CHAPTER 15
DISCUSSION QUESTIONS
1.
Five priority sequencing rules are:

First come, first served (FCFS); or First in, first out (FIFO): Jobs are sequenced in the order in
which they arrive at the workstation.

Earliest due date (EDD): Jobs are sequenced in the order in which they are due for delivery to
the customer.

Shortest processing time (SPT): Jobs are sequenced in order of the processing time required at
the workstation, with the job requiring the least processing time at the workstation scheduled
first.

Longest processing time (LPT): Jobs are sequenced in order of the processing time required at
the workstation, with the job requiring the longest processing time at the workstation
scheduled first.

Critical ratio (CR): Jobs are sequenced in order of increasing critical ratio (the ratio of time
required by work left to be done to time left to do the work)
2.
Johnson’s rule is used to sequence several jobs through two or three work centers.
6.
The are a number of criteria for evaluating job sequencing rules. Criteria discussed in the text
include:

Average job completion time

Average number of jobs in the system

Average job lateness.
Additional criteria include: average wait time, average total completion time, and variance in
completion times.
END-OF-CHAPTER PROBLEMS
15.10
Job
A
B
C
D
E
(a)
Due Date
313
312
325
314
314
Duration (Days)
8
16
40
5
3
FCFS (first come, first served):
Because all jobs arrived on day 275, and presumably in the order given, the FCFS sequence is:
A, B, C, D, E
Chapter 15: Short Term Scheduling
1
(b)
EDD (earliest due date):
Job Sequence
B
A
D
E
C
(c)
Due Date
312
313
314
314
325
SPT (shortest processing time)
Job Sequence Processing Time
E
3
D
5
A
8
B
16
C
40
(d)
LPT (longest processing time)
Job Sequence
C
B
A
D
E
Scheduling
Rule
FCFS
EDD
SPT
LPT
Processing Time
40
16
8
5
3
Average
Tardiness
14.8
4.2
4.2
20.8
15.12
Job
A
B
C
D
2
Due Date
212
209
208
210
Average
Flow Time
47.4
34.6
26.2
60.2
Average Number
of Jobs in System
3.3
2.4
1.8
4.2
Remaining
Processing Time
6
3
3
8
Instructor’s Solutions Manual t/a Operations Management
Minimize total lateness. Comparing the scheduling efficiency of the several algorithms presented in
terms of lateness:
(a)
First Come, First Served (FCFS):
Job
A
B
C
D
(b)
End
Days Late
210
0
213
4
216
8
224
14
Total: 26 days
Processing Time
3
3
6
8
Due Date
209
208
212
210
Start
205
208
211
217
End
Days Late
207
0
210
2
216
4
224
14
Total: 20 days
Processing Time
8
6
3
3
Due Date
210
212
208
209
Start
205
213
219
222
End
Days Late
212
2
218
6
221
13
224
15
Total: 36 days
Due Date
208
209
210
212
Start
205
208
211
219
End
Days Late
207
0
210
1
218
8
224
12
Total: 21 days
Earliest Due Date (EDD):
Job
C
B
D
A
(e)
Start
205
211
214
217
Longest Processing Time (LPT):
Job
D
A
C
B
(d)
Due Date
212
209
208
210
Shortest Processing Time (SPT):
Job
B
C
A
D
(c)
Processing Time
6
3
3
8
Processing Time
3
3
8
6
Critical Ratio:
Job
A
B
C
D
Due Date
212
209
208
210
Remaining Processing Time
6
3
3
8
Critical Ratio 
Job Sequence
D
C
A
B
Chapter 15: Short Term Scheduling
