Project planning

6/18/20201
DEREJE JIMA
Construction Planning and Management
Department of Civil Engineering
School of Engineering
Semester I
2020
Welcome to Heartiest Students

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Introduction
Lecture
On
Project Planning

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Introduction
Chapter Coverage
Deals with preparing projects plans in terms of
defining: work breakdown structure, activities,
logical relations, durations and activities direct
cost.
Terminology of project planning
Project network representation using different
graphical methods including: activity on arrow

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Introduction
What is Project?
A project is a temporary and one-time exercise which
varies in duration.
It is undertaken to address a specific need in an
organization, which may be to create a product like
building or to change a business process.

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Introduction
Project Characteristics
Single unit or unique products
Many related activities
Temporary endeavor
Difficult production planning and inventory control
General purpose equipment
High labor skills

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Introduction
Building Construction Project
Road Construction Project
Examples of Projects

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Introduction
The Role of project Manager
All necessary activities are finished in order and on
time
The project comes in within budget
The project meets quality goals
The people assigned to the project receive motivation,
direction, and information

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Introduction
The project manager should be:
Good coaches
Good communicators
Able to organize activities from a variety of disciplines

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Introduction
Management of Projects
Planning - goal setting, defining the project, team
organization
Scheduling - relates people, money, and supplies to
specific activities and activities to each other
Controlling - monitors resources, costs, quality, and
budgets; revises plans and shifts resources to meet
time and cost demands

 Planning
Objectives
Resources
Work break-down
schedule
Organizational
break-down
structure
 Scheduling
Project activities
Start & end
times
Network
 Controlling
Monitor, compare, revise,
action
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Introduction
Project Management Activities

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Introduction
Figure 3.1
Before Start of project During
project Timeline project
Planning, Scheduling, and Controlling

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Introduction
Figure
3.1

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Introduction
Figure 3.1

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Introduction
Figure 3.1

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Introduction
Figure 3.1
Budgets
Delayed activities report
Slack activities report
Time/cost estimates
Budgets
Engineering diagrams
Cash flow charts
Material availability
details
CPM/PERT
Gantt charts
Milestone charts
Cash flow schedules

Project Planning
Failing to Plan is Planning to Fail!!!
Once you plan your work, you must work your plan!!!
Scheduling
Planning
It is about time …

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Project Planning
Establishing objectives
Defining project
Creating work breakdown structure
Determining resources
Forming organization

Project Planning
Planning is sets a clear road map that should be
followed to reach a destination.
Used at different levels to mean different things.
It involves the breakdown of the project into
definable, measurable, and identifiable
tasks/activities,
Then establishes the logical interdependences
among them.

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Project Planning
Generally, planning answers the following
questions:
What will be performed? : Answered by
determining the final project product necessary for
achieving project success. This is done in the
initiation phase before the development of your
WBS.
How will it be performed? : Answered by

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Project Planning
Where will it be performed? : Answer varies for each
type of project. For example, if it’s a construction project,
the “where” will be the physical location of the building or
road etc.
Who will perform the work? : Answered by determining
if the work will be contracted or will use in-house
resources. If a contractor, what type of contractor, and
if company resource, what department and who in
each department?

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Project Planning
In construction, for example, plans may exist at
several levels:
Corporate strategic plans,
Pre-tender plans,
Pre-contract plans,
Short-term construction plans, and
Long-term construction plans.

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Project Planning
The above plans are different from each other;
however, all these plans involve four main steps:
Performing breakdown of work items involved in the
project into activities.
Identifying the proper sequence by which the activities
should be executed.
Activities representation.
Estimating the resources, time, and cost of individual

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Project Planning
Detailed planning for tendering purposes and the
preparation of construction needs to be conducted
through brainstorming sessions among the
planning team.
The inputs and outputs of the planning process are
shown in figure below.

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Project Planning
Planning requires a rigorous effort by the planning
team.
A planner should know the different categories of
work and be familiar with the terminology and
knowledge used in general practice.
Planning team should seek the opinion of experts
including actual construction experience.
This helps produce a realistic plan and avoids
problems later on site.

