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PROJECT PRESENTATION

BYONYIA CHUKWUKA OBINNA

AGU VICTORIA CHINONSO

ON

PROJECT MANAGEMENTUSING CPM/PERT METHODS

(A CASE STUDY OF HELICON ASSOCIATES,OWERRI).


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CHAPTER ONE

INTRODUCTION Project management is the discipline of planning, organizing and managing

resources to bring about the successful completion of specific project goalsand objectives.

Project management has been practiced since early civilization. Two fathersof project management are Henry Gantt, the father of planning and controltechniques, which is famous for his use of Gantt chart as a projectmanagement tool. And Henry Fayol for his creation of a projectmanagement function which forms the foundation of the body of knowledge associated with project and project control management. The1950s marked the beginning of the modern project management era. Atthat time, two mathematical project scheduling models were developed.The Critical Path Method (CPM) developed as a joint venture between

Dupont Corporation and Remington Rand Corporation for managing plantmaintenance projects. And the Program Evaluation and Review Technique(PERT) developed by Booz-Allen and Hamilton as part of the United StatesNavys Polaris missile submarine program. These mathematical techniquesquickly spread into many private enterprises.


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Basically, CPM/PERT are project managementtechniques which have been created out of the need ofwestern industrial and military establishment to planschedules and control complex projects. Its graphic wayof showing and managing events and activities in aproject provides a clear and efficient method to analyze

and allocate resources in order to meet deadlines in aproject.

In this work, we present a study that describes themethod and models that are applied in estimating thedurations involved in project management.Traditionally, the managers or experts estimate thedurations of each activity in a project and this is oftenbased on their knowledge, experience or historic data.This paper presents research that provides more

accurate method to achieve the objectives.


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Objective of the Study

The major objective of this study is to;1 Identify the duration of the project.

2 Identify the critical and non-critical activities in theproject.

3 Calculate the real duration of the project.

4 Calculate the probability of completing the projectwithin a specified period.

1.3 Aim of the Study.1 To avoid delay in projects.

2. To construct a 3-bedroom bungalow within 105 days(i.e. 3 months and 1 week).


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1.4 Scope of the Study

This work is aimed at applying two techniques i.e. the CPM and PERT methods

in evaluating the statement plan of HELICON ASSOCIATES in the construction of

a 3-bedroom bungalow and to bring into focus the implication andconsequence of the plan. These techniques make use of networks to help plan

and display the coordination of all the activities

1.5 Motivation of the Study

HELICON ASSOCIATES wants to construct a 3-bedroom bungalow within 4months and 1 week. The motivation of this study is to bring the project in on

schedule and perhaps even finish early within 3 months and 1 week using the

CPM/PERT method.


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1.7 Literature Review

Since the development of CPM/PERT in the 1950s the techniques have been

the subject of hundreds of research papers. Research has generally been

focused on PERT since the deterministic CPM represents few problems of

interest. The research on PERT can be categorized into five general categories.

The first category includes the research on the error and bias due to

assumptions made by PERT. The second involves finding the distribution

function of a project completion time through exact analysis, approximation

and bonding methods. Third, Monte Carlo sampling has been used to study the

distribution of PERT networks. The fourth involves resource allocation

problems and load leveling. The fifth area is the crashing of PERT networks.

The literature review will focus on the research most directly related to this

study of CPM and PERT networks.

Construction projects are normally executed in an environment characterized

by varying degrees of uncertainties. Factors (Faniran et al.1998) such as

weather, labour skills, site conditions and management quality can influence

the duration of construction activities. Many researches (cox 1995: Ben-Haim

and Laufer 1998, Ayman 2000) have investigated the completion time

distribution


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under uncertain conditions. Research studies have indicated that construction

planning efforts usually fail to achieve their objectives.

During the construction of the resource constrained schedule (forward pass)

the sources of each activitys resources are noted and this information is then

used to create additional links explicitly representing the resource

dependencies in the network (Bowers 1995, p.81).

Using resource constraints is required in construction scheduling. Otherwise,

the schedule is not realistic, since some resources are highly limited in most

construction projects and start ability of certain activities is determined by the

limited resources. Many resource scheduling (RCS) have been developed to

apply resource constraints (Kelly, 1963; Moder et al, 1983). These traditional

resource constrained scheduling successfully generate resource constrained

schedules in which all activities can be executed without resource constraints.

