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248 CHAPTER 15 SH O R T -T E R M SC H E D U L I N G
15.21
Period
1
2
3
4
Total
Planned input
80
80
100
100
360
Actual input
85
85
85
85
340
Deviation
+5
+5
–15
–15
–20
Planned output
90
90
90
90
360
Actual output
85
85
80
80
330
Deviation
–5
–5
–10
–10
–30
Backlog: 30
30
30
35
40
Analysis: The completed input/output report shows that the Grinding
work center did not process all the jobs that were available during the
15.22 (a) Assign:
Job
to
Machine
1
A
2
D
3
B
4
C
(b) Total cost: 23
Subtracting the smallest number from each column:
15.20
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Worker 1
4
4
5
6
7
Worker 2
3
4
5
6
4
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
Worker 7
1
1
1
Note: Seven employees are needed: six have 2 consecutive days off. The 7th
worker has 4 days off and works only 3 days.
CHAPTER 15 SH O R T -T E R M SC H E D U L I N G 249
Subtracting the smallest uncovered number (200) from all
uncovered numbers, and adding it to the numbers at the
intersections of the lines:
Again, draw the minimum number of lines needed to cover
the zeros:
The solution is now optimal, and the assignments can be
made in the following manner:
Assignment
Cost
Divorce case to Attorney 3
1,200
Felony case to Attorney 1
500
Discrimination case to Attorney 2
1,000
$2,700
250 CHAPTER 15 SH O R T -T E R M SC H E D U L I N G
Subtracting the smallest number from every column:
252 CHAPTER 15 SH O R T -T E R M SC H E D U L I N G
The following optimal assignments can now be made:
Assignments
Cost
Component G99 to Plant 1
0.55
Component E2 to Plant 2
0.07
Component C81 to Plant 3
0.04
Component D5 to Plant 4
0.30
Component D44 to Plant 5
0.10
Component C53 to Plant 6
0.06
Component E35 to Plant 8
0.06
Total Cost:
$1.18
Plant 7 will not be given a component.
15.26
Job
Due Date
Duration (Days)
010
260
30
020
258
16
030
260
8
040
270
20
050
275
10
(a) FCFS (first come, first served):
Because all jobs arrived and begin on day 210, and
010, 020, 030, 040, 050
(b) EDD (earliest due date):
030
260
040
270
050
275
Note that the tie breaker of longest processing time was
used; however, job 030 could come before job 010.
Average
Number
Scheduling
Average
Average
of Jobs in
Rule
Lateness
Flow Time
System
FCFS
6.8
57.6
3.4
EDD
6.8
54.8
3.3
SPT
6.6
39.6
2.4
LPT
12.0
61.2
3.6
Beginning time is 210 and day 210 is a work day.
15.27
Job
Data Entry (Hours)
Verify (Hours)
A
2.5
1.7
B
3.8
2.6
C
1.9
1.0
D
1.8
3.0
Using Johnson’s Rule, the optimal sequence is:
D, B, A, C
1. The assignment algorithm can be utilized to yield the fastest
time to complete a table:
Person
Job
Time (Minutes)
Tom
Preparation
100
Cathy
Assembly
70
CHAPTER 15 SH O R T -T E R M SC H E D U L I N G 253
If Cathy is assigned to the finishing task, the optimum assign-
254 CHAPTER 15 SH O R T -T E R M SC H E D U L I N G
1. Hoffman currently uses these factors in forecasting weekly
cafe sales: (1) last year’s sales, (2) convention center data, (3)
hotel occupancy rates, (4) concerts scheduled at Hard Rock Live.