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Project Planning
Project Planning Steps: Checklist to develop a
project plan:
Define the scope of work, method statement, and
sequence of work.
Generate the work breakdown structure (WBS) to
produce a complete list of activities.
Develop the organization breakdown structure
(OBS) and link it with work breakdown structure to

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Project Planning
Planning steps cont’d
Determine the relationship between activities.
Estimate activities time duration, cost expenditure,
and resource requirement.
Develop the project network.

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Project Planning
Planning Steps: Work Breakdown Structures
[WBS]
WBS is a hierarchical structure which is designed
to logically sub-divide all the work-elements of the
project into a graphical presentation.
The full scope of work for the project is placed at
the top of the diagram, and then sub-divided
smaller elements of work at each lower level of the
breakdown.

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Project Planning
WBS Cont’d
At the lowest level of the WBS the elements of work is
called a work package.
A list of project’s activities is developed from the work
packages
There is not necessarily a right or wrong structure
because what may be an excellent fit for one
discipline may be an awkward burden for another.

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Project Planning
WBS: Level
1. Project
2. Major tasks in the project
3. Subtasks in the major tasks
4. Activities [or work packages] to be completed

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Project Planning
WBS and their description
As shown in Figure above, level 1 represents the full
scope of work for the house.
Level 1

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Project Planning
Example: The WBS for a warehouse is as follow:

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Project Planning
For more details, another two levels (third and
fourth levels) can be added as shown below

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Project Planning
Accordingly, a complete WBS for the warehouse
project can be shown as follow:

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Project Planning
WBS and organizational breakdown structure
(OBS)
WBS elements at various levels can be related to
the contractor’s organizational breakdown structure
(OBS)
OBS defines the different responsibility levels
and their appropriate reporting needs.
The figure below, also, shows that work packages are

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Project Planning
A sample Project organization
Marketing Finance
Human
Resources Design
Quality
Mgt
Production
President
Test
Engineer
Mechanical
Engineer
Project 1 Project
Manager
Technician
Technician
Project 2 Project
Manager
Electrical
Engineer
Computer
Engineer

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Project Planning
Project Organization
Marketing Operations Engineering Finance
Project 1
Project 2
Project 3
Project 4

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Project Planning
WBS coding
A project code system provides the framework for
project planning and control in which each work
package in a WBS is given a unique code that is used
in project planning and control.
The coding system provides a comprehensive checklist
of all items of work that can be found in a specific type of
construction.
Also, it provides uniformity, transfer & comparison

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Project Planning
WBS linked to the OBS

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Project Planning
Planning Steps: Project Activities
An activity is defined as any function or decision in
the project that: consumes time, resources, and
cost.
Activities are classified to three types:

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Project Planning
1. Production activities: activities that involve the
use of resources such as labor, equipment,
material, or subcontractor.
This type of activities can be easily identified by
reading the project’s drawings and specifications.
Examples: excavation, formwork, reinforcement,
concreting etc
Each production activity can have a certain quantity

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Project Planning
2. Procurement activities: activities that specify the
time for procuring materials or equipment that are
needed for a production activity.
 Examples are: brick procurement, cement
manufacturing and delivery, etc.
3. Management activities: activities that are related to
management decisions such as approvals,
vacations, etc.

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Project Planning
Project activities Cont’d
This level of activity details depends on the purpose of
preparing the project plan.
In the pre construction stages, less detailed
activities can be utilized, however, in the construction
stages, detailed activities are required.
Accordingly, level of details depends on: planning
stage, size of the project, complexity of the
work, management expertise.

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Project Planning
Planning Steps: Activities Relationships
To identify the relationships among activities, it needs to
answer the following questions for each activity in the
project:
a. Which activities must be finished before the current one
can start?
b. What activity(ies) may be constructed concurrently
with the current one?
c. What activity(ies) must follow the current one?

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Project Planning
A circle of activity precedence will result in an
impossible plan.
For example, if activity A precedes activity B, activity B
precedes activity C, and activity C precedes activity A,
then the project can never be started or
completed.

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Project Planning
Example: Suppose that a site preparation and
concrete slab foundation construction project consists
of nine different activities:
A. Site clearing (of brush and minor debris),
B. Removal of trees,
C. General excavation,
D. Grading general area,

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Project Planning
Cont’d
E. Excavation for utility trenches,
F. Placing formwork and reinforcement for concrete,
G. Installing sewer lines,
H. Installing other utilities,
I. Pouring concrete.

