Basics CPM&PERT.ppt

BUSS953 Lecture 5 Slide 1
 Fundamentals of Project Management
 PERT/CPM Techniques
 Network Diagrams
 Determining the Critical Path
 Project Scheduling
 Uncertain Activity Duration Times
Project Planning, Scheduling & Control:
An Intro to PERT/CPM Techniques

Fundamentals of Project Management
What is a Project?
 Is a body of work required to be performed to meet a specific goal
or objective. Its outcome is a deliverable, a carefully defined and
agreed upon tangible product, whose delivery to the specified
degree of quality constitutes successful completion.
What is Project Management?
 Is the overall planning, control and co-ordination of a project from
inception to completion aimed at meeting the clients requirements
and ensuring completion on time, within cost and to required
quality standards.

It is assumed that:
 A project defines a set of interrelated activities (jobs) that must
be performed in a specified sequence in order that the project be
completed successfully within specified resource constraints.
 The relationships (dependencies) between project activities are
either logical or resource constraint, whereby some activities
must be completed before others can be started.
 A project activity requires both time and resources for its
completion. E.g. Your study towards a degree.

Let’s look at this simple example.
Coffee is made by pouring water which has just been boiled
through a filter which contains ground coffee. Milk is boiled
and added to the filtered coffee and the resulting white
coffee served.
1. Identify the activities making up the “Coffee Preparation
Project”.
2. Identify the logical relationships (dependencies) between
the activities.
3. List the resources you would need for the project.
4. Assign some time and draw a network diagram for the for
the project.

The primary activities of project management are:
 Planning,
 Scheduling, and
 Controlling
which usually occur in that sequence over time.
 For medium- to large-scale projects this cycle may
be iterated many times.

 Initial Planning involves :
 Breaking the project down into distinct activities,
 Assigning known or estimated completion times to each activity,
 Identifying any logical relationships that exist between activities,
 Draw up a schedule to minimise completion time.
 Scheduling activities involves:
 assigning the necessary resources and a start time to each activity.
 Controlling involves:
 Monitoring project progress against the plan
 Taking corrective action where necessary, including altering the
current plan and re-scheduling and reallocating money or
resources to improve scheduling.

PERT/CPM Techniques
 PERT (Program Evaluation and Review Technique)
/CPM (Critical Path Method also called Critical Path
Analysis (CPA)) are useful tools in handling the
complexity of inter-dependencies among activities
 Both have their foundations in the mathematical theory
of graphs, in particular, a restricted class of graphs called
digraphs (for directed graphs).
 Graphs comprise points (called nodes) and lines (called
arcs) that interconnect them to form a network, much like
a road map where the roads are the arcs and the towns
are the nodes.

 The distinction between them lies primarily in
 PERT treating the time taken to complete an activity as an
estimate (probabilistic), while
 CPM treats it as known (deterministic).
 Other differences were in terminology and graphical representation
 PERT uses mathematical graph theory terminology and representation
more closely than CPM.
 Gantt Chart provides a standard form for displaying project schedule
information by listing the project activities and their corresponding start
and finish dates in a calendar format
 Both PERT and CPM can be converted to Gantt Chart and vice versa.
PERT/CPM Techniques

 A Network Diagram of activities in a project shows the interdependencies
and precedence relationships among the activities.
 Definitions:
Activity : An activity or job is an operation consuming time only or time
and resources.
 May be physical (eg. building a wall) or abstract (eg. when a designer
accomplishes a particular stage in a design calculation).
 Represented by an arc with an arrow head at one end.
Event : An event (milestone) is a state of a project when all preceding
activities have been completed and before any succeeding activity has been
started except for two special events usually designated as the START and
Finish events for the project.
 An event is represented by a circle.
Network Diagrams

 The START (Source) event has no activities prior to it and the
FINISH (Sink) event has no activities after it.
 An activity can thus be described in terms of two events: the
tail event of the arrow and the head event of the arrow.
 Activities that begin at an event cannot be started until all
activities that end at that event are finished.
 The lengths of the arrows need not be (and usually are not)
proportional to the duration of the activity.
1
2
A
Network Diagrams

