e)

Summary Introduction

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)

Expert Solution
Check Mark

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.

Critical ratio=(Due datePresent date)Remaining days=2122056=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.

Critical ratio=(Due datePresent date)Remaining days=2092053=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.

Critical ratio=(Due datePresent date)Remaining days=2082053=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.

Critical ratio=(Due datePresent date)Remaining days=2102058=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 D=Start day+(Duration 1)=205+(81)=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 C=Start day+(Duration 1)=213+(31)=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 A=Start day+(Duration 1)=216+(61)=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.

End day of Job B=Start day+(Duration 1)=222+(31)=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 D=End dayDue date=212210=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 C=End dayDue date=215208=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 A=End dayDue date=221212=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.

Lateness of Job B=End dayDue date=224209=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 tartiness=Total latenessNumber of jobs=264=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 flow time=Total flow timeNumber of jobs=474=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.

Average flow time=Total flow timeTotal duration=4720=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 tartiness=Total latenessNumber of jobs=204=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 flow time=Total flow timeNumber of jobs=514=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.

Average flow time=Total flow timeTotal duration=5120=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 tartiness=Total latenessNumber of jobs=364=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 flow time=Total flow timeNumber of jobs=594=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.

Average flow time=Total flow timeTotal duration=5920=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 tartiness=Total latenessNumber of jobs=214=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 flow time=Total flow timeNumber of jobs=434=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.

Average flow time=Total flow timeTotal duration=4320=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 tartiness=Total latenessNumber of jobs=364=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 flow time=Total flow timeNumber of jobs=564=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.

Average flow time=Total flow timeTotal duration=5620=4.8

Conclusion

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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