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Project Planning
Precedence relations for above example

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Project Planning
Logical relationship considering resource
constraints
For efficient use of resources or in case of constrained
resources, it might be beneficial to consider the
resources when determining the logical relationship
among the activities that use the same resources.
Consider provision of form work for concrete.

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Project Planning
Overlap or lag
Overlap between activities (negative lag) is
defined as how much a particular activity must be
completed before a succeeding activity may start.
The absence of overlap means that the first activity
must finish before the second may start.
A negative overlap means a delay is required
between the two activities (Figure below)

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Project Planning
Overlap among activities

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Project Planning
Types of activities relationships
Four types of relationships among activities
Typically, relationships are defined from the
predecessor to the successor activity.
a) Finish to start (FS): The successor activity can
begin only when the current activity completes.
b) Finish to finish (FF): The finish of the successor
activity depends on the finish of the current activity.

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Project Planning
Cont’d
c) Start to start (SS). The start of the successor activity
depends on the start of the current activity.
d) Start to finish (SF). The successor activity cannot
finish until the current activity starts.

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Project Planning
Types of relationships
Start to Finish
Start to Start
Finish to FinishFinish to Start

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Project Planning
Planning Steps: Drawing Project Network
A network is a graphical representation of the project
activities and their relationships.
A project network is a set of arrows and nodes.
Before drawing the network, it is necessary to ensure
that the project has a unified starting and ending
point.
The need for this start activity arises when there is
more than one activity in the project that has no

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Project Planning
Project Network Cont’d
The end activity is needed when there is more than
one activity that has no successors.
Two ways to draw a network diagram for a project:
1. Activity on Arrow (AOA) representation.
2. Activity on Node (AON) representation

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Project Planning
Activity on Arrow network (AOA)
Here the arrows represent activities while the nodes
represent the start and the end of an activity (i.e.
events).
The length of the arrow connecting the nodes has
no significance and may be straight, curved, or
bent.
When one activity depends upon another, both

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Project Planning
Basic patterns of AOA diagrams

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Project Planning
Rule in AOA network diagram
Each activity must have a unique i – j numbers, where i
(the number at the tail of the arrow) is smaller than j (the
number at the head of the arrow).
It is recommended to have a gap between numbers (i.e.,
5, 10, 15, etc.) [for accommodation of missed activities].
Avoid back arrows.

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Project Planning
Dummy Activity: When more than one arrow leave the
same node and arrive at another node, dummy
activities must be used.
It is an activity with zero duration, consumes no
resources, drawn as dashed lines, and used to adjust
the network diagram.
It is also used when one activity depends upon two
preceding activities and another activity depends only
upon one of these two preceding activities as shown

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Project Planning
Use of dummy activities

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Project Planning
Activity on node network (AON)
It is also called the precedence diagram method
[PDM].
Here the nodes represent activities and the arrows
represent logical relationships among the activities.
If the arrow starts from the end side of an activity
(activity A) and ends at the start side of another activity
(activity B), then A is a predecessor of B
(Successor of A).

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Project Planning
AON representation allows the overlap or lag
representation on the relationship arrows connecting
activities.

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Project Planning
A Comparison of AON and AOA Network
ConventionsActivity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
A comes before B,
which comes
before C
(a) A B C
BA C
A and B must both
be completed
before C can start
(b)
A
C
C
B
A
B
B and C cannot
begin until A is
completed
(c)
B
A
C
A
B
C

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Project Planning
AON and AOA Comparison Cont’d
Activity on Activity Activity on
C and D cannot
begin until A and B
have both been
completed
(d)
A
B
C
D B
A C
D
C cannot begin until
both A and B are
completed; D cannot
begin until B is
completed. A dummy
activity is introduced
in AOA
(e)
CA
B D
Dummy activi
A
B
C
D

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Project Planning
AON and AOA Comparison Cont’d
Activity on Activity Activity on
B and C cannot
begin until A is
completed. D
cannot begin until
both B and C are
completed. A
dummy activity is
(f)
A
C
DB A B
C
D
Dumm
y
activity

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Project Planning
Summary Comparison of AON and AOA
Similarity: Both networks can be used to
represent a project network.
Difference:
There is no need for the use of dummy activities
in AON representation.
AON are more easily to draw and to read.