 In drawing the network diagram it is advantageous to label events with
successive integers such that each head event has a larger number than all
directly connected tail events.
 If you cannot do this (ie, it is impossible to do), then you have a circuit in
your network. This means that either your network diagram is incorrect or
that your analysis of the precedence relationships among the activities is
logically incorrect.
The Network Diagram below represents the sequence that activity D(4-5) cannot
start until activity C(3-4) is completed and that activity C cannot start until both
activities A(1-3) and B(2-3) are completed.
1
2
3 4 5
A
B
C D
Network Diagrams

Rules for constructing network diagrams
 Rule 1
Represent each activity by one and only one arrow in the network diagram.
 In the case where an activity is split up into sub-activities, each sub-activity must
be represented by one arrow in the diagram.
 Rule 2
All activities must start and finish with an event and only two terminal
events, the START and FINISH events, are permissible in a network
diagram.
 An activity is a blind alley or a useless operation if it has no start or finish event.
 Rule 3
Closed loops are not permissible.
 They represent an illogical relationship.
Network Diagrams

 Rule 4
No two (or more) activities can be identified by the same head and tail
events.
 This situation may arise when two or more activities can be worked on in
parallel, as shown in Figure 1(a) below. The technique for resolving this
problem is to introduce a dummy activity, as shown in Figure 1(b).
 Note that a dummy activity, by definition, does not consume time or
resources.
 A dummy activity is represented by dashed or dotted line with an arrow head as
shown in Figure 1(b).
 Dummy activities are also useful in displaying logical relationships which could
not otherwise be represented correctly on a network diagram.
Network Diagrams

1 2
A
B
(a)
(b)
1
3
A
B
2
D
1
2
A
D
3
B
OR
Figure 1
Network Diagrams

 Rule 5
No single event may have 2 or more succeeding activities and 2 or more
preceding activities unless the succeeding activities are dependent on
the completion of all the preceding activities.
 For example, in Figure 2(a) if activities A and B must be completed before
either activity C or activity E can commence, then 2(a) is permissible, else if
either activity C or activity E is only preceded by either A or B, but not both,
then 2(a) is not permissible.
 The correct way to represent these dependencies, if all succeeding activities
are not dependent on the completion of all preceding activities, is by the use
of a dummy activity, as shown in Figure 2(b).
Network Diagrams

6
1
2
5
3
A
B
(a)
3
1 5
4
2 6
A C
E
B
D
(b)
Figure 2
Network Diagrams

 The Critical Path
Is the path in a network diagram which has the largest amount of time
associated with it and on which the Earliest Start Time (EST) is equal to
the Latest Finish Time (LFT) of all events on it.
 The essence of such a path is that, if one or more of the critical activities on
the path fall behind schedule then the whole project will fall behind schedule,
unless re-scheduling actions are available and can be used on later critical
activities on that path.
 It is normally represented by bold, double or coloured line with arrow head
( ) in the network.
i
EST LFT
where i is the event #
Network Diagrams

Let us look at the following specifications for two separate and unrelated
projects and develop the respective network diagram solution for them.
Project 1 Specifications
Tender requirements for the project were worked on for one day and
another one day was spent to put in call for tenders from prospective
bidders. It took 14 days to receive and acknowledge responses from
bidders and 7 days to prepare a short list. Four days was spent after the
call for tenders to develop criteria for evaluating the tenders to be received
and 5 days on the evaluation process. One day was spent on selecting the
successful bid.
Draw the network diagram for the project. How long did it take to complete
the project?
Network Diagrams -
Some Examples

Solution: Work Breakdown Structure(WBS)
Step 1: List the activities and their durations and resources, if any.
Step 2: Identifying any logical relationships that exist between the activities.
Step 3: Draw the network diagram bearing in mind the rules.
Activity Duration Dependency
A: Begin tender process 1 -
B: Call for tenders 1 A
C: Receive & acknowledge 14 B
D: Short list 7 C
E: Develop criteria 4 B
F: Evaluate bids 5 D, E
G: Select successful bid 1 F
Network Diagrams -
Some Examples

