Solved Problem 11-1 To complete the wing assembly for an experimental aircraft, Scott DeWitte has laid out the major steps and seven activities involved. These activities have been labeled A through G in the following table, which also shows their estimated completion times (in weeks) and immediate predecessors. Determine the expected time and variance for each activity.
ACTIVITY | a | m | b | IMMEDIATE PREDECESSORS |
---|---|---|---|---|
A | 1 | 2 | 3 | — |
B | 2 | 3 | 4 | — |
C | 4 | 5 | 6 | A |
D | 8 | 9 | 10 | B |
E | 2 | 5 | 8 | C, D |
F | 4 | 5 | 6 | B |
G | 1 | 2 | 3 | E |
Although not required for this problem, a diagram of all the activities can be useful. A PERT diagram for the wing assembly is shown in Figure 11.13.
Expected times and variances can be computed using the formulas presented in the chapter. The results are summarized in the following table:
ACTIVITY | EXPECTED TIME (WEEKS) | VARIANCE |
---|---|---|
A | 2 | |
B | 3 | |
C | 5 | |
D | 9 | |
E | 5 | 1 |
F | 5 | |
G | 2 |
Solved Problem 11-2 Referring to Solved Problem 11-1, now Scott would like to determine the critical path for the entire wing assembly project, as well as the expected completion time for the total project. In addition, he would like to determine the earliest and latest start and finish times and the slack times for all activities.
The critical path, earliest start times, earliest finish times, latest start times, latest finish times, and slack times can be determined using the procedures outlined in the chapter. The results are shown in Figure 11.14 and are summarized in the following table:
ACTIVITY TIME | |||||
---|---|---|---|---|---|
ACTIVITY | ES | EF | LS | LF | SLACK |
A | 0 | 2 | 5 | 7 | 5 |
B | 0 | 3 | 0 | 3 | 0 |
C | 2 | 7 | 7 | 12 | 5 |
D | 3 | 12 | 3 | 12 | 0 |
E | 12 | 17 | 12 | 17 | 0 |
F | 3 | 8 | 14 | 19 | 11 |
G | 17 | 19 | 17 | 19 | 0 |
The activities along the critical path are B, D, E, and G. These activities have zero slack, as shown in the table. The expected project completion time is 19 weeks. The earliest and latest start and finish times are shown in the table.