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Project Planning
Summary Cont’d
In AOA, an activity can only start when all its
predecessors have finished.
AON allows for overlap/lag representation.
AON allows for the representation of the four types
of relationships while AOA allows only for the finish
to start relationship.

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Project Planning
Example: Construct an AOA and AON networks for
the activities.

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Project Planning
Solution: A. AOA Network:- Forming an AOA
network for this set of activities might begin be
drawing activities A, B and C as shown below.
At this point, we note that two activities (A and B)
lie between the same two event nodes; for
clarity, we insert a dummy activity X and
continue to place other activities.

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Project Planning
Placing activity G in the figure presents a
problem, however, since we wish both activity D
and activity E to be predecessors.
Inserting an additional dummy activity Y along with
activity G completes the activity network, as shown
below.
AOA Network Diagram

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Project Planning
B. AON Network:-
This is done by placing the activities in a sequence
step order.
A sequence step [SS] may be defined as the
earliest logical position in the network that an
activity can occupy while maintaining the logical
relationships.
After all sequence step numbers have been

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Project Planning
Determining the sequence steps

Project Planning
AON representation is shown below, including
project start and finish nodes.
Note that dummy activities are not required for
expressing precedence relationships in activity-on-
node [AON] networks.

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Project Planning
Planning Steps: Estimating Activity Duration and
Direct Cost
A. Activity Duration: Having defined the work activities,
each activity has associated time duration.
These durations are used in preparing a schedule.
Activity duration is the amount of time assinged to
complete a particular activity.

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Project Planning
Durations and predecessors for a four-activity project
Schedules use only whole members. With new
construction or renevation, workdays are typically
used as the time unit.

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Project Planning
Duration Cont’d
However, in fast moving facilities, maintenance work
hours or even minutes may be a more appropriate
time unit.
Durations can be figured in a number of ways:
1. Duration can be determined by examining past similar
projects. Many projects use the same activities over
and over, so by maintaning good records managers
can predict durations accurately.

Project Planning
2. Durations for work that will be subcontracted,
deliveries and vendor items, and work that will be
performed by other divisions can be best determined
by talking to the appropriate people.
3. Published cost data books can be used as a source of
duration information. Means defines standartd crew
size and crew productivity.
`

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Project Planning
Duration Cont’d
It also defines a man-hour unit.
The time it takes for one worker to complete one unit.
This information can be used to establish durations,
particularly when the scheduler has little past project
experience

Project Planning
Activity Duration:
Activity duration = Quantity of work / Number of
crews x Daily crew [resource] output
Having defined an activity duration, it means that
the planner have already defined the number of
resources that will be employed in a particular
activity.
Knowing activity duration and resources employed,
it is simple to estimate the activity direct cost.

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Project planning
Example: If the daily production rate for a crew that
works in an activity is 175 units/day and the total crew
cost per day is 1800 birr. The material needed for daily
work is 4.5 units at 100 birr/unit.
A. Calculate the time and cost it takes the crew to finish
1400 units
B. Calculate the total unit cost. Consider an eight hour
work day.

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Project Planning
Solution
[a]. Duration (units of time) = Quantity / Production per
unit of time x number of crews = 1400 / 175 x 1 = 8 days
Cost (labor cost) = Duration (units of time) x crew cost
per unit of time = 8 days x 1800 birr / day =14400 birr
Total direct cost =14,400 birr + 4.5 units of material x
100 birr / day x 8 days = 18,000 birr
[b]. Unit cost = Total cost / Quantity = 18,000 birr / 1400 =
12.86 birr / unit

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Project Planning
End of Lecture
Thank You!!!
Next: Project Scheduling [CPM]

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Project Scheduling
How long the total project duration is?
Evaluate the early and late times at which
activities start and finish.
Identify the group of critical activities so that special
care is taken to make sure they are not delayed.
All these statements are the basic objectives of the
scheduling process,
Scheduling = Planning + Time.

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Project Scheduling
Scheduling is the determination of the timing
of the activities comprising the project to enable
managers to execute the project in a timely
manner.