The following resources have been allocated to the project:
Activity Resource
A: Begin tender process 1 Person (Jo)
B: Call for tenders 1 Person (Sue)
C: Receive & acknowledge 7 Receipting Clerks
D: Short list 3 People (Mary, Max)
E: Develop criteria 1 Person (Pat)
F: Evaluate bids 2 Person (Jack, Jill)
G: Select successful bid 1 Person (Mary)
Assuming the following:
 the project begins Tuesday Aug 19, 2003;
 productive hours per day is 7 based on a 40 hour week;
 Monday Aug 25 is a public holiday
 no work during the weekends
How long will it to complete the project?
Network Diagrams -
Some Examples

Project 2 Specifications
It took 90 days to recruit a DP Manager for the project. The DPM initially
spent 90 days in recruiting staff and planning the department and he spent
20 days in selecting computers while doing the recruitment and planning. It
took 60 days for the staff to design the system. The design was agreed
upon and stationery ordered in 15 days and it took 20 days for the
stationery to be delivered. The construction of the system took 60 days. It
took 80 days for the computers to be delivered. The designing of the
computer room took 20 days and another 60 days was spent in building it.
The installation of power , etc. took 30 days. System testing took 30 days
and another 30 days was spent on parallel run.
Draw the network diagram for the project. How long did it take to complete
the project?
Network Diagrams -
Some Examples

Free Float (Free Slack): The amount of time a task can be
delayed before it delays another task.
Total Float (Total Slack): The amount of time a task can be
delayed before it delays the project finish date.
Network Diagrams

Calculating the Duration of a Project, the Free Float, the Total Float and
the Critical Path manually
Step 1: Prepare a Work Breakdown Structure of the project.
Step 2: Calculate the Earliest Start (ES) and Earliest Finish (EF) of each task.
The EF of the last task = Duration of the project.
Step 3: Calculate the Latest Start (LS) and the Latest Finish (LF) of each task.
Step 4: Subtract EF from LF for each task to give you its Free Float (FF). ie.
FF = LF - EF
Step 5: Subtract ES from LS to give you the Total Float (TF), ie. TF = LS - ES.
Step 6: Inspect the calculated value of TF for each task. All tasks with TF = 0
lie on the Critical Path.
Network Diagrams

How to calculate ES and EF manually
Step 1: Set the ES of the first task(s) in the network to zero or the
project start date.
Step 2: Add the duration of the task to the ES to obtain its EF, ie.
EF = ES + Task Duration
Step 3: The ES of each task is equal to the EF of its predecessor
(or the last of the EFs of its predecessors if there are more
than one).
Network Diagrams

How to calculate LS and LF manually
Step 1: For the last task in the network set the LF equal to its
previously determined EF.
Step 2: Subtract the duration of the task from the LF to obtain its LS,
ie. LS = LF - Task Duration.
Step 3: The LF of each task is equal to the LS of its successor (or the
first of the LSs of its successors if there are more than one).
How to calculate the Free Float manually
Subtract EF from LF for each task to give you its Free Float (FF). ie.
FF = LF - EF
Network Diagrams

Example:
Calculate manually the Duration, the Total Float and the Critical Path for
Project 1 above.
Network Diagrams

Scheduling Exercise:
Food for Thought - The Problem
Suppose you are planning a dinner for two. Your menu consists of a very special soup and baked chicken
main course. The soup must be boiled for 35 minutes and you should allow 15 minutes to serve and
consume it. The chicken dish requires a fair amount of preparation: You have to boil rice (for 30 minutes),
lightly fry the chicken (for 15 minutes), and then bake the chicken and rice for 15 minutes. It takes 5 minutes
to prepare a sauce and 15 minutes to boil peas. You have bought a good red wine. Allow 5 minutes to
uncork it (very carefully) and let it stand for 30 minutes before serving it. Allow 25 minutes to serve and eat
the main meal and wine.
You have unlimited staff at your disposal to assist you with for the preparation of the meal. The utensils at
your disposal are two boiling pots, a frying pan, a saucepan and a cork-screw.
Prepare the Work Breakdown Structure (WBS) for the project if there were no resource constraints at all.
Determine manually (without the help of a project scheduling software):
1. The earliest start and the earliest finish of each task for the dinner.
2. The latest start and the latest finish of each task for the dinner.
3. How quickly you can prepare and consume the entire dinner.
4. The Free Slack for each task.
5. The Total Slack for each task.
6. The Critical Path of the network.
7. What adjustments you would make for the fact that there are only 2 pots.
Network Diagrams

Basics CPM&PERT.ppt

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