Download key ideas

CHAPTER 17
PROJECT MANAGEMENT
KEY IDEAS
1.
A project is a set of activities or specialized functions all directed toward achieving a unique
objective or goal, usually within a specified time frame.
2.
The Gantt Chart displays the component activities or tasks within a project in chronological
order. Its advantage is its simplicity in preparation and interpretation.
3.
PERT stands for Program Evaluation and Review Technique. CPM stands for Critical Path
Method. For all practical purposes, they are the same.
4.
A PERT diagram is a graphic representation of a project that that shows major project activities
and their interrelationships. 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.
There are two types of PERT diagrams, activity-on-arrow (AOA) and activity-on-node
(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 total of activity times is called the critical path, and the activities on that
path are called critical activities. 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.
5.
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 two diagrams on the left side of Table 17-2 in your textbook.
6.
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.
7.
Probabilistic PERT introduces uncertainty into a PERT model. For each activity there are three
time estimates:
(1) to  optimistic, or shortest estimated completion time
(2) tm  most likely time
(3) t p  pessimistic, or longest estimated completion time
The average time , t e , for completing an activity is a weighted average of t o , t m , and t p .
te 
to  4tm  t p
6
.
The variance of activity completion time is
 
2
(t p  to ) 2
36
.
t e and  2 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 te , for the critical path activities.
The variance of project completion time is the sum of the variances,  2 , for critical path
activities.
The standard deviation of project completion time,  path 

2
.
The distribution of completion times can be represented by a normal distribution with mean equal
to the sum of expected times,
to  path .
t
e
, for the activities on the path, and a standard deviation equal
In order to find the probability of completing the project in any specified time, ts , use the
following formula to obtain z for that path:
z path 
8.
ts   te
 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. 96 in 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.
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.
9.
10.
11.
Crashing can reduce slack time on non-critical activities. Therefore, it may happen that as you
begin to crash, the slack times for activities on non-critical paths reduce to a point where they
become critical also. This results in more than one critical path. You can continue crashing
beyond this point, but only by crashing all critical paths.
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.
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.
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.
TIPS FOR SOLVING PROBLEMS
Computing Algorithm
It can be helpful in working with the computing algorithm to think of nodes with multiple entering or
exiting arrows (branches) as being analogous to a train station, and the arrows as arriving or leaving
trains. Now, in a forward pass (see diagram), think of A and B as arriving trains and C as a leaving train.
Train C cannot leave (according to policy) until both A and B have arrived. Consequently, the train that
has the latest arrival time (B in this example), establishes the earliest starting time for train C (12 in this
example). Hence, the rule is: Use the largest EF time of entering arrows (e.g., A = 7, B = 12) for the ES
of the leaving arrow.
A
7
C
12
B
12
For a backward pass, when LS and LF times are being determined, the most complex case is when a node
has multiple leaving arrows (see diagram below). The question is how to determine the LF for the
entering arrow (D in this example). The rule is, use the smaller of the LS times (E = 10, F = 18, so use
10) of the leaving arrows. Again, think of trains E and F leaving a train station. But this time, think of
the trains as leaving according to a set schedule: E must leave at 10 and F must leave at 18. Therefore,
the latest that D can arrive (LF) so that its passengers can make either train, is 10, the earliest of the
leaving (LS) times.
D
10
10
18
E
F
Computing Probabilistic Completion Times
1. Always determine the probability of finishing before the specified time (i.e., the area under the
normal curve to the left of the specified time), even for problems that call for the probability of
crashing after. In the latter case, find P(before) and subtract from 1.00 to find P(after).
2. Compute a z-value for every path in the network. If z is equal to or greater than +3.00, treat the
probability of that path finishing by the specified time at 100 percent. Use Appendix Table B to
obtain normal probabilities.
3. Multiply all path probabilities together to obtain P(crash by specified time). Note that because the
normal distribution is continuous, so that the probability of finishing exactly at the time specified is
theoretically equal to zero, P(finish before) is equivalent to P(finish by) and to P(finish on or
before).
Crashing
Only consider crashing activities that are on the critical path. After each crash, redetermine the critical
path(s), and include any new critical activities in the next round of crashing.