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Project scheduling
Purpose:
Knowing the activities timing and the project
completion time.
Having resources available on site in the correct
time.
Making correction actions if schedule shows that
the plan will result in late completion.
Assessing the value of penalties on project late

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Project Scheduling
Purpose Cont’d
Evaluating the effect of change orders on the project
completion time.
Determining the value of project delay and the
responsible parties

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Project Scheduling [Critical Path
Analysis]
Basic Concepts and Formula
1. Frameworks of PERT/CPM
The PERT and CPM models are extremely useful for
the purpose of planning, scheduling and
controlling the progress and completion of large and
complex projects
They are useful for carrying out the analysis of these
three managerial functions.

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Project Scheduling
Cont’d
A network is a graphical representation of a project,
depicting the flow as well as the sequence of well-
defined activities and events.
Both CPM (Critical Path Method) and PERT
[Programme Evaluation and Review Technique] are
network techniques/ models.

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Project Scheduling
2. Network : It is, then, a graphical representation of a
project plan, showing the inter-relationship of the
various activities.
Networks are also called arrow diagrams.
When the results of time estimates and
computations have been added to a network, it may
be used as a project schedule.

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Project Scheduling
3. Steps in PERT/CPM Model: PERT/CPM model
building consists of following five steps:
a. Analyze and break down the project in terms of
specific activities and/ or events.
b. Determine the interdependence and sequence of
specific activities and prepare a network.
c. Assign estimates of time, cost or both to all the
activities of the network.

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Project Scheduling
Cont’d
d. Identify the longest or critical path through the network.
e. Monitor, evaluate and control the progress of the
project by re-planning, rescheduling and reassignment
of resources.
4. Critical Path: The longest path is the critical path
because it equals the minimum time required to
complete the project.
Al other paths other than the critical path (i.e. non-
critical or slack paths) offer flexibility in scheduling and

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Project Scheduling
5. Activity : An activity is a distinct operation or an
element of a project which consumes time or resources
and has a definable beginning and ending.
Commonly used terms synonymous with "activity" are
"task" and "job".
6. Conventions Adopted In Drawing Networks
There are two conventions normally adopted while
drawing networks: [a] Time flows from left to right and
[b] Head events always have a number higher than that
of the tail events.

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Project Scheduling
7. Graphical Representation of Events and Activities
Events are represented by numbers within circles.
Activities are represented by arrows; the arrow-heads
represent the completion of the activities.
The length and orientation of the arrow are of no
significance.

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Project Scheduling
8. Fundamental Properties Governing the
Representation of
Events and Activities
The representation of events and activities is
governed by one simple dependency rule which
requires that an activity which depends upon another
activity is shown to emerge from the head event of the
activity upon which it depends and that only
dependent activities are drawn in this way.

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Project Scheduling
9. Logical Sequencing and Connection of
Activities
A project entails several activities. The arrows are
arranged to show the plan of logical sequence in which
the activities of the project are to be accomplished.
Sequence is ascertained for each activity by three
queries viz:
a. Which activity or activities must be completed before
the start of a particular activity?
b. Which activity or activities should follow this?

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Project Scheduling
10. Errors in logical sequencing
Two types of errors in logic may arise while drawing a
network, particularly when it is a complicated one.
These are known as looping and dangling.
11. Dummy activity
It is a hypothetical activity which consumes no
resource and time. It is represented by dotted lines
and is inserted in the network to clarify activity pattern
under the following situations:

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Project Scheduling
Cont’d
a. It is created to make activities with common starting
and finishing events distinguishable.
b. to identify and maintain the proper precedence
relationship between activities that are not connected
by events.
c. to bring all "loose ends" to a single initial and a
single terminal event in each network using

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Project Scheduling
Definition of Important Terms
Forward pass: The process of navigating through a
network from start to end and calculating the
completion date for the project and the early dates for
each activity.
Early dates: The early start date and early finish date
of an activity.

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Project Scheduling
Definition Cont’d
Early finish (EF): The earliest date on which an
activity can finish within project constraints.
Early start (ES): The earliest date on which an
activity can start within project constraints.

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Project Scheduling
Definition cont’d
Backward pass: The process of navigating through a
network from end to start and calculating the late
dates for each activity.
The late dates (along with the early dates) determine
the critical activities, the critical path, and the amount
of float each activity has.