However, they do not provide correct float data and the critical path of the

schedules (Wiest, 1964; Woodworth and Shanahan, 1988; Fondahl, 1991; Just

and Murphy, 1994; Bowers, 1995; Lu and Li, 2003).


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A resource constrained schedule contains resource dependencies between

activities as well as technological relationships. The traditional RCS do not

consider the resource dependencies resulting to incorrect activity float data

and then incorrect critical path. Correct float data and the critical path are

prerequisites in construction scheduling and control. Without this information,

the project would be very hard to control since every activity should be treated

as a critical activity. In addition, the total float of an activity is very important in

delay impact analyses because of its sharing property with other activities and

amount of impact on the project completion time (de la Garza et al, 1991;

Callahan et al, 1992; Bartholomew, 1998).

The other drawback of a resource-constrained schedule is inflexibility in

activity schedules. Traditional RCS normally generate a single fixed early start

schedule. However depending on the resource usage and the network

condition, there could be alternative start and finish time for certain activitiesin the same schedule without delaying the project completion time (Bowers,

2000). If these alternative schedules are comprehended initially, the schedule

will be more flexible and thus better able to deal with unanticipated events

such as equipment failure, delays in material delivery, etc.


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Uncertainty of duration on the construction activities (Williams 1990) were

summarized as the activity duration, the resource requirements of activities,

resource availability of the structure of the network itself, the precedence

relations or even the existence of particular activities.

Risks associated with project delays (Shen 1997) were identified. These risks

were described as insufficient or incorrect design information, shortage of

materials/plan resources, inaccuracy of project program, subcontractors

manpower shortage, variation in ground and weather conditions, abortive

works due to poor workmanship, shortage of skills/techniques and poorco-coordination with subcontractors

Source of risks affecting schedules (Mulholland and Christian 1999) are

categorized as four classes: engineering design, procurement, site construction

and project management. Since the critical path method (CPM) was used to

plan for large project schedules, many models have been presented to copewith the uncertainties in the project planning. The two basic network techniques areCPM and PERT.


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CHAPTER TWO2.1 METHOD OF DATA COLLECTION

Data on project was collected from the directors officewith the help of a site engineer.

Two methods of data collection were employed in thedata collection. The first method was to identify what

should be and what should not be regarded as an activityin the project. The lists of activities were compiled andthe activity durations were given.

After all the activities were identified, the secondmethod of data collection involved the determination of

the interdependencies and precedence relationshipsamong the activities. These were arrived at by finding,for each activity, its immediate predecessors; after whichthe data were re-arranged for modeling.


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To allow for the usage of PERT analysis, which is a stochastic model in clearing

uncertainties, three time estimates of duration namely optimistic duration i.e.

the time required to complete each activity if execution is extremely good, the

most likely time i.e. the normal duration, and the pessimistic duration i.e. the

time required for the completion of the project if execution is extremely bad,

were computed.


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Table 1 shows the activities and the activity duration in the plan using the CPM technique.

Table 1;

Code Activity Immediate Duration

Predecessor

A Site clearing -

2

B Bringing of materials A

2C Setting- out (pegging) A,B

2

D Excavation (including septic tank) C 5

E Placing of columns D 1

F Blinding of foundation E 1

G Forming of block work to DPC level (including septic tank) F 3

H Backfilling and ramering G 2

I Casting of German floor H 3J Flooring of septic tank I 1

K Placing of formwork and reinforcement of columns I 2

L Block work to lintel stage K 10

M Formwork for lintel and slab (for septic tank) L 3

N Casting of columns, lintel and slab (for septic tank) M 5

O Leveling with block work N 3

P Carpentry work for roofing O 7


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2.3 PLANNING, SCHEDULING AND CONTROL:

The planning phase use the project rules as a foundation and defines the path

to achieve the project goals either by CPM/PERT as the path to be chosen. It is

performed by the manager and the core project team which interfaces with

appropriate elements of the organization and identifies the actual work to be

done. It includes estimating schedule and resources required to perform the

work and produces plans to serve as a baseline and direct the work. A key part

of schedule planning is identifying the critical path. This is the chain of

interdependent, sequential project activities that takes the longest time to

complete and thus determines the minimum schedule for the project. Planning

also includes the risk identification and risk reduction efforts. The results of the

planning phase become the project plan.


