SOLUTION \blacktriangleright
1. The FCFS sequence shown in the next table is simply A–B–C–D–E.
| JOB SEQUENCE |
JOBWORK
(PROCESSING) TIME |
FLOW
TIME |
JOB DUE
DATE |
JOB
LATENESS |
| A |
6 |
6 |
8 |
0 |
| B |
2 |
8 |
6 |
2 |
| C |
8 |
16 |
18 |
0 |
| D |
3 |
19 |
15 |
4 |
| E |
9 |
28 |
23 |
5 |
|
28 |
77 |
|
11 |
The FCFS rule results in the following measures of effectiveness:
a. Average completion time = \frac{Sum of total flow time}{Number of jobs} = \frac{77 days}{5} = 15.4 days
b. Utilization metric = \frac{Total job work (processing) time}{Sum of total flow time} = \frac{28}{77} = 36.4%
c. Average number of jobs in the system = \frac{Sum of total flow time}{Total job work (processing) time} = \frac{77 days}{28 days} = 2.75 jobs
d. Average job lateness = \frac{Total late days}{Number of jobs} = \frac{11}{5} = 2.2 days
2. The SPT rule shown in the next table results in the sequence B–D–A–C–E. Orders are sequenced according to processing time, with the highest priority given to the shortest job.
| JOB SEQUENCE |
JOBWORK
(PROCESSING) TIME |
FLOW
TIME |
JOB DUE
DATE |
JOB
LATENESS |
| B |
2 |
2 |
6 |
0 |
| D |
3 |
5 |
15 |
0 |
| A |
6 |
11 |
8 |
3 |
| C |
8 |
19 |
18 |
1 |
| E |
9 |
28 |
23 |
5 |
|
28 |
65 |
|
9 |
Measurements of effectiveness for SPT are:
a. Average completion time = \frac{65}{5} = 13 days
b. Utilization metric = \frac{28}{65} = 43.1%
c. Average number of jobs in the system = \frac{65}{28} = 2.32 jobs
d. Average job lateness = \frac{9}{5} = 1.8 days
3. The EDD rule shown in the next table gives the sequence B–A–D–C–E. Note that jobs are ordered by earliest due date first.
| JOB SEQUENCE |
JOBWORK
(PROCESSING) TIME |
FLOW
TIME |
JOB DUE
DATE |
JOB
LATENESS |
| B |
2 |
2 |
6 |
0 |
| A |
6 |
8 |
8 |
0 |
| D |
3 |
11 |
15 |
0 |
| C |
8 |
19 |
18 |
1 |
| E |
9 |
28 |
23 |
5 |
|
28 |
68 |
|
6 |
Measurements of effectiveness for EDD are:
a. Average completion time = \frac{68}{5} = 13.6 days
b. Utilization metric = \frac{28}{68} = 41.2%
c. Average number of jobs in the system = \frac{68}{28} = 2.43 jobs
d. Average job lateness = \frac{6}{5} = 1.2 days
4. The LPT rule shown in the next table results in the order E–C–A–D–B.
| JOB SEQUENCE |
JOBWORK
(PROCESSING) TIME |
FLOW
TIME |
JOB DUE
DATE |
JOB
LATENESS |
| E |
9 |
9 |
23 |
0 |
| C |
8 |
17 |
18 |
0 |
| A |
6 |
23 |
8 |
15 |
| D |
3 |
26 |
15 |
11 |
| B |
2 |
28 |
6 |
22 |
|
28 |
103 |
|
48 |
Measures of effectiveness for LPT are:
a. Average completion time = \frac{103}{5} = 20.6 days
b. Utilization metric = \frac{28}{103} = 27.2%
c. Average number of jobs in the system = \frac{103}{2} = 3.68 jobs
d. Average job lateness = \frac{48}{5} = 9.6 days
The results of these four rules are summarized in the following table:
| RULE |
AVERAGE
COMPLETION
TIME (DAYS) |
UTILIZATION
METRIC
(%) |
AVERAGE NUMBER
OF JOBS IN
SYSTEM |
AVERAGE
LATENESS
(DAYS) |
| FCFS |
15.4 |
36.4 |
2.75 |
2.2 |
| SPT |
13.0 |
43.1 |
2.32 |
1.8 |
| EDD |
13.6 |
41.2 |
2.43 |
1.2 |
| LPT |
20.6 |
27.2 |
3.68 |
9.6 |
INSIGHT \blacktriangleright LPT is the least effective measurement for sequencing for the Avanti Sethi firm. SPT is superior in 3 measures, and EDD is superior in the fourth (average lateness).
LEARNING EXERCISE \blacktriangleright If job A takes 7 days (instead of 6), how do the 4 measures of effectiveness change under the FCFS rule? [Answer: 16.4 days, 35.4%, 2.83 jobs, 2.8 days late.]
RELATED PROBLEMS \blacktriangleright 15.15, 15.17a–d, 15.18, 15.19 (15.15 alternate, 15.24 are available in MyOMLab)
EXCEL OM Data File Ch15Ex5.xls can be found in MyOMLab.
ACTIVE MODEL 15.1 This example is further illustrated in Active Model 15.1 in MyOMLab.