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Chapter 5

Scheduling the Project

EUT443 – ENGINEERING MANAGEMENT

Project Management Triangle

5.1PERT AND CPM NETWORKS

Convert a project plan (Chap3.) or

WBS into a convenient form for

monitoring and controlling project

activities


History

• Late 1950s

– Program Evaluation and Review Technique

(PERT)

• U.S. Navy, Booz-Allen Hamilton, and Lockeheed

Aircraft

• Probabilistic activity durations

– Critical Path Method (CPM)

• Dupont De Nemours Inc.

• Deterministic activity durations


PERT and CPM Networks

• Both methods employed networks to schedule and

display task sequences.

• Both methods identified a critical path of tasks that could

not be delayed without delaying the project.

• Both methods identified activities with slack (or float) that

could be somewhat delayed without extending the time

required to complete the project.

• While PERT and CPM used slightly different ways of

drawing the network of activities, anything one could do

with PERT, one could also do with CPM and vice versa.


The Language of PERT/CPM

• Activity

– task or set of tasks

– use resources and time

• Event

– state resulting from completion of one or more

activities

– consume no resources or time

– predecessor activities must be completed


The Language of PERT/CPM continued• Milestones

– events that mark significant progress

• Network

– diagram of nodes and arcs

– used to illustrate technological relationships

– drawn with a “Start” node on the left and a “Finish”

node on the right

– arcs are always tipped with an arrowhead to show the

direction of precedence

• Path

– series of connected activities between two events


The Language of PERT/CPM concluded

• Critical Path

– set of activities on a path that if delayed will

delay completion of project

• Critical Time

– time required to complete all activities on the

critical path


Building the Network

• AOA Network

– Activity on Arrow

– associated with PERT

• AON Network

– Activity on Node (AON)

– by showing each task as a node and linking

the nodes with arrows that show their

technological relationship

– often associated with CPM


Table 5-1 A Sample Set of Project Activities and Precedences

Task Predecessor

a --

b --

c a

d b

e b

f c, d

g e


Figure 5-1 Stage 1 of a Sample AON Network

Because tasks a and b have no predecessors, they follow the Start node. We connect them to the starting node with arrows


Figure 5-2 Stage 2 of a Sample AON Network

Task c has a as a predecessor and that tasks d and e have b as their common predecessor


Figure 5-3 A Completed Sample AON Network

Task f has both c and d as predecessors, while g follows e . Because there are no more tasks, we can tie all loose ends to a node labelled Finish


Figure 5-4 Stage 1 of a Sample AOA Network

Start node from which flow all activities that have no predecessors, in this case a and b . The completion of these activities results in events (nodes, often drawn as circles) numbered 1 and2 for easy identification


Figure 5-5 Stage 2 of a Sample AOA Network


Figure 5-6a A Completed Sample AOA Network


Figure 5-6b A Completed Sample AOA Network Showing the Use of a Dummy Task


AON or AOA?• We will use AON networks throughout this

course because they are used by most of the

popular project management software.

• An important advantage of AON notation is that

the networks are easy to draw.

• AOA networks, particularly when they have more

than 15 or 20 activities, are difficult to draw by

hand.

• With modern software (eg. Microsoft Project) this

is not a serious problem, but the software that

generates AOA networks is quite expensive.


Table 5-2 A Sample Problem for Finding the Critical Path and Critical Time

Activity Predecessor Duration

a -- 5 days

b -- 4

c a 3

d a 4

e a 6

f b, c 4

g d 5

h d, e 6

i f 6

j g, h 4


Table 5-2 A Sample Problem for Finding the Critical Path and Critical Time

Activity Predecessor Duration

a -- 5 days

b -- 4

c a 3

d a 4

e a 6

f b, c 4

g d 5

h d, e 6

i f 6

j g, h 4

Stage 1

Stage 2

Stage 3


Figure 5-7 Stage 1 of a Sample Network


Figure 5-8 A Complete Network


Figure 5-8 A Complete Network

• Avoid having several of the arrows crossing one another;

• Due to f follows both b and c


Figure 5-9 Information Contents in an AON Node (common practice)


Figure 5-10 The Critical Path and Critical Time for Sample Project

Using forward pass and backward pass

The shortest time for completion of the network is equal to the longest path

through the network, in this case ‘a-e-h-j’