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There are many variation of CPM/PERT which have been useful in planning

costs, scheduling manpower and machine time. CPM/PERT can ensure the

following important questions;

1.How long will the entire project take to be completed? What are the risks

involved?

2.Which are the critical activities or tasks in the project which could delay the

entire project if they were not completed on time?

3.Is the project on schedule, behind schedule or ahead of schedule?

2.3 THE FRAME WORK FOR CPM AND PERT

Essentially, there are six steps which are common to both the techniques. The

procedures are

listed below;

i. Define the project and all of its significant activities or tasks. The project

(made up of several

tasks) should have only a single start activity and a single finish activity.

ii. Develop the relationships among the activities. Decide which activities must

precede and which

must follow others.


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iii. Draw the network connecting all the activities. Each activity should have

unique event

numbers. Dummy arrows are used where required to avoid giving the same

numbering to two

activities.

iv. Assign time and/or cost estimates to each activity.

v. Compute the longest time path through the network. This is called the

critical path.

vi. Use the network to help plan schedule, monitor and control the project.

The key concept used by CPM/PERT is that a small set of activities which make

up the longest path through the activity network control the entire project. If

these critical activities could be identified and assigned to responsible

persons, management resources could be optimally used by concentrating on

the few activities which determine the fate of the entire project.


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Non-critical activities can be preplanned, rescheduled and resources for them

can be reallocated flexibly, without affecting the whole project.

Five useful questions to ask when preparing an activity network are;

i. Is this a start activity?

ii. Is this a finish activity?

iii. What activity precedes this?

iv. What activity follows this?

v. What activity is concurrent with this?

Some activities are serially linked. The second activity can begin only after the

first activity is completed. In certain cases, the activities are concurrent

because they are independent of each other and can stint simultaneously. This

is especially the case in organizations, which have supervisory resources so

that work can be delegated to various departments which will be responsible

for the activities and their completion as planned.

When work is delegated like this, the need for constant feedback and co-

ordination becomes an important senior management pre-occupation.


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2.4 DEFINITION OF TERMS

Project: A project is defined as a collection of interrelated activities with each

activity consuming time and resources.

Activity: An activity can be defined as any task or job of its own which

requires both time and other resources for its completion. Determination of

what should be or should not be regarded as activity in a project depends on the

management.

Critical Activity: An activity is said to be critical if there is no leeway in

determining its start and finish times.

Non-Critical Activity: This allows some scheduling slack so that the start time

of the activity may be advanced or delayed within limits without affecting the

completion data of the entire project.

Event: This is defined as a point in time which activities are terminated and

others are started. In terms of the network, an event cone points to a node.The chain goes from project activities

events.


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Forward Pass (Earliest Occurrence Time, ): This determines the earliest

occurrence time of the events. The computation starts at node 1 and ends at

node n. It starts by setting 1=0 to indicate that the project starts at time 0.Given that p, q, , v are linked directly to node j by incoming activities (p,j),

(q,j),,and (v,j) and that the earliest occurrence times of events (nodes)

p,q,,and v have already been computed, then the earliest occurrence time of

event j is computed as;

j = max p + Dpj, q + Dqj,, v + Dvj .The forward pass is complete when n at node n has been computed.

By definition, j represents the longest path (duration) to node j.


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Backward Pass (Latest Occurrence Time, ): This calculates the latest

occurrence time of the events. Following the completion of the forward pass,

the backward pass computation starts at node n and ends at node 1. It startsby setting n = n to indicate that the earliest and latest occurrences of the

last node of the project are the same. Given that the nodes p, q,, and v are

linked directly to node j by outgoing activities (j,p), (j,q),, and (j,v) and that

the latest occurrence times of nodes p, q,, and v have already been

computed, the latest occurrence time of node j is computed as;j = min p Djp, q Djq,, v Djv .

The backward pass is complete when 1 at node 1 is computed. At this

point, 1 = 1 (=0).

Based on the preceding calculations, an activity (i,j) will be critical if it

satisfies three conditions;1. i = i2. j = j3. j - i = j - i = Dij.


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The three conditions state that the earliest and latest occurrence times of end

nodes I and j are equal and the duration Dij fit tightly in the specified time

span. An activity that does not satisfy all three conditions is thus noncritical.

The critical activities of a network must constitute an uninterrupted path that

spans the entire network from start to finish.

Total Float: This is the spare time available when all the preceding activities

occur at the earliest possible time and all succeeding activities occur at the

latest possible time.

