DECISION MAKING AND PROBLEM SOLVING

PROJECT REPORT BY:

DIVYA RAJASRI TADI #13

YAN XINGZHOU #18

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

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

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

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

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,

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.

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).

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

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.

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

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

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.

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.

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.

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.

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

$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.

REFERENCES

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