2. CONTENTS
INTRODUCTION
PROJECT: GLOBAL OIL CREDIT CARD OPERATION
OUR PROBLEM STATEMENT
THE NETWORK DIAGRAM
USE OF DUMMY ACTIVITIES
FINDING THE CRITICAL PATH
CRASHING THE COST
SUMMARY
REFERENCES
3. INTRODUCTION
The task of managing major projects is an ancient and honorable art.
Around 2600 B.C., the Egyptians claimed that 400,000 men worked
for 20 years to build the Great Pyramid for King Khufu. Modern
projects ranging from building a suburban shopping center to putting
a man on the moon are amazingly large, complex, and costly.
Completing such projects on time and within the budget is a
herculean task. In particular, the complicated problems of scheduling
massive projects are often structured by the interdependence of
activities. While dealing with projects involving thousands of
dependency relations, managers seek various effective methods of
analysis.
The PERT (project evaluation and review technique) commonly used
in conjunction with the critical path method (CPM), is one such
statistical tool used in project management. PERT is a method to
analyze the involved tasks in completing a given project, especially
the time needed to complete each task, and to identify the minimum
time needed to complete the total project. It was developed primarily
to simplify the planning and scheduling of large and complex projects
for the U.S. Navy Special Projects Office in 1957 to support the U.S.
Navy's Polaris nuclear submarine project. It was able to incorporate
uncertainty by making it possible to schedule a project while not
4. knowing precisely the details and durations of all the activities. It is
more of an event-oriented technique rather than start- and
completion-oriented, and is used more in projects where time is the
major factor rather than cost. It is applied to very large-scale, one-
time, complex, non-routine infrastructure and Research and
Development projects. An example of this was for the 1968 Winter
Olympics in Grenoble which applied PERT from 1965 until the
opening of the 1968 Games.
PROJECT: THE GLOBAL OIL CREDIT CARD
OPERATION
A crucial project for Rebecca Goldstein and Global Oil is, moving
their credit card operations from the home office in Dallas to Des
Moines, Iowa. Global Oil board of directors have set a deadline of 22
weeks to accomplish this project.
This project involves the following tasks –
Real estate selecting one of three available office sites
Personnel determining
how many employees move from Dallas
how many new employees will be hired
who will train the newly hired employees
5. Systems group must implement the operating procedures
Treasurer’s office must organize the financial arrangements
Architects have to design the interior space and oversee
needed structural improvements
Each of the sites that Global is considering is an existing building with
the appropriate amount of open space. However, office partitions,
computer facilities, furnishings, and so on, must all be provided. A
second complicating factor is that there is an interdependence of
activities. In other words, some parts of the project cannot be started
until other parts are completed like Global cannot construct the
interior of an office before it has been designed. Neither can it hire
new employees until it has determined its personnel requirements.
OUR PROBLEM STATEMENT
As the managers in the Operations Analysis Group, we are in charge
of planning the move, seeing that everything comes off according to
plan, and making sure that the deadline is met.
We know that PERT and CPM are specifically designed for projects
of this sort. We begin with the first step in the process that is to define
the activities in the project and to establish the proper precedence
6. relationships. This is an important first step since errors or omissions
at this stage can lead to a disastrously inaccurate schedule.
Table 14.1 shows the first activity list that we have prepared for the
move (the columns labeled “Time” and “Resources” are indications of
things to come). Each activity is placed on a separate line, and its
immediate predecessors are recorded on the same line. The
immediate predecessors of an activity are those activities that must
be completed prior to the start of the activity in question. For
example, in Table 14.1 we see that Global cannot start activity C,
determine personnel requirements, until activity B, create the
organizational and financial plan, is completed. Similarly, activity G,
7. hire new employees, cannot begin until activity F, select the Global
personnel that will move from Texas to Iowa, is completed. This
activity, F, in turn, cannot start until activity C, determine personnel
requirements, is completed.
THE NETWORK DIAGRAM
Defining in the PERT network diagram:
Branch – the arrow representing each activity
Node – the circle indicating the beginning and end of each activity
Event - represents the completion of activities that lead into a node
Referring to the activity list in Table 14.1, we see that “select office
site” is termed activity A. When this activity is completed, the event
“office site selected” occurs. Constructing the Network Diagram
Figure 14.2 shows a network diagram for activities A through C. We
emphasize at the outset that the numbers assigned to the nodes are
arbitrary.
8. They are simply used to identify events and do not imply anything
about precedence relationships. Indeed, we shall renumber the node
that terminates activity C several times as we develop the network
diagram for this project, but correct precedence relationships will
always be preserved. In the network diagram each activity must start
at the node in which its immediate predecessors ended. For example,
in Figure 14.2, activity C starts at node 3 because its immediate
predecessor, activity B, ended there. We see, that complications
arise as we attempt to add activity D to the network diagram. Both A
and C are immediate predecessors to D, and since we want to show
any activity such as D only once in our diagram, nodes 2 and 4 in
Figure 14.2 must be combined, and D should start from this new
node. This is shown in Figure 14.3. Node 3 now represents the event
that both activities A and C have been completed. Note that activity
E, which has only D as an immediate predecessor, can be added with
no difficulty. However, as we attempt to add activity F, a new problem
arises. Since F has C as an immediate predecessor, it would
emanate from node 3 (of Figure 14.3).
9. We see, however, that this would imply that F also has A as an
immediate predecessor, which is incorrect.
USE OF DUMMY ACTIVITIES
This diagramming dilemma is solved by introducing a dummy activity,
which is represented by a dashed line in the network diagram in
Figure 14.4.
