1. A project is a set of activities or specialized functions all directed toward
achieving a unique objective or goal.
2. A network diagram is a graphic representation of a project that that shows
major project activities. It is made up of arrows and nodes. The arrows indicate
sequential relationships among activities. This information is extremely important
for project planning, for time and cost estimation, and for allocating resources.
(AON). In AOA diagrams, the arrows represent activities and the nodes represent
the beginning and/or ending of activities. In AON diagrams, activities are represented
by nodes, and the arrows simply indicate the direction of sequential relationships.
A path is a sequence of activities beginning with the first node and ending
with the last node. The path with the longest set of times is called the critical
path, and the activities on that path are called criticalactivities.
The term critical refers to timely project completion; if any activities on
the critical path take more time than expected, and the increased time isn?t
offset by a decrease somewhere else in that path, the project duration will
increase.
3. AOA networks sometimes require the use of a dummy activity to clarify relationships.
These zero-time activities are represented by a dashed arrow. A dummy activity
would be used, for example, when two (or more) activities have some, but not
all, predecessors in common. See the last diagram on the left side of Table
18-1 (p. 778) of your textbook.
4. Some A0A diagrams include dummy activities. These zero-time activities,
represented by dashed lines, are used to clarify relationships. One use is where
two activities both begin and end at the same node. Another use is where two
activities have some but not all predecessors in common.
5. For deterministic time estimates, the algorithm for finding the critical
path involves two passes through the data: first, a forward pass to find the
early start (ES) and early finish (EF) times for each activity, and then a backward
pass to find the late finish (LF) and late start (LS) times. The critical path
is the path for which ES = LS and EF = LF for every member of
that path. The slack time is the difference between LS and ES. Thus the activities
on the critical path all have zero slack. The critical path duration is equal
to the project duration.
For the forward pass, assign the time zero to the starting node. This is the
ES of every activity emanating from the source; the EF is the time t of completion.
The general formula for ES is:
ES = largest early completion time, EF, of all immediately preceding
activities The early finish for an activity is EF = ES + t, where t is the activity
time. The forward pass computes both ES and EF for every activity.
The time it takes to get to the final node is the estimated time for the project.
This will show up as the LF for all activities ending at the final node.
The backward pass is reverse of the forward pass. Start the backward pass at
the final node at LF time. For every activity ending at the final node, LS=
LF - t. Then
LS becomes the LF for all preceding activities; the formula is:
LF = smallest late completion time, LS, of all immediate successors.
When you are through with the backward pass, all critical activities will show
up as having zero slack.
6. Probabilistic PERT introduces uncertainty into a PERT model. For each activity
there are three time estimates:
(1)<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image123.gif::/sites/dl/free/0072443901/24520/Image123.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image123.gif (0.0K)</a>Image123.gif
optimistic, or shortest estimated completion time
(2) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image124.gif::/sites/dl/free/0072443901/24520/Image124.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image124.gif (0.0K)</a>Image124.gif
most likely time
(3) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image125.gif::/sites/dl/free/0072443901/24520/Image125.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image125.gif (0.0K)</a>Image125.gif
pessimistic, or longest estimated completion time
The average time ,<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image126.gif::/sites/dl/free/0072443901/24520/Image126.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image126.gif (0.0K)</a>Image126.gif ,
for completing an activity is a weighted average of ,<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image127.gif::/sites/dl/free/0072443901/24520/Image127.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image127.gif (0.0K)</a>Image127.gif
, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image128.gif::/sites/dl/free/0072443901/24520/Image128.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image128.gif (0.0K)</a>Image128.gif
and <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image129.gif::/sites/dl/free/0072443901/24520/Image129.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image129.gif (0.0K)</a>Image129.gif .
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image132.gif::/sites/dl/free/0072443901/24520/Image132.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image132.gif (0.0K)</a>Image132.gif
and <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image133.gif::/sites/dl/free/0072443901/24520/Image133.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image133.gif (0.0K)</a>Image133.gif are
respectively the mean and variance of activity completion time under a beta
probability distribution.
Assuming there is just a single critical path and there are no parallel critical
paths, the expected time for completion of the project is the sum of times <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image134.gif::/sites/dl/free/0072443901/24520/Image134.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image134.gif (0.0K)</a>Image134.gif ,
for the critical path activities.
The variance of project completion time is the sum of the variances, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image135.gif::/sites/dl/free/0072443901/24520/Image135.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image135.gif (0.0K)</a>Image135.gif ,
for critical path activities.
The standard deviation of project completion time, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image136.gif::/sites/dl/free/0072443901/24520/Image136.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image136.gif (1.0K)</a>Image136.gif .
The distribution of completion times can be represented by a normal distribution
with mean equal to the sum of expected times, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image137.gif::/sites/dl/free/0072443901/24520/Image137.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image137.gif (0.0K)</a>Image137.gif ,
for the activities on the path,
and a standard deviation equal to <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image138.gif::/sites/dl/free/0072443901/24520/Image138.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image138.gif (0.0K)</a>Image138.gif .
In order to find the probability of completing the project in any specified
time, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image139.gif::/sites/dl/free/0072443901/24520/Image139.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image139.gif (0.0K)</a>Image139.gif ,
use the following formula to obtain z for that path:
Look up the probability in the table of areas under the normal curve. For example,
if z =1.96, the probability of completion is 97.5 percent (look
up z = 1. 96in Appendix Table B).
If there are multiple independent paths with probabilistic time estimates,
use the approach described in Examples 5 and 6 and Solved Problem 3 in the text.
7. Shortening the time for completion can reduce costs and enhance profitability
in several ways:
(1) Indirect, or supervision, costs are reduced.
(2) Bonuses are frequently earned for early completion.
(3) Resources are freed to be used for other projects.
Under these conditions, it is worthwhile to incur some increases in direct
costs to attain the benefits of reducing the total time by crashing the project.
Give priority to those critical path activities that have the lowest cost per
day in crashing.
Rank the critical activities in order of lowest per day crashing cost. Assign
funds available for crashing successively to the lowest cost per day until either
those funds are all used up or the desired schedule is obtained.
Crashing can reduce slack time on noncritical activities. Therefore, it may
happen that as you begin to crash, the slack times for activities on noncritical
paths reduce to a point where they become critical too. This results in parallel
critical paths. You can continue crashing beyond this point, but only by crashing
all parallel paths.
8. PERT has the advantage of forcing managers to organize and quantify the
decision-making process. The graphs, tables, and critical path calculations
are helpful in showing up how the organization fits together and where to move
resources around to achieve the best possible results. For large projects, PERT
must be computerized.
9. Key decisions in project management include deciding which projects to implement,
choosing a project manager, assembling a project team, designing the project,
managing and controlling resources, and deciding if, and when, an ongoing project
should be terminated.
10. Project managers are responsible for managing the work, human resources,
communications, quality, time, and costs. They are also responsible for risk
management. Risks include unforeseen circumstances that can negatively impact
the project. Risk is highest early in a project, but the cost to overcome the
occurrence of a risk event is highest near the end of the project.
