Solved Problem 2,3
Job Sequencing
<Back Notes
Current Date: 0
Process. Due Remain CR Critical Flow Days
Job Time Date Oper. Sequence Ratio Slack S/O Time Late
a12 15 1.25 312 0
b 6 24 418 18 0
Totals 42 031 139 75
Method FCFS
Notes:
1. Enter Job Name, Processing Time, and Due Date for each job.
2.
For the FCFS, SPT, and DD rules, simply press the appropriate button.
3. For the CR rule, perform the following BEFORE pressing the CR button:
a. Select job with lowest Critical Ratio
c. Add the processing time for that job to the current date.
e. Then press the CR button.
4. Fill in the Remaining Operations column and then press the S/O button.
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40
A B C D E F
Days Late
Clear
FCFS
SPT
DD
CR
S/O
Page 18
c14 20 1.4285714 632 12
Solved Problem 4
Job Sequencing
<Back Notes
Current Date: 0
Process. Due Remain CR Critical Flow Days
Job Time Date Oper. Sequence Ratio Slack S/O Time Late
C10 6 2 0.6 -4 -2 10 4
B11 18 51.6363636 71.4 21 3
Method S/O
Average Flow Time 31.25 A27
Average Tardiness 12.00 B 3
See notes below.
Notes:
1. Enter Job Name, Processing Time, and Due Date for each job.
2.
For the FCFS, SPT, and DD rules, simply press the appropriate button.
3. For the CR rule, perform the following BEFORE pressing the CR button:
a. Select job with lowest Critical Ratio
b. Schedule that job next by entering next sequence number (start with 1) in the
CR Sequence cloumn.
c. Add the processing time for that job to the current date.
d. Repeat steps a, b, and c until all jobs have been schduled (i.e. the CR
Sequence column is filled in).
e. Then press the CR button.
4. Fill in the Remaining Operations column and then press the S/O button.
Back to top
30
Days Late
Clear
FCFS
SPT
DD
CR
S/O
Page 19
D16 23 41.4375 71.75 37 14
Solved Problem 5
Clear
Page 20
Chapter 16 – Problems 1-8 Note: This worksheet displays results only, you must copy the shaded
<Back area into the corresponding template to make additional calculations.
1.
Assignment Model
Input Matrix: Worker/Machine
A B C D E
1 5 8 6 1
Total Jobs = 3
Total Workers/Machines = 3
Solution Matrix: Worker/Machine
A B C D E
1100001
2010001
3001001
4000000
2.
Assignment Model
Input Matrix: Worker/Machine
A B C D E
1-5 -8 -6 1
2-6 -7 -9 1
3-4 -5 -3 1
Total Jobs = 3
Total Workers/Machines = 3
Solution Matrix: Worker/Machine
A B C D E
1010001
2001001
3100001
4000000
3.
Assignment Model
2 6 7 9 1
3 4 5 3 1
Input Matrix: Worker/Machine
A B C D E
1459871
2648351
Total Jobs = 5
Total Workers/Machines = 5
Solution Matrix: Worker/Machine
A B C D E
1100001
3000101
4010001
4.
Assignment Model
Input Matrix: Worker/Machine
A B C D E
112 811 1
213 10 8 1
314 914 1
410 712 1
Total Jobs = 4
Total Workers/Machines = 3
Solution Matrix: Worker/Machine
A B C D E
1010001
2001001
3000000
4100001
5a.
Assignment Model
Input Matrix: Worker/Machine
A B C D E
114 18 20 17 18 1
214 15 19 16 17 1
312 16 15 14 17 1
411 13 14 12 14 1
4525581
11111
Total Jobs = 5
Total Workers/Machines = 5
Solution Matrix: Worker/Machine
A B C D E
1100001
5b.
Assignment Model
Input Matrix: Worker/Machine
A B C D E
1999 18 20 17 18 1
214 15 19 16 17 1
312 16 15 14 17 1
411 13 14 12 14 1
11111
Total Jobs = 5
Total Workers/Machines = 5
Solution Matrix: Worker/Machine
A B C D E
1000011
2010001
3001001
4000101
11111
6. Job Sequencing
FCFS: Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
A14 20 1.43 6.00 14.00 0.00
B10 16 1.60 6.00 24.00 8.00
Average Tardiness
2010001
3001001
4000101
11111
Average Number of Jobs 2.86
SPT: Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
D 6 17 2.83 11.00 6.00 0.00
C 7 15 2.14 8.00 13.00 0.00
Method SPT
Average Flow Time 19.75
Average Tardiness
6.00
Average Number of Jobs 2.14
DD: Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
C 7 15 2.14 8.00 7.00 0.00
D 6 17 2.83 11.00 23.00 6.00
A14 20 1.43 6.00 37.00 17.00
Method DD
Average Flow Time 21.00
Average Tardiness
6.00
Average Number of Jobs 2.27
After iterating to establish CR Sequence:
CR:
Process. Due Remain CR Critical Flow Days
Job Time Date Oper.