This dummy activity is fictitious in the sense that it requires no time or
resources. It merely provides a pedagogical device that enables us to
10. draw a network representation that correctly maintains the
appropriate precedence relationships. Thus, Figure 14.4 indicates
that activity D can begin only after both activities A and C have been
completed. Similarly, activity F can occur only after activity C is
completed.
Figure 14.5 shows the network diagram for the first activity list as
presented in Figure 14.5.
A dummy activity can be used to cure this condition. Figure 14.6
illustrates the procedure. Since the dummy activity requires no time,
the correct time and precedent relationships are maintained.
11. This new representation has been introduced into Figure 14.7. Many
software packages do not require that these dummy activities be
input. Thus, for our purposes, they serve mainly the pedagogical goal
of correctly portraying the precedence relations (i.e., as used in
Figure 14.4).
We note that activities G and H both start at node 6 and terminate at
node 7. This does not present a problem in portraying the appropriate
precedence relationships, since only activity J starts at node 7. This
might, however, create a problem for certain software packages used
to solve PERT and CPM problems. In some of these programs, each
12. activity is identified by the number of its starting and ending node. If
such a program is to be used, the representation of G and H in Figure
14.5 would lead the computer to regard them as the same activity.
This would be incorrect, since in fact activities G and H are not the
same.
FINDING THE CRITICAL PATH
The Critical Path Method (CPM) is one of several related techniques
for doing project planning. CPM is for projects that are made up of a
number of individual "activities." If some of the activities require other
activities to finish before they can start, then the project becomes a
complex web of activities. Now, as mentioned earlier we have a 10
steps activity list.
A. Selecting Office Site
B. Creating Organizational and Financial Plan
C. Determining Personnel Requirements
D. Designing Facility
E. Constructing Interior
F. Selecting Personnel to Move
G. Hiring New Employees
H. Moving Records, Key Personnel, etc.
I. Making Financial Arrangements
13. J. Training New Personnel
After listing all these steps above, we need to collect data to estimate
the expected activity time. As what we have learned from the class,
we know there are three different types of estimate from different
perspectives.
Optimistic time (a): is the minimum time, which requires
everything has to go perfectly to achieve this time.
Most probable time (m): is the most likely time, where everything
is under normal circumstances.
Pessimistic time (b): is the maximum time, which follows where
something can go wrong.
By understanding these different perspectives of estimate we have
come with a table shown below.
14. Based on the original development of the PERT approach (during the
late 1950s), the procedure for estimating the expected value of the
activity times was motivated by the assumption that the activity time
was random variable with a particular probability distribution.
The figure shows the Construct Interior time use the probability
distribution, which gives us these formula above the chart.
The next step is to draw the Network Diagram to show the
relationships and the project process. And it is also the same time to
use CPM find critical path, which is the route cost most of your time in
this project. To complete the Network Diagram, we need to use some
dummy path the cure the incorrect relationship between activities and
crate a smooth path through the whole process.
15. Then we will find several path through 1 (the start) to 9 (the end).
1. A,D,E,J: and the total time will cost it = 3+4+8+3 = 18
2. B,C,D,E,J: and the total time will cost it = 5+3+4+8+3 = 23, which is
the CP.
3. B,C,F,H,J: and the total time will cost it = 5+3+2+2+3 = 15
4. B,C,F,G,J: and the total time will cost it = 5+3+2+4+3 = 17
5. B,I: and the total time will cost it = 5+5 =10
By finding the critical path, we will know is we let this project go, it will
spend more time as the board directors required. In the case, we need
to do the crash to this project.
16. CRASHING THE COST
Because the company usually does not share this information with
the public, so we created the chart below to demonstrate the
process of crashing the cost.
The critical path is B,C,D,E,J under this crash situation, the total
time will be: 3+1+2+5+1=11, which is almost half of what the board
directors want. The total cost of crushing will be
2*150+2*250+2*2500+3*10000+2*2500 =
300+500+5000+30000+5000 = $40800. As the CP is already
crashed, we need to crash the other paths to 11 to meet the final
goal along with the CP.
17. This figure above is the new Network Diagram which shows the normal
time and also the crash time.
On analyzing all the other paths again, we found that:
1. A,D,E,J = 3+2+5+1= 11 which does not need any change as it meets
the CP after the crash.
2. B,C,F,H,J = 3+1+2+2+1= 9 also does not need any crash.
3. B,C,F,G,J = 3+1+2+4+1= 11 same result as first path.
4. B,I = 3+5 =8 which was always less and does not need to crash.
So to the final decision is that we just need to crash the CP to get what
we want for this project, and the cost will be $40800.
As we all know, CPM and PERT try to reduce the time and cost of a
project. From the chart above, we find the original cost is $148400, and
the normal cost is $97700. However, we do not need to spend all of the
18. $148400 to finish the project within 11 weeks. The cost for 11 weeks will
be $40800+$97700= $138500. And this saves about $9900.
SUMMARY
Using the PERT and CMP give us an opportunity to eliminate extra cost
on unnecessary activity, which does not affect the total project time, to
not only save the cost, but also reduce the time for the project.
We started with a strategic analysis, as we aimed to keep the cost as
minimum as possible. Our responsibility was to move the credit card
operations from Dallas office to Iowa office for Global Oil within 22
weeks and $148400.
Implementing all the skills and techniques learnt in this class, we came
to a conclusion that PERT and CPM work best for this type of a project.
We started by making an activity list and then build network diagrams
and finally crashed the time as well as the cost required to implement
this project. We have been successful in determining how this project
can be completed within 11 weeks of time and with an expenditure of
$138500 only.
Thus, we have achieved our goal and made this project a success.