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Project Scheduling
Definition Cont’d
Late dates: The late start date and late finish date of
an activity.
Late finish (LF): The latest date on which an activity
can finish without extending the project duration.
Late start (LS): The latest date on which an activity
can start without extending the project duration.

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Project Scheduling
The Critical Path
Method (CPM)

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Project Scheduling [CPM]
Developed in the 1950s by the U.S Navy
…Originally, the critical path method considered only
logical dependencies between terminal elements
…Since then, it has been expanded to allow for the
inclusion of resources related to each activity, through
processes called activity-based resource assignments
and resource leveling.
…Critical Path Method for the construction industry

6/18/2020105
John Fondahl
Stanford CE Professor Emeritus – 35 years
…Passed away last September 13th, 2008
…US Marine Corps Sergeant in Iwo Jima
…Co-founder of the CEM program
…1961 Paper for the US Navy – "Non-Computer
Approach to the Critical Path Method for the
Construction Industry"

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What is CPM?
The Critical Path Method or Critical Path Analysis, is a
mathematically based algorithm for scheduling a set
of project activities
…It is an important tool for effective project
management …Commonly used with all forms of
projects, including construction, software
development, research projects, product
development, engineering, and plant maintenance,

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Cont’d
Any project with interdependent activities can apply this
method of scheduling.
The essential technique for using CPM is to construct a
model of the project that includes the following:
a. †A list of all activities required to complete the project
(also known as Work Breakdown Structure)
b. †The time (duration) that each activity will take to
completion

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Why CPM?
The CPM formally identifies tasks which must be
completed on time for the whole project to be completed
on time
Identifies which tasks can be delayed for a while if
resource needs to be reallocated to catch up on missed
tasks
It helps you to identify the minimum length of time
needed to complete a project

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The CPM is a systematic scheduling method for a
project network and involves four main steps:
1. A forward path to determine activities early-start times;
2. A backward path to determine activities late-finish
times;
3. Float calculations; and
4. Identifying critical activities.

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Calculations for the Critical Path Method
The inputs to network scheduling of any project
are simply the AOA or the AON networks with the
individual activity duration defined.
The network scheduling process for AOA and AON
networks, however, is different.

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AON Example
Activity Description
Immediate
Predecessors
A Build internal components —
B Modify roof and floor —
C Construct collection stack A
D Pour concrete and install frame A, B
E Build high-temperature burner C
F Install pollution control system C
G Install air pollution device D, E
H Inspect and test F, G

6/18/2020112
AON Network
A
Start
B
Activity A
(Build Internal Components)
Activity B
(Modify Roof and Floor)

6/18/2020113
AON Network
A
Start
B
C
D
Activity A Precedes Activity C
Activities A and B
Precede Activity D

6/18/2020114
AOM Network
CA
Start
DB G
E
F
H
Arrows Show Precedence
Relationships

6/18/2020115
AOA Network
1
3
2
5D
(Pour
Concrete/
Install
4
C
(Construct
Stack)
Dummy
Activity
6
H
(Inspect/
Test)
7

6/18/2020116
Determining the project schedule
Perform a Critical Path Analysis
The critical path is the longest path through the network
The critical path is the shortest time in which the project
can be completed
Any delay in critical path activities delays the project
Critical path activities have no slack time

6/18/2020117
Activity Description Time (weeks)
A Build internal components 2
B Modify roof and floor 3
C Construct collection stack 2
D Pour concrete and install frame 4
E Build high-temperature burner 4
F Install pollution control system 3
G Install air pollution device 5
H Inspect and test 2
Total Time (weeks) 25

6/18/2020118
Activity Description Time (weeks)
A Build internal components 2
B Modify roof and floor 3
C Construct collection stack 2
D Pour concrete and install frame 4
E Build high-temperature burner 4
F Install pollution control system 3
G Install air pollution device 5
H Inspect and test 2
Total Time (weeks) 25
Earliest start (ES) =earliest time at which an activity can
start, assuming all predecessors
have been completed
Earliest finish (EF) = earliest time at which an activity can
be finished
Latest start (LS) =latest time at which an activity can
start so as to not delay the
completion time of the entire project
Latest finish (LF) =latest time by which an activity has to
be finished so as to not delay the
completion time of the entire project

6/18/2020119
A
Activity Name
or Symbol
Activity Duration
2
Earliest
Start
ES
Earliest
FinishEF
Latest
Start
LS Latest
Finish
LF