Sequence
Ratio Slack S/O Time Late
A14 20 1 6 14 0
C 7 15 2 8 21 6
D 6 17 311 27 10
Method CR
Average Flow Time 24.75
Average Tardiness
9.25
Average Number of Jobs 2.68
7. Job Sequencing
A14 20 1.43 6.00 37.00 17.00
FCFS:
Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
A 7 4 0.57143 -3 7 3
Method FCFS
Average Flow Time 17.40
SPT:
Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
C 2 12 610 2 0
B 4 10 2.5 6 6 0
A 7 4 0.57143 -3 13 9
Method SPT
Average Flow Time 14.80
DD:
Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
A 7 4 0.57143 -3 7 3
B 4 10 2.5 611 1
C 2 12 610 13 1
Average Flow Time 16.80
After iterating to establish CR sequence, note tie at 3rd job.
CR:
Process. Due Remain CR Critical Flow Days
Job Time Date Oper.
Sequence
Ratio Slack S/O Time Late
A 7 4 1 -3 7 3
B 4 10 2 6 11 1
B 4 10 2.5 611 1
C 2 12 610 13 1
Method CR
Average Flow Time 16.80
Average Tardiness
4.60
Average Number of Jobs 2.63
8. Job Sequencing
FCFS: Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
A 8 20 22.50 12.00 6.00 8.00 0.00
B10 18 41.80 8.00 2.00 18.00 0.00
D11 17 31.55 6.00 2.00 34.00 17.00
Method FCFS
Average Flow Time 25.20
Average Tardiness
5.00
Average Number of Jobs 2.93
S/O: Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
B10 18 41.80 8.00 2.00 10.00 0.00
D11 17 31.55 6.00 2.00 21.00 4.00
A 8 20 22.50 12.00 6.00 34.00 14.00
Method S/O
Average Flow Time 26.80
Average Tardiness
5.40
Average Number of Jobs 3.12
D11 20 5 9 32 12
Chapter 16 – Problems 9-18 Note: This worksheet displays results only, you must copy the shaded
<Back area into the corresponding template to make additional calculations.
9. Johnson’s Rule
Step 1 – Fill in jobs and times: Resulting schedule:
Job Time1 Time2 Job Start 1 Done 1 Start 2 Done 2 Idle 2
A1.2 1.4 B 0 0.9 0.9 2.2 0.9
C 2 0.8 G2.1 3.4 3.6 5 0
E1.6 1.8 F 5 7.2 7.2 8.95 0.4
G1.3 1.4 C8.9 10.9 10.9 11.7 0.45
Idle time-> 0.8 1.75
Step 2 – Assign job order:
A B A G E F D C
11. Johnson’s Rule
Step 1 – Fill in jobs and times: Resulting schedule:
Job Time1 Time2 Job Start 1 Done 1 Start 2 Done 2 Idle 2
A20 27 B 0 16 16 46 16
B16 30 A16 36 46 73 0
C43 51 C36 79 79 130 6
D60 12 E79 114 130 158 0
Idle time-> 12 56
Step 2 – Assign job order:
A B A C E F D
12. Johnson’s Rule
Step 1 – Fill in jobs and times: Resulting schedule:
Job Time1 Time2 Job Start 1 Done 1 Start 2 Done 2 Idle 2
a27 45 b 0 18 18 51 18
b18 33 a18 45 51 96 0
Idle time-> 23 37
Step 2 – Assign job order:
a b a c d e
13. Johnson’s Rule
Step 1 – Fill in jobs and times: Resulting schedule:
Job Time1 Time2 Job Start 1 Done 1 Start 2 Done 2 Idle 2
A 2 3 G 0 1 1 5 1
B 4 3 A 1 3 5 8 0
C 5 2 E 3 5 8 11 0
Idle time-> 1 1
Step 2 – Assign job order:
A G A E D B C F
15. Job Sequencing
FCFS: Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
a4.5 10 22.22 5.50 2.75 4.50 0.00
b 6 17 42.83 11.00 2.75 10.50 0.00
c5.2 12 32.31 6.80 2.27 15.70 3.70
d1.6 27 516.88 25.40 5.08 17.30 0.00
e2.8 18 36.43 15.20 5.07 20.10 2.10
c70 30 c45 115 115 145 19
d26 24 d115 141 145 169 0
e15 10 e141 156 169 179 0
f3.3 19 15.76 15.70 15.70 23.40 4.40
Totals 23.4 18 79.6 91.5 10.2
Method FCFS
SPT:
Process. Due Remain Critical Flow
Job Time Date Oper. Ratio Slack S/O Time
d1.6 27 516.88 25.40 5.08 1.60
e2.8 18 36.43 15.20 5.07 4.40
f3.3 19 15.76 15.70 15.70 7.70
a4.5 10 22.22 5.50 2.75 12.20
c5.2 12 32.31 6.80 2.27 17.40
b 6 17 42.83 11.00 2.75 23.40
Totals 23.4 18 79.6 66.7
Method SPT
DD:
Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
a4.5 10 22.22 5.50 2.75 4.50 0.00
c5.2 12 32.31 6.80 2.27 9.70 0.00
e2.8 18 36.43 15.20 5.07 18.50 0.50
f3.3 19 15.76 15.70 15.70 21.80 2.80
d1.6 27 516.88 25.40 5.08 23.40 0.00
Totals 23.4 18 79.6 93.6 3.3
Method DD
After iterating to establish CR sequence:
CR:
Process. Due Remain CR Critical Flow Days
Job Time Date Oper.