Figure 5-10 The Critical Path and Time for Sample Project

• If any activity on the a-e-h-j path is even slightly delayed, the project will be

delayed

• and that identifies a-e-h-j as the critical path and 21 days as the critical time

(bold line)


Calculating Activity Slack

• Slack or Float

– The amount of time a noncritical task can be

delayed without delaying the project

– Exclude task in critical path (zero slack)

LST - EST = LFT - EFT = Slack

5.2PROJECT UNCERTAINTY AND

RISK MANAGEMENT

Determine the likelihood that a

project can be completed by some

predetermined time or cost


Calculating Probabilistic Activity Times

• Three Time (Point) Estimates

– pessimistic (a)

– optimistic (b)

– most likely (m) or ‘normal’


Figure 5-13 The Statistical Distribution of all Possible Times for an Activity Using Beta Distribution

The beta distribution is used because it is far more flexible than the more

common normal distribution and because it more accurately reflects actual time

and cost outcomes.

The calculation itself is using weights of 1- 4 - 1, respectively. For triangular

distribution, its weights is 3)


Activity Expected Time (TE), Standard Deviation (σ) and Variance (σ2)

99% Level

2

2

E

6

)(Var

6

)(

6

)4(T

ab

ab

bma

Mean of Distribution

Standard Deviation (σ)

Variance (σ2)


95 Percent Level

• Task will be a or lower 5 percent of the

time

• Task will be b or greater 5 percent of the

time

3.3

)( ab


90 Percent Level

• Task will be a or lower 10 percent of the

time

• Task will be b or greater 10 percent of the

time

6.2

)( ab


95 Percent Level (Alternative Interpretation)

• Task will be between a and b 95 percent of

the time

92.3

)( ab


90 Percent Level (Alternative Interpretation)

• Task will be between a and b 90 percent of

the time

29.3

)( ab


Study Case:


Figure 5-14 Probabilistic Network


The Probability of Completing the Project on Time

2

)(

DZ


The Probability of Completing the Project on Time

=NORMDIST(D,,,TRUE)

Using the Z value, refer to Table of Cumulative (Single Tail)

Probabilities of the Normal Probability Distribution (Areas

under the Normal Curve from ∞ to Z) or

Using Excel syntax:


Figure 5-18 The Statistical Distribution of Completion Times of the Path a-b-d-g-h


Selecting Risk and Finding D

• Condition where need to give a firm date to

customer with associated percent of

probability

• Eg. 95% meeting the promised date

• Manipulate the Z formula above, we can

find D

• From the table, for a .95 probability, Z will

have a value of 1.645


Selecting Risk and Finding D

2

ZD

Excel Syntax:

NORMINV(probability,,,TRUE)

In our example, this function would be used as

follows:

NORMINV (.95, 47, 2.719)

MEM 612 Project Management

5.3SIMULATION


Traditional Statistics Versus Simulation

• Similarities

– must enumerate alternate paths

• Differences

– simulation does not require assumption of path

independence

• Because of the computational effort required by

the statistical method, simulation are the

preferred tool for risk analysis - after, and only

after, the analyst understands the underlying

theory of the analysis.


5.4THE GANTT CHART


The Gantt Chart

• Henry Gantt, a major figure in the

“scientific management ” movement of the

early twentieth century, developed the

Gantt chart around 1917.

• A Gantt chart displays project activities as

bars measured against a horizontal time

scale.

• It is the most popular way of exhibiting

sets of related activities in the form of

schedules.


Figure 5-23 A Gantt Chart of a Sample Project

WBS = Work Breakdown Structure


Figure 5-24 A Gantt Chart of Sample Project Showing Critical Path, Path Connections, Slack, EST,

LST, EFT, and LFT


Figure 5-25 A Gantt Chart of a Day Care Project Showing Expected Durations, Critical Path, Milestone, and Resource Requirements


Figure 5-26 A Progress Report on a Day Care Project Showing Actual Progress Versus Baseline


5.5EXTENSIONS TO PERT/CPM


Precedence Diagramming

• Finish-to-start linkage

• Start-to-start linkage

• Finish-to-finish linkage

• Start-to-finish linkage


Figure 5-27 Precedence Diagramming Conventions


Other Methods

• Graphical Evaluation and Review

Technique (GERT)

– combines flowgraphs, probabilistic networks,

and decision trees

– allows loops back to earlier events and

probabilistic branching

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