6/18/2020120
Forward Pass: Begin at starting event and work
forward
Earliest Start Time Rule:
If an activity has only one immediate predecessor, its
ES equals the EF of the predecessor
If an activity has multiple immediate predecessors, its
ES is the maximum of all the EF values of its
predecessors
ES = Max (EF of all immediate
predecessors)

6/18/2020121
Forward Pass Cont’d
Earliest Finish Rime Rule:
The earliest finish time (EF) of an activity is the sum of
its earliest start time (ES) and its activity time
EF = ES + Activity
time

6/18/2020122
ES/EF Network:
Start
0
0
ES
0
EF = ES + Activity time

6/18/2020123
ES/EF Network:
Start
0
0
0
A
2
0
ES
of A
2
EF of A =
ES of A + 2

6/18/2020124
ES/EF Network:
Start
0
0
0
A
2
20
B
3
0
ES
of B
3
EF of B =
ES of B + 3

6/18/2020125
ES/EF Network:
Start
0
0
0
A
2
20
B
3
0 3
C
2
2 4
D
4
3
= Max (2, 3)

6/18/2020126
ES/EF
Start
0
0
0
A
2
20
B
3
0 3
C
2
2 4
D
4
3 7
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7

6/18/2020127
Backward Pass: Begin with the last event and work
backwards
Latest Finish Time Rule:
If an activity is an immediate predecessor for just a
single activity, its LF equals the LS of the activity that
immediately follows it
If an activity is an immediate predecessor to more than
one activity, its LF is the minimum of all LS values of all
activities that immediately follow itLF = Min (LS of all immediate following activities)

6/18/2020128
Latest Finish Time Rule:
The latest start time (LS) of an activity is the
difference of its latest finish time (LF) and its activity
timeLS = LF – Activity time

6/18/2020129
LE/EF
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
20
LF = Min(LS of
following activity)
10 13

6/18/2020130
LF/EF
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
10 13
8 13
4 8
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
20
LF = Min(4, 10)
42

6/18/2020131
LF/EF
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
10 13
8 13
4 8
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
20
42
84
20
41
00

6/18/2020132
Computing Slack Time
After computing the ES, EF, LS, and LF times for all
activities, compute the slack or free time for each
activity
Slack is the length of time an activity can be delayed
without delaying the entire project
Slack = LS – ES or Slack = LF – EF

6/18/2020133
Computing Slack Time
Earliest Earliest Latest Latest On
Start Finish Start Finish Slack Critical
Activity ES EF LS LF LS – ES Path
A 0 2 0 2 0 Yes
B 0 3 1 4 1 No
C 2 4 2 4 0 Yes
D 3 7 4 8 1 No
E 4 8 4 8 0 Yes
F 4 7 10 13 6 No
G 8 13 8 13 0 Yes
H 13 15 13 15 0 Yes

6/18/2020134
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
10 13
8 13
4 8
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
20
42
84
20
41
00

6/18/2020135
ES – EF Gantt Chart
A Build internal
components
B Modify roof and floor
C Construct collection
stack
D Pour concrete and
install frame
E Build high-
temperature burner
F Install pollution
control system
G Install air pollution
device
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

6/18/2020136
LS – LF Gantt Chart
A Build internal
components
B Modify roof and
floor
C Construct collection
stack
D Pour concrete and
install frame
E Build high-
temperature burner
F Install pollution
control system
G Install air pollution
device
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

6/18/2020137
Example 2: Draw the logic network and perform the
CPM calculations for the schedule shown next.
DurationIPAActivity
5-A
8AB
6AC
9BD
6B,CE
3CF
1D,E,FG

6/18/2020138
Forward Pass Calculations
In mathematical terms, the ES for activity j is as
follows :
ESj =max( EFi )
Where (EFi) represents the EF for all preceding
activities.
Likewise, the EF time for activity j is as follows :
EF j= ESj + Dur j

6/18/2020139
Solution
A
5
G
1
C
6
D
9
B
8
E
6
F
3
0,5
5,13
5,11
13,19
11,14
13,22
22,23

6/18/2020140
Backward Pass Calculations
In mathematical terms, late finish LF for activity j is as
follows :
LFj =min(LSk
Where (LSk) represents the late start date for all
succeeding activities.
Likewise, the LS time for activity j (LS j) is as follows :
LS j= LFj - Dur j