Critical Ratio
6  117
.
209  205 3  133
.
208  205 3  100
.
210  205 8  0.63
212  205
Need date  today’s date
Days required to complete job
Critical Ratio
0.63
1.00
1.17
1.33
3
Critical Ratio:
Job
D
C
A
B
Processing Time
8
3
6
3
Due Date
210
208
212
209
Start
205
213
216
222
End
212
215
221
224
Total:
Days Late
2
7
9
15
33 days
A minimum total lateness of 20 days seems to be about the least we may achieve.
Scheduling
Rule
FCFS
SPT
LPT
EDD
Critical Ratio
15.13
Job
010
020
030
040
050
(a)
Average
Tardiness
6.5
5.0
9.0
5.2
8.3
Due Date
260
258
260
270
275
Average
Flow Time
11.8
10.2
14.8
10.8
14.0
Average Number
of Jobs in System
2.4
2.1
3.0
2.2
2.8
Duration (Days)
30
16
8
20
10
FCFS (first come, first served):
Because all jobs arrived on day 210, and presumably in the order given, the FCFS sequence is:
010, 020, 030, 040, 050
(b)
EDD (Earliest due date):
Job Sequence
020
010
030
040
050
(c)
Due Date
258
260
260
270
275
Note that the breaker of longest processing time was used; however, job 030 could come
before job 010.
SPT (shortest processing time):
Job Sequence Processing Time
030
8
050
10
020
16
040
20
010
30
4
Instructor’s Solutions Manual t/a Operations Management
(d)
LPT (longest processing time):
Job Sequence
010
040
020
050
030
Scheduling
Rule
FCFS
EDD
SPT
LPT
*
15.14
Average
Tardiness
(7.4)*
6.8
(7.4)*
6.8
(6.8)*
6.6
(12.6)*
12.0
Date Order Due
180
200
175
230
210
FCFS (first come, first served):
Date Order Received
110
120
122
125
130
EDD (earliest due date):
Job Sequence
C
A
B
E
D
(c)
Average Number
of Jobs in System
3.4
3.3
2.4
3.6
Due Order Received Production Days Needed
110
20
120
30
122
10
125
16
130
18
Job Sequence
A
B
C
D
E
(b)
Average
Flow Time
57.6
54.8
39.6
61.2
If current time is 210.
Job
A
B
C
D
E
(a)
Processing Time
30
20
16
10
8
Due Date
175
180
200
210
230
SPT (shortest processing time):
Job Sequence Processing Time
C
10
D
16
E
18
A
20
B
30
Chapter 15: Short Term Scheduling
5
(d)
LPT (longest processing time):
Job Sequence Processing Time
B
30
A
20
E
18
D
16
C
10
Scheduling
Rule
FCFS
EDD
SPT
LPT
15.16
Job
1
2
3
4
5
Average
Tardiness
5.4
0.0
7.2
9.6
Average
Flow Time
60.0
54.4
47.6
65.2
Date Job Received Production Days Needed
215
30
220
20
225
40
240
50
250
20
Average Number of
Jobs in System
3.2
2.9
2.5
3.5
Date Job Due
260
290
300
320
340
Critical Ratio
0.33
2.00
1.25
1.40
4.50
Jobs should be scheduled in the sequence 1, 3, 4, 2, 5 if scheduled by the critical ratio scheduling
rule.
15.17
Job
A
B
C
D
Data Entry (Hours)
2.5
3.8
1.9
1.8
Verify (Hours)
1.7
2.6
1.0
3.0
Using Johnson’s Rule, the optimal sequence is:
D, B, A, C
Job
Entry
Time
Job
Verify
Time
D
B
A
1.8
5.6
D
1.8
C
8.1
B
4.8
10.0
A
8.2
C
9.9
11.0
Idle
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Instructor’s Solutions Manual t/a Operations Management
15.18
Job
A
B
C
D
E
F
Opn 1 (Hours) Opn 2 (Hours)
10
5
7
4
5
7
3
8
2
6
4
3
Using Johnson’s Rule, the optimal sequence is:
E, D, C, A, B, F
Job E D
C
Operation 1
Time 0 2
5
10
Job
Operation 2
Time
E
2
A
F
20
D
8
B
27
C
16
A
23
31
B
28
F
32 35
Idle
Chapter 15: Short Term Scheduling
7