Sequence
Ratio Slack S/O Time Late
a4.5 10 2 1 5.5 2.75 4.5 0
e2.8 18 3 4 15.2 5.06667 18.5 0.5
d1.6 27 5 6 25.4 5.08 23.4 0
Totals 23.4 18 79.6 93.6 3.3
Method CR
Average Flow Time 15.60
16. Job Sequencing
S/O: Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
b 6 5 4 0.83 (1.00) (0.25) 6.00 1.00
c 9 10 41.11 1.00 0.25 15.00 5.00
e 8 10 21.25 2.00 1.00 23.00 13.00
Totals 35 15 10 107 62
Method S/O
Average Flow Time 21.40
17. Job Sequencing
FCFS: Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
c5.2 12 3 2 6.8 2.26667 9.7 0
a3.5 72.00 3.50 3.50 0.00
b 2 6 3.00 4.00 5.50 0.00
Method FCFS
Average Flow Time 12.50
SPT:
Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
b 2 6 3.00 4.00 2.00 0.00
e2.5 41.60 1.50 4.50 0.50
a3.5 72.00 3.50 8.00 1.00
c4.5 18 4.00 13.50 12.50 0.00
Method SPT
Average Flow Time 11.33
DD:
Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
e2.5 41.60 1.50 2.50 0.00
b 2 6 3.00 4.00 4.50 0.00
a3.5 72.00 3.50 8.00 1.00
c4.5 18 4.00 13.50 12.50 0.00
Method DD
c4.5 18 4.00 13.50 10.00 0.00
e2.5 41.60 1.50 17.50 13.50
Average Flow Time 11.58
After iterating to establish CR sequence:
CR: Process. Due Remain CR Critical Flow Days
Job Time Date Oper.
Sequence
Ratio Slack S/O Time Late
e2.5 4 1 1.5 2.5 0
a3.5 7 2 3.5 6 0
c4.5 18 513.5 18.5 0.5
Method CR
Average Flow Time 12.08
Average Tardiness
0.67
Average Number of Jobs 3.09
18. Job Sequencing
DD: Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
A64 160 2.50 96.00 64.00 0.00
Method DD
Average Flow Time 165.60
Average Tardiness
Average Tardiness
0.42
Average Number of Jobs 2.96
SPT:
Process. Due Remain Critical Flow Days
Job Time Date Oper. Ratio Slack S/O Time Late
E 4 220 55.00 216.00 4.00 0.00
Method SPT
Average Flow Time 111.20
Chapter 16 – Problems 23-25 Note: This worksheet displays results only, you must copy the shaded
<Back area into the corresponding template to make additional calculations.
23. Cyclical Scheduling
Mon Tue Wed Thu Fri Sat Sun
Staff Needed 2 3 1 2 4 3 5
Unmet Need 0 0 0 0 0 0 5
Worker 1 w w w w 4
Worker 2 w w w w 4
Worker 3 w w w w 4
24. Cyclical Scheduling
Mon Tue Wed Thu Fri Sat Sun
Staff Needed 3 4 2 3 4 5
Unmet Need 0 0 0 0 0 0 0
Worker 1 w w w w 4
Worker 2 w w w w 4
Worker 3 w w w w 4
Worker 4 w w w w 4
Worker 5 w w w 3
Worker 6 w w 2
Worker 7 0
Worker 8 0
25. Cyclical Scheduling
Mon Tue Wed Thu Fri Sat Sun
Staff Needed 4 4 5 6 7 8
Unmet Need 0 0 0 0 0 0 0
Worker 1 w w w w 4
Worker 2 w w w w 4
Worker 3 w w w w 4
Worker 4 w w w w 4
Worker 5 w w w w 4
Worker 6 w w w w 4
Worker 7 w w w w 4
Worker 8 w w w w 4
Worker 4 w w w 3
Worker 5 0
Worker 6 0
Worker 7 0
Worker 8 0