6/18/2020141
Solution
A
5
G
1
C
6
D
9
B
8
E
6
F
3
0,5
0,5
5,13
5,13
5,11
10,16
13,19
16,22
13,22
13,22
11,14
19,22
22,23
22,23
CPM ( ES = LS , EF = LF , TF = FF = 0)

6/18/2020142
Types of Float
There are several types of float. The simplest and
most important type of float is Total Float (TF).
Total float (TF): The maximum amount of time an
activity can be delayed from its early start without
delaying the entire project.
TF = LS – ES OR TF = LF - EF OR TF = LF -
Dur - ES

6/18/2020143
Free Float: may be defined as the maximum amount
of time an activity can be delayed without delaying the
early start of the succeeding activities
FFi = min(ESi+1) - EFi
where min (ESi+1) means the least (i.e., earliest) of
the early start dates of succeeding activities

6/18/2020144
In the previous example we can find the free float and
total float for each activity as the following :
Activity C’s free float, FF = 11 - 11 = 0 days
Activity C’s total float, TF =16 - 11= 5 days …… and
so on.
 Note : We must always realize that FF ≤ TF

6/18/2020145
Project scheduling [CPM]
A, B, D and G are critical activities [Because, their
TF is Zero]
FFTFLFLSEFESDuratio
n
Activity
0050505A
001351358B
0516101156C
00221322139D
33221619136E
88221914113F
00232223221G

6/18/2020146
Interfering float: may be defined as the maximum
amount of time an activity can be delayed without
delaying the entire project but causing delay to the
succeeding activities.
Int. F = TF – FF

6/18/2020147
Independent float (Ind. F): we may define it as the
maximum amount of time an activity can be delayed
without delaying the early start of the succeeding
activities and without being affected by the allowable
delay of the preceding activities
Ind. Fi = min(ESi+1) – max(LFi-1) – Duri
Note: make sure that Ind. F ≤ FF

6/18/2020148
Node Format
Activity Name
Activity ID
Duration
ES EF
LS LF
TF FF

6/18/2020149
Event Times in Arrow Networks
The early event time, TE, is the largest (latest) date
obtained to reach an event (going from start to finish).
The late event time, TL, is the smallest (earliest) date
obtained to reach an event (going from finish to start).

6/18/2020150
Examples: Perform the CPM calculations, including
the event times, for the arrow network shown below.
Arrow network for example
10 30
40
20 60
C
EB
50
D
F
70
A
G
H
10
5
7
8
9
4
5
8
d1
d2

6/18/2020151
The preceding logic is similar to that of the forward
and backward passes: When you are going forward,
pick the largest number.
When you are going backward, pick the smallest
number.
i j
Act. Name
Dur.
TEi
TLi
TEj
TLj
CPM

6/18/2020152
Forward and Backward Pass Calculation in AOA
10 30
40
20 60
C
EB
50
D
F
70
A
G
H
10
5
7
8
9
4
5
8
d1
d2
(0,10)
(0,5)
(0,7)
(10,18)
(10,19)
(7,11)
(19,24)
(19,27)
(19,27)
(22,27)
(10,19)
(11,19)
(15,19)
(0,10)
(5,10)
(8,15)
0
0
10
10
10
10
7
15
19
19
24
27
27
27

6/18/2020153
Float Calculations From Event Times
Total Float [TF]
TFij = TLj - TEi – Tij
Example ( In the previous network )
TF40-50 = TL50 – TE40 – T40-50
= 19 – 7 – 4 = 8

6/18/2020154
Free Float [FF]
FFij = TEj - TEi – Tij
Example: FF40-50 = TE50 – TE40 – T40-50
= 19 – 7 – 4 = 8

6/18/2020155
Interfering Float [Int. F]
INTFij = TLj – TEj
Example: INTF40-50 = TL50 – TE50
= 19 – 19 = 0
Independent Float
INDFij= TEj – TLi - Tij
Example: INDF40-50 = TE50 – TL40 – T40-50
= 19 – 15 – 4 = 0

6/18/2020156
End of Lecture
Thank You!!!
Next: Project Scheduling [PERT]

Project planning

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