Principles Of Operations Management
Principles Of Operations Management
11th Edition
ISBN: 9780135173930
Author: RENDER, Barry, HEIZER, Jay, Munson, Chuck
Publisher: Pearson,
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Chapter 15, Problem 15P

a)

Summary Introduction

To determine: Thesequence of jobs based on the decision rule, i.e, First Come First Served (FCFS).

Introduction: The 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 15P

The sequence is A-B-C-D-E.

Explanation of Solution

Given information:

The following information has been given below:

Job Due date Duration (days)
A 313 8
B 312 16
C 325 40
D 314 5
E 314 3

All the jobs have arrived on day 275.

Determine the sequence of the job by using FCFS:

Job Due date Duration (days) Flow time Start End Lateness
A 313 8 8 275 282
B 312 16 24 283 298
C 325 40 64 299 338 13
D 314 5 69 339 343 29
E 314 3 72 344 346 32
Total 72 237 74

Working note:

The duration and due date for the jobs has been given. The flow time is the cumulative value of the duration. The jobs arrival rate is given as 275.

End day of Job A:

The jobs arrival rate is given as 275. The 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 282.

End day of Job A=Start day+(Duration 1)=275+(81)=282

End day of Job B:

The start day of Job B is the next day of the end day of Job A. The 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 298.

End day of Job B=Start day+(Duration 1)=283+(161)=298

End day of Job C:

The start day of Job C is the next day of the end day of Job B. The 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 338.

End day of Job C=Start day+(Duration 1)=299+(401)=338

End day of Job D:

The start day of Job D is the next day of the end day of Job C. The 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 343.

End day of Job D=Start day+(Duration 1)=339+(51)=343

End day of Job E:

The start day of Job E is the next day of the end day of Job D. The 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 346.

End day of Job E=Start day+(Duration 1)=344+(31)=346

Lateness of Job A and Job B:

The end day of Job A and Job B is less than its respective due date. Hence, there is 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 13.

Lateness of Job C=End dayDue date=338325=13

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 29.

Lateness of Job D=End dayDue date=343314=29

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 32.

Lateness of Job E=End dayDue date=346314=32

b)

Summary Introduction

To determine: The sequence of jobs based on the decision rule, i.e, Earliest Due Date (EDD).

Introduction: The 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 go on from the earliest due date to the latest due date.

b)

Expert Solution
Check Mark

Answer to Problem 15P

The sequence is B-A-D-E-C.

Explanation of Solution

Given information:

The following information has been given below:

Job Due date Duration (days)
A 313 8
B 312 16
C 325 40
D 314 5
E 314 3

All the jobs have arrived on day 275.

Determine the sequence of the job by using EDD:

Job Due date Duration (days) Flow time Start End Lateness
B 312 16 16 275 290
A 313 8 24 291 298
D 314 5 29 299 303
E 314 3 32 304 306
C 325 40 72 307 346 21
Total 72 173 21

Working note:

The duration and due date for the jobs have been given. The flow time is the cumulative value of the duration. The jobs arrival rate is given as 275. The job should be arranged based on the due date. The due date should be assembled in the ascending order.

End day of Job A:

The jobs arrival rate is given as 275. The 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 290.

End day of Job A=Start day+(Duration 1)=275+(161)=290

End day of Job B:

The start day of Job B is the next day of the end day of Job A. The 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 298.

End day of Job B=Start day+(Duration 1)=291+(81)=298

End day of Job C:

The start day of Job C is the next day of the end day of Job B. The 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 303.

End day of Job C=Start day+(Duration 1)=299+(51)=303

End day of Job D:

The start day of Job D is the next day of the end day of Job C. The 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 306.

End day of Job D=Start day+(Duration 1)=304+(31)=306

End day of Job E:

The start day of Job E is the next day of the end day of Job D. The 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 346.

End day of Job E=Start day+(Duration 1)=307+(401)=346

Lateness of Job A, Job B, Job C, and Job D is given below:

The end day of Job A, Job B, Job C, and Job dare less than its respective due date. Hence, there is no lateness.

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 21.

Lateness of Job E=End dayDue date=346325=21

c)

Summary Introduction

To determine: The sequence of jobs based on the decision rule, i.e, Shortest Processing Time (SPT).

Introduction: The Shortest Processing Time is the scheduling rule, which helps to arrange the sequence in the order. Here, the job with the shortest duration is served first. Then, the process would be go on from the shortest to the largest duration.

c)

Expert Solution
Check Mark

Answer to Problem 15P

The sequence is E-D-A-B-C.

Explanation of Solution

Given information:

The following information has been given below:

Job Due date Duration (days)
A 313 8
B 312 16
C 325 40
D 314 5
E 314 3

All the jobs are arrived on day 275.

Determine the sequence of the job by using SPT:

Job Due date Duration (days) Flow time Start End Lateness
E 314 3 3 275 277
D 314 5 8 278 282
A 313 8 16 283 290
B 312 16 32 291 306
C 325 40 72 307 346 21
Total 72 131 21

Working note:

The duration and due date for the jobs have been given. The flow time is the cumulative value of the duration. The jobs arrival rate is given as 275. The job should be arranged based on the duration (processing time). The duration should be assembled in the ascending order.