TFij

=j

-i

- Dij

Free Float: This is defined as the excess of the time span defined from

the earliest occurrence of event i to the earliest occurrence of event j

over the duration of (i,j) i.e., TFij = j - i - Dij.

By definition, FFij TFij.


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Red-Flagging Rule: For a noncritical activity (i,j)

(a) If FFij = TFij, then the activity can be scheduled anywhere within its ( j ,

i ) span without causing schedule conflict.(b) If FFij TFij, then the start of the activity can be delayed by at most FFij

relative to its earliest start time ( i) without causing schedule conflict.

Any delay larger than FFij (but not more than TFij) must be coupled with an

equal delay relative to j in the start time of all the activities leaving

node j.

The implication of the rule is that a non critical activity (i,j) will be red-flagged if

its FFij = TFij. This red flag is important only if we decide to delay the start of the

activity past its earliest start time, i, in which case we must pay attention to the

start times of the activities leaving node j to avoid schedule conflicts.


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The critical path is the longest duration path through the network. The

significance of the critical path activities that lie on it cannot be delayed

without delaying the project. Because of its analysis is an important aspect of

project planning.The critical path can be identified by determining the following four

parameters for each activity;

1. ES Earliest start time: The earliest time at which the activities must be

completed first. This is represented mathematically as ECij = ESij + Dij,

where ECij is the earliest completion time which are defined for activity(i,j).2. EF Earliest finish time: This is equal to the earliest start time for the

activity plus the time required to complete the activity i.e. EFij = ESi + Dij3. LF Latest finish time: The latest time at which the activity can be

completed without delaying the project.

4. LS Latest start time: This is the latest time an event can begin withoutdelaying the entire project. This is represented mathematically as LSij = LCj Dij,

where LC is the latest completion and Dij is the duration. Therefore LCn = ESn, as

we observed.


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The slack indicates how much delay in reaching n event can be tolerated

without delaying the entire project completion time. Suppose ESi is the earliest

start time of all the activities emanating from event i, then ESi represents the

earliest occurrence time of event i. If i = 0 is the start event, then

conventionally for the critical path computation ESo = 0. Let Dij be the duration

of activity (i,j). The forward pass calculation is obtained from the formula;

ESj = Max ESi + Dij for all (i,j) activities.

While the backward pass is given by;

LCj = Min LCj Dij for all (i,j) activities.


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2.5 CPM LIMITATIONS

CPM does not allow any uncertainty in duration tasks or in the project

completion time. Whilst, this makes the analysis and the path analysis to be

simpler, it does not reflect real life, where tasks may be delayed or may be

completed ahead of schedule. This uncertainty limits the extent to which CPM

is useful in the real world.

2.6 PERT LIMITATIONS

In PERT analysis, all the estimates for the tasks durations and the probability

distributions of these durations are quite subjective. In cases where the

probability distribution of the times is known not to be a beta distribution,

PERT applies a beta distribution anyway which can cause inaccuracy. Even if

the tasks duration have beta distribution, the overall probability distribution of

the project duration will not necessarily be the same as the distribution of the

critical path. In particular, delays to other activities and improvements to the

critical path can cause other paths to become critical, hence PERT tends to

consistent underestimate the overall project duration.


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CHAPTER THREE

METHOD OF ANALYSIS

3.1 MODEL OF ASSUMPTION

CRITICAL PATH METHOD ASSUMPTION;

CPM is a deterministic model. It assumes that the project duration

can be predicted accurately, i.e. the duration of each activity is not a

random variable. CPM makes use of a one time estimate. This

assumption implies that the cost of executing a project can be

accurately determined for the entire project duration.


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PROGRAM EVALUATION AND REVIEW TECHNIQUE ASSUMPTION;

This allows for uncertainty in activity durations by making use of three time

estimates i.e. the optimistic time denoted by a (which is the unlikely but

possible time of completing a task if every thing goes well), the most likely

time denoted by m (the most realistic estimate of the time the activity might

require) and the pessimistic time denoted by b (the unlikely but possible time if

every thing goes wrong). PERT assumption includes the following;

1. The activity times are statistically independent.

2. The critical path always requires a longer total elapsed time than anyother path.

3. The project time is asymptotically normal.

Most PERT analysis assumes a beta distribution for the job as shown in

the figure below:


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beta distribution

a m b

Where represents the average length of time of the job duration. The value of

m depends on how close the value of a and b are relative to m. The expectedtime to complete an activity is approximated as:

= a + 4m + b

6

The variance of the time is given as:V2 = b a 2

6


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The spread of the distribution is equal to six times the standard deviation ,

thus;

6 = b a or = b a

6


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3.2 TABULATION AND ANALYSIS OF CPM.

