260 CHAPTER 15 SH O R T –T E R M SC H E D U L I N G
15.16
Job
Due Date
Remaining Days
Critical Ratio
103
214
10
1.40
205
223
7
3.29
309
217
11
1.55
412
219
5
3.80
517
217
15
1.13
Jobs should be scheduled in the sequence 517, 103, 309, 205, 412
if scheduled by the critical ratio scheduling rule.
15.17
Job
Due date
A
212
B
209
C
208
D
210
Minimize total lateness. Comparing the scheduling efficiency of
Job
Processing
Time
Due
Date
Start
End
Days Late
A
6
212
205
210
0
B
3
209
211
213
4
C
3
208
214
216
8
D
8
210
217
224
14
Total: 26 days
(b) Shortest processing time (SPT):
Job
Processing
Time
Due
Date
Start
End
Days Late
B
3
209
205
207
0
C
3
208
208
210
2
A
6
212
211
216
4
D
8
210
217
224
14
Total: 20 days
Job
Processing
Time
Due
Date
Start
End
Days Late
D
8
210
205
212
2
A
6
212
213
218
6
C
3
208
219
221
13
B
3
209
222
224
15
Total: 36 days
(d) Earliest due date (EDD):
Job
Processing
Time
Due
Date
Start
End
Days Late
C
3
208
205
207
0
B
3
209
208
210
1
D
8
210
211
218
8
A
6
212
219
224
12
Total: 21 days
Job
Due
Date
Remaining
Processing
Time
Critical Ratio
A
212
6
(212 – 205)/6 = 1.17
B
209
3
(209 – 205)/3 = 1.33
C
208
3
(208 – 205)/3 = 1.00
D
210
8
(210 – 205)/8 = 0.63
Job Sequence
Critical Ratio
D
0.63
C
1.00
A
1.17
B
1.33
Critical ratio:
Job
Processing
Time
Due
Date
Start
End
Days Late
D
8
210
205
212
2
C
3
208
213
215
7
A
6
212
216
221
9
B
3
209
222
224
15
Total: 33
days
least we may achieve.
Average
Number
Scheduling
Average
Average
of Jobs in
Rule
Lateness
Flow Time
System
FCFS
6.5
11.8
2.4
SPT
5.0
10.25
2.1
LPT
9.0
14.8
3.0
EDD
5.25
10.8
2.2
Critical ratio
8.3
14.0
2.8
SPT is best on all criteria.
262 CHAPTER 15 SH O R T –T E R M SC H E D U L I N G
(b) The best flow time is SPT; (c) best utilization is SPT;
B
30
15.19
10
16
18
20
(d) LPT (longest processing time):
A
20
E
18
D
16
C
10
Job
Date
Order
Received
Production
Days
Needed
Date
Order
Due
CHAPTER 15 SH O R T –T E R M SC H E D U L I N G 263
15.22 (a, c) The jobs should be processed in the sequence
V–Y–U–Z–X–W–T, for a total time of 57.
times.
(d) Binding is idle from 0 to 4 and from 51 to 54 for a
total of 7 hours.
020
258
010
260
Job Sequence
finished any sooner, but other jobs are completed ½ hour
earlier.
15.23
Job Sequence
Processing Time
Using Johnson’s rule, the optimal sequence is:
15.24*
Job
Due Date
Duration (Days)
010
260
30
020
258
16
030
260
8
040
270
20
050
275
10
presumably in the order given, the FCFS sequence is:
010, 020, 030, 040, 050
(b) EDD (earliest due date):
Job Sequence
Due Date
030
260
040
270
050
275
Note that the tie breaker of longest processing time was
030
8
050
10
020
16
010
30
(d) LPT (longest processing time):
Job
Operation 1 (Hours)
Operation 2 (Hours)
Job Shop Scheduling Flow Time
Printer
Binder
Order
Printer
Binder
264 CHAPTER 15 SH O R T –T E R M SC H E D U L I N G
Average
Number
Scheduling
Average
Average
of Jobs in
Rule
Lateness
Flow Time
System
SPT
6.6
39.6
2.4
15.25*
Job
Data Entry (Hours)
Verify (Hours)
A
2.5
1.7
B
3.8
2.6
1.9
1.0
Worker 2
5
4
4
4
5
Worker 3
4
3
4
4
3
Worker 4
3
3
3
2
3
Worker 5
2
2
2
3
2
Worker 6
1
Worker 3
3
3
4
5
3
Worker 4
2
3
3
4
2
Worker 5
2
2
2
2
3
Worker 6
1
1
1
1
2
15.26
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Worker 1
6
5
5
5
6
15.27
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Worker 1
4
4
5
6
7
Worker 2
3
4
5
6
4
266 CHAPTER 15 SH O R T –T E R M SC H E D U L I N G
VIDEO CASE STUDIES
FROM THE EAGLES TO THE MAGIC: CONVERTING THE AMWAY CENTER
This case study works best if the short (9-minute) video, made specifically for this text, is shown and accompanies the written case.
1. Concert to Basketball Conversion Task:
2. Floor is scheduled to be ready at 5:35 A.M.
3. Only crew of 10 is required for the first 15 min.
Only crew of 6 is required for the retractable seating.
Only crew of 12 is required for end–of-shift activities.
Students should be able to determine crew requirements from the
1
CHAPTER 15 SH O R T –T E R M SC H E D U L I N G 267
SCHEDULING AT HARD ROCK CAFE
This case study works best if the 7-minute video, made specifically
for this text, is shown and accompanies the written case.
1. Hoffman currently uses these factors in forecasting weekly
cafe sales: (1) last year’s sales, (2) convention center data, (3)
ADDITIONAL CASE STUDY
(AVAILABLE IN MYOMLAB)
PAYROLL PLANNING, INC.
The first step in tackling this case study is to translate the due
dates into minutes. Thus, for the monthly clients, the due dates are
2