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 19P

a)

Summary Introduction

To determine: Sequence of jobs 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 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 A=Start day+(Duration 1)=130+(201)=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 B=Start day+(Duration 1)=150+(301)=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 C=Start day+(Duration 1)=180+(101)=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 D=Start day+(Duration 1)=190+(161)=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.

End day of Job E=Start day+(Duration 1)=206+(181)=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 C=End dayDue date=189175=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.

Lateness of Job E=End dayDue date=223210=13

b)

Summary Introduction

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)

Expert Solution
Check Mark

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 C=Start day+(Duration 1)=130+(101)=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 A=Start day+(Duration 1)=140+(201)=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 B=Start day+(Duration 1)=160+(301)=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 E=Start day+(Duration 1)=190+(181)=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.

End day of Job D=Start day+(Duration 1)=208+(161)=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)

Summary Introduction

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)

Expert Solution
Check Mark

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 C=Start day+(Duration 1)=130+(101)=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 D=Start day+(Duration 1)=140+(161)=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 E=Start day+(Duration 1)=156+(181)=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 A=Start day+(Duration 1)=174+(201)=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.

End day of Job B=Start day+(Duration 1)=194+(301)=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 A=End dayDue date=193180=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.

Lateness of Job B=End dayDue date=223200=23

d)

Summary Introduction

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)

Expert Solution
Check Mark

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 B=Start day+(Duration 1)=130+(301)=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 A=Start day+(Duration 1)=160+(201)=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 E=Start day+(Duration 1)=180+(181)=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 D=Start day+(Duration 1)=198+(161)=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.

End day of Job C=Start day+(Duration 1)=214+(101)=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.

Lateness of Job C=End dayDue date=223175=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 tartiness=Total latenessNumber of jobs=275=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 flow time=Total flow timeNumber of jobs=3005=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.

Average flow time=Total flow timeTotal duration=30094=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 tartiness=Total latenessNumber of jobs=05=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 flow time=Total flow timeNumber of jobs=2725=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.

Average flow time=Total flow timeTotal duration=27294=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 tartiness=Total latenessNumber of jobs=365=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 flow time=Total flow timeNumber of jobs=2385=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.

Average flow time=Total flow timeTotal duration=23894=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 tartiness=Total latenessNumber of jobs=485=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 flow time=Total flow timeNumber of jobs=3265=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.

Average flow time=Total flow timeTotal duration=32694=3.5

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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