The table and diagram below shows the various events and calculates the

Forward Pass, Backward Pass, Total Float and Free Float for the CPM method.


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1

2

3 4 5 6 7 8 9 11 12 13 16

0

2

2 9 10 11 14 16 19 21 31 34 39 42 49

41 15

49

54

26

80

81

31

81

80

30

80

80

28

80

77

27

77

72

25

7279

29

79

68

24

68

9

20

77

67

23

67

4

18

62

53

17

53

57

19

57

60

21

60

20

10

53

42393431211916141110940

2

C=2

g=1 h=1 i=3 j=2 k=3 m=2 0=10 p=3 q=5 r=3 s=7

u=5

f=5

Am=1

Aj=1

ak=1

ab=2

ai=2

X=

5

d=5

W=5

62

22

62

ad=5ac=2

y=3 v=4

z=3

af=4

ag=5

Ah=3

l=1

n=4

l=4

a=2

C=4

b=2

an=1

Ae=1

al=1

THE ACTIVITIES NETWORK OF CRITICAL PAHT METHOD DIAGRAM.


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ACTIVITY 1-3 (b): START TIME = 2, DELAY relative to its EARLIEST START = 2,

FREE FLOAT = 2.

ACTIVITY 1-18 (c): START TIME = 12, DELAY relative to its EARLIEST START = 12,

FREE FLOAT = 0. Because delay exceeds FREE FLOAT by 12, succeeding activities(w, x) cannot start earlier than time 16. CAUTION: Activities following (w, x) if

any, are not checked for possible delay. This step is done manually by assigning

zero delay to (w, x).

ACTIVITY 1-20 (d): START TIME = 15, DELAY relative to its EARLIEST START = 15,

FREE FLOAT = 4. Because delay exceeds FREE FLOAT by 11, succeeding activities(ab) cannot start any earlier than time 20. CAUTION: Activities following (ab), if


zero delay to (ab).


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ACTIVITY 9-10 (l): START TIME = 39, DELAY relative to its EARLIEST START = 20,

FREE FLOAT = 0. Because delay exceeds FREE FLOAT by 20, succeeding activities

(n) cannot start earlier than time 40. CAUTION: Activities following (n), if any,

are not checked for possible delay. This step is done manually by assigning zero

delay to (n).

ACTIVITY 10-19 (n): START TIME = 44, DELAY relative to its EARLIEST START =

24, FREE FLOAT = 33.

ACTIVITY 16-26 (u): START TIME = 75, DELAY relative to its EARLIEST START =

26, FREE FLOAT = 0. Because delay exceeds FREE FLOAT by 26, succeeding

activities (an) cannot start


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earlier than time 80. CAUTION: Activities following (an), if any, are not checked

for possible delay. This step is manually by assigning zero delay to (an).

ACTIVITY 18-23 (w): START TIME = 4, DELAY relative to its EARLIEST START = 0,

FREE FLOAT = 58. FINISH preceding activities (c) must be moved back to time 4

(or earlier if possible).

ACTIVITY 18-20 (x): START TIME = 30, DELAY relative to its EARLIEST START = 26,

FREE FLOAT = 0. Because delay exceeds FREE FLOAT by 26, succeeding activities

(ab) cannot start any earlier than time 35. CAUTION: Activities following (ab), if


zero delay to (ab).

ACTIVITY 19-28 (z): START TIME = 65, DELAY relative to its EARLIEST START = 8,

FREE FLOAT = 20.

ACTIVITY 20-29 (ab): START TIME = 47, DELAY relative to its EARLIEST START =

38, FREE FLOAT = 68.


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19 21 Setting of aluminum frames for windows

21 22 Fixing of doors and windows

22 23 Fixing of window protectors

23 24 Rendering of walls (inside)

24 25 Covering of septic tank with slabs

25 27 Flooring (with tiles)

27 28 Rendering of walls (outside)

27 29 Internal furnishing

28 31 Landscaping

29 30 Disposal of unwanted materials from site30 31 Handover

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