Page 600 - Sensors and Control Systems in Manufacturing

Economic and Social Inter ests in the Workplace
The activity of steelwork erection leading to completion event o4 553
cannot begin until after both the preceding completions, o2 and o3,
have occurred. Other intermediate completion events must take place
before any entire project is finally completed, event o6.
Time estimates must be made for each of the activities. Since
actual activity time is uncertain, probability calculations are used in
computing the expected time t and the variance v associated with the
e
expected time.
The problem for project management is to determine the expected
time for completion of the entire project and to identify the activities
that could cause bottlenecks. PERT enables the management to
accomplish this and thus schedule work activities for the earliest pos-
sible completion.
For example, in Fig. 11.6, work leading to completion event o2 is
expected to be completed ten weeks after the start. From this point,
two network paths lead to event o4: the path 2–4, with an expected
completion time of 12 weeks, and the path 2–3–4, with a completion
time of 14 weeks. The total expected completion time for event o4 is
the larger of the total completion times on the two network paths that
lead to the events. The path 1–2–4 has a total expected time of T = 22,
E
and the path 1–2–3–4 has a total expected time of T = 24. Thus, the T
E E
for event o4 is 24. The variance associated with T = 24 is v = 5, the
E
sum of the variances along the 1–2–3–4 path.
Thus, the manager can expect completion of event o2 in ten weeks,
event o4 in 24 weeks, and event o6 in 44 weeks after work is started.
One other time variable must be taken into account, however: the lat-
est time T that can be allowed for an event without disturbing the T
L E
of the final event in the network (event o6).
If event o6 must be completed in 44 weeks, then T for event o6
L
is 44. Since T for event o6 is also 44, the allowable lag time is zero
E
(T –T ). In order to complete event o6 in 44 weeks, event o4 must be
L E
completed in 24 weeks. Thus, T for event o4 is 24 and allowable slack
L
time is also zero. T and slack time can be calculated for each event by
L
working backward from event o6.
The critical path through the network—the path in which there is
least amount of slack—is identified by noting the events where allow-
able slack time is zero. In Fig. 11.6, the critical path lies through events
1–2–4–6. Any construction delay in these events will increase the total
completion time for the project. Event o5, however, is not on the criti-
cal path. The tasks on the path segment 3–5–6 could be delayed for as
much as eight weeks in all without affecting the final completion time
for event o6. The activities represented by the path segment 2–4 could
be delayed two weeks without delaying the final completion of the
project. Resources could, if necessary, be shifted from these activities
to other tasks to ensure completion of the entire project on schedule.
Note that T and T are expected values. Statistical variances are
E L
associated with each of these measures. The expected time estimates