Other factors could include (1) weather forecasts (most tourists
ADDITIONAL CASE STUDY*
Jobs in
Average
Average
Rule
Systems
Flow Time
Lateness
Earliest due date (EDD)
20.80
928
193
SPT
12.03
537
135
Critical ratio
22.82
1,018
273
$120
248 CHAPTER 15 SH O R T -T E R M SC H E D U L I N G
15.21
Period
1
2
3
4
Total
Planned input
80
80
100
100
360
Actual input
85
85
85
85
340
Deviation
+5
+5
–15
–15
–20
Planned output
90
90
90
90
360
Actual output
85
85
80
80
330
Deviation
–5
–5
–10
–10
–30
Backlog: 30
30
30
35
40
Analysis: The completed input/output report shows that the Grinding
work center did not process all the jobs that were available during the
15.22 (a) Assign:
Job
to
Machine
1
A
2
D
3
B
4
C
(b) Total cost: 23
Subtracting the smallest number from each column:
15.20
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Worker 1
4
4
5
6
7
Worker 2
3
4
5
6
4
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
Worker 7
1
1
1
Note: Seven employees are needed: six have 2 consecutive days off. The 7th
worker has 4 days off and works only 3 days.
CHAPTER 15 SH O R T -T E R M SC H E D U L I N G 249
Subtracting the smallest uncovered number (200) from all
uncovered numbers, and adding it to the numbers at the
intersections of the lines:
Again, draw the minimum number of lines needed to cover
the zeros:
The solution is now optimal, and the assignments can be
made in the following manner:
Assignment
Cost
Divorce case to Attorney 3
1,200
Felony case to Attorney 1
500
Discrimination case to Attorney 2
1,000
$2,700
250 CHAPTER 15 SH O R T -T E R M SC H E D U L I N G
Subtracting the smallest number from every column:
252 CHAPTER 15 SH O R T -T E R M SC H E D U L I N G
The following optimal assignments can now be made:
Assignments
Cost
Component G99 to Plant 1
0.55
Component E2 to Plant 2
0.07
Component C81 to Plant 3
0.04
Component D5 to Plant 4
0.30
Component D44 to Plant 5
0.10
Component C53 to Plant 6
0.06
Component E35 to Plant 8
0.06
Total Cost:
$1.18
Plant 7 will not be given a component.
15.26
Job
Due Date
Duration (Days)
010
260
30
020
258
16
030
260
8
040
270
20
050
275
10
(a) FCFS (first come, first served):
Because all jobs arrived and begin on day 210, and
010, 020, 030, 040, 050
(b) EDD (earliest due date):
030
260
040
270
050
275
Note that the tie breaker of longest processing time was
used; however, job 030 could come before job 010.
Average
Number
Scheduling
Average
Average
of Jobs in
Rule
Lateness
Flow Time
System
FCFS
6.8
57.6
3.4
EDD
6.8
54.8
3.3
SPT
6.6
39.6
2.4
LPT
12.0
61.2
3.6
Beginning time is 210 and day 210 is a work day.
15.27
Job
Data Entry (Hours)
Verify (Hours)
A
2.5
1.7
B
3.8
2.6
C
1.9
1.0
D
1.8
3.0
Using Johnson’s Rule, the optimal sequence is:
D, B, A, C
1. The assignment algorithm can be utilized to yield the fastest
time to complete a table:
Person
Job
Time (Minutes)
Tom
Preparation
100
Cathy
Assembly
70
CHAPTER 15 SH O R T -T E R M SC H E D U L I N G 253
If Cathy is assigned to the finishing task, the optimum assign-
254 CHAPTER 15 SH O R T -T E R M SC H E D U L I N G
1. Hoffman currently uses these factors in forecasting weekly
cafe sales: (1) last year’s sales, (2) convention center data, (3)
hotel occupancy rates, (4) concerts scheduled at Hard Rock Live.
Other factors could include (1) weather forecasts (most tourists
ADDITIONAL CASE STUDY*
Jobs in
Average
Average
Rule
Systems
Flow Time
Lateness
Earliest due date (EDD)
20.80
928
193
SPT
12.03
537
135
Critical ratio
22.82
1,018
273
$120