End day of Job A:

The jobs arrival rate is given as 275. The 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 277.

End day of Job A=Start day+(Duration 1)=275+(31)=277

End day of Job B:

The start day of Job B is the next day of the end day of Job A. The 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 282.

End day of Job B=Start day+(Duration 1)=278+(51)=282

End day of Job C:

The start day of Job C is the next day of the end day of Job B. The 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 290.

End day of Job C=Start day+(Duration 1)=283+(81)=290

End day of Job D:

The start day of Job D is the next day of the end day of Job C. The 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 306.

End day of Job D=Start day+(Duration 1)=291+(161)=306

End day of Job E:

The start day of Job E is the next day of the end day of Job D. The 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 346.

End day of Job E=Start day+(Duration 1)=307+(401)=346

Lateness of Job A, Job B, Job C, and Job D is as follows:

The end day of Job A, Job B, Job C, and Job D are less than its respective due date. Hence, there is no lateness.

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 21.

Lateness of Job E=End dayDue date=346325=21

d)

Summary Introduction

To determine: The sequence of jobs based on the decision rule, i.e, Longest Processing Time (LPT).

Introduction: The Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, the job with the largest duration is served first. Then, the process would go on from the largest to the shortest duration.

d)

Expert Solution
Check Mark

Answer to Problem 15P

The sequence is C-B-A-D-E.

Explanation of Solution

Given information:

The following information has been given below:

Job Due date Duration (days)
A 313 8
B 312 16
C 325 40
D 314 5
E 314 3

All the jobs have arrived on day 275.

Determine the sequence of the job by using LPT:

Job Due date Duration (days) Flow time Start End Lateness
C 325 40 40 275 314
B 312 16 56 315 330 18
A 313 8 64 331 338 25
D 314 5 69 339 343 29
E 314 3 72 344 346 32
Total 72 301 104

Working note:

The duration and due date for the jobs have been given. The flow time is the cumulative value of the duration. The jobs arrival rate is given as 275. The job is arranged based on the duration (processing time). The duration should be assembled in the descending order

End day of Job A:

The jobs arrival rate is given as 275. The 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 314.

End day of Job A=Start day+(Duration 1)=275+(401)=314

End day of Job B:

The start day of Job B is the next day of the end day of Job A. The 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 330.

End day of Job B=Start day+(Duration 1)=315+(161)=330

End day of Job C:

The start day of Job C is the next day of the end day of Job B. The 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 338.

End day of Job C=Start day+(Duration 1)=331+(81)=338

End day of Job D:

The start day of Job D is the next day of the end day of Job C. The 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 343.

End day of Job D=Start day+(Duration 1)=339+(51)=343

End day of Job E:

The start day of Job E is the next day of the end day of Job D. The 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 346.

End day of Job E=Start day+(Duration 1)=344+(31)=346

Lateness of Job A:

The end day of Job A is less than its respective due date. Hence, there is 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 18.

Lateness of Job B=End dayDue date=330312=18

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 25.

Lateness of Job C=End dayDue date=338313=25

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 29.

Lateness of Job D=End dayDue date=343314=29

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 32.

Lateness of Job E=End dayDue date=346314=32

Summary:

Decision rule Average tardiness Average flow time Average number of jobs in system
FCFS 14.8 47.4 3.3
EDD 4.2 34.6 2.4
SPT 4.2 26.2 1.8
LPT 20.8 60.2 4.2

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 14.8.

Average tartiness=Total latenessNumber of jobs=745=14.8

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 47.4.

Average flow time=Total flow timeNumber of jobs=2375=47.4

Average number of jobs in the system:

It is calculated by dividing the total flow time with the total duration of all the jobs. Hence, the average number of jobs in the system is 3.3.

Average flow time=Total flow timeTotal duration=23772=3.3

Earliest Due Date (EDD):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 4.2.

Average tartiness=Total latenessNumber of jobs=215=4.2

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 34.6.

Average flow time=Total flow timeNumber of jobs=1735=34.6

Average number of jobs in the system:

It is calculated by dividing the total flow time with the 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=17372=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 4.2.

Average tartiness=Total latenessNumber of jobs=215=4.2

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 26.2.

Average flow time=Total flow timeNumber of jobs=1315=26.2

Average number of jobs in the system:

It is calculated by dividing the total flow time with the total duration of all the jobs. Hence, the average number of jobs in the system is 1.8.

Average flow time=Total flow timeTotal duration=13172=1.8

Largest processing time (LPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 20.8.

Average tartiness=Total latenessNumber of jobs=1045=20.8

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 60.2.

Average flow time=Total flow timeNumber of jobs=3015=60.2

Average number of jobs in the system:

It is calculated by dividing the total flow time with the total duration of all the jobs. Hence, the average number of jobs in the system is 4.2.

Average flow time=Total flow timeTotal duration=30172=4.2

Conclusion

Shortest processing time has the minimum average tardiness, average flow time, and the average number of jobs in systems. Hence, SPT is the best decision rule.

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