Network Anaysis_ critical path methods

02/02/10 Professional Practice CPM (Element 3) Lecturer: Dr Andrew Kimmance
1 Construction Project Management Skills | University of Central Lancashire
Construction Project Management Skills
Operational Research: Critical Path Methods
1. INTRODUCTION TO NETWORK ANALYSIS
Network analysis is the general name given to certain specific techniques which can
be used for the planning, scheduling, management and control of projects. It is a vital
technique used in construction project management, which enables managers to
take a systematic quantitative structured approach to the problem of planning
and controlling a project through to successful completion.
Furthermore, as will become clear in these notes, it has a graphical representation
which means it can be understood and used by those with a less technical
background. These short NOTES will provide a basic understanding of networking
critical path analysis (CPA) principles before applying them to the computer.
Two different techniques for network analysis were developed independently for
planning and controlling the progress of projects in the late 1950’s - these were:
 CPM (Critical Path Management), and
 PERT (for Program Evaluation and Review Technique).
1.1 Critical Path Analysis
Critical path analysis is a planning technique which can be applied to a wide range
of projects; e.g., construction, facility management (maintenance), computer
development projects, etc.
There are 3 basic stages to any project:
I. Planning
II. Analysing and scheduling
III. Controlling
In the planning stage a network of all the activities (or job) is developed (drawn),
which represents (make–up) the project, including their required logical sequence
which is obtained from the precedence relationships between activities or tasks?
There are 2 ways of drawing a network:
I. ACTIVITY – ON – ARROW
II. ACTIVITY – ON – NODE
Both ways present the same information and have the same analyses performed.

2 1. INTRODUCTION TO NETWORK ANALYSIS | University of Central Lancashire
In analysing the scheduling stage of a project there are 2 types of possible ways:
I. Time Analysis
II. Resource Analysis
This first section will only deal with time analysis and its variants in project planning.
Resource analysis will be covered with heuristic methods at a later date, and is not
consider in the first section of these notes.
1.2 Frequently Ask Question in Project Planning
 What is the most likely time of completion of a project?
 Which activities must be completed on time and if not will they delay the entire
project? (critical activities)
 Activity Planning Schedule
 When should each activity be started so that the project is
completed on time?
 What is the float or Slack?
 How can the non-critical activities be delayed without delaying the completion
of the entire project?
1.3 Reason for using Network Analysis Techniques
Due to a range of limitations of Gantt charts and sequencing linear methods the
follow list identifies various constraints when using Gantt charts:
 Each activity is not easily visually incorporated into the project planning due to
the precedence constraints.
 The estimated duration of completion for an activity cannot be determined
precisely.
 Usually, only able to be implemented into small to medium scale and simple
cost effective projects.
 Not suitable for complex project that involved large number of controlled &
uncontrolled variables.
1.4 Strength of Network Path Method
Network Path Methods helps Critical Path Methods in:
1) Providing Clarity:
 Provides a means to clearly identify the various activities & events to
complete a project.
2) Network Linking:
 Different activities & events can be logically interrelated into a network.

3) Estimate Duration Time:
 Each activity and event can be estimated; the activity assigned into
duration time, events assigned into estimated time to start and finish.
4) Identifying Critical Activities and FLOAT (slack) for non-critical activities:
 Different activities are classified for their criticality in completing the
project at the minimum time.
 Activities which define the total completion time along the project path
are considered as critical path and critical activities.
 For non-critical activities, float times are estimated.
 Float times = the time duration which the project completion time is not
affected.
1.5 Brief Definition of Critical Path
Critical path is based on distinction between any path, defined as a series of
sequential activities, and the actual critical path (CP) is a continuous path of the
most optimal sequence of a projects critical activities.
A critical path generally has 5 distinctive characteristics:
1. It starts at the 1st
node.
2. It is continuous.
3. It ends at the last node.
4. It has no float / Total float is zero.
5. It is the longest path.
1.6 Activities (work tasks)
Effective planning of projects requires careful thought and the application of logic. To
illustrate this planning tool, let's consider the construction of a small structure. Some
typical processes could involve:
a) Planning Stage: (project sequence, design, requirements, scope)
b) Excavating stage: (digging and levelling)
c) Inspecting Stage: (testing, approval of works, hand over)
d) Concreting Foundation (substructure)
e) Organising Stage: (site resources)
f) Constructing Stage: (superstructure)
All these processes are called the project ‘ACTIVITIES’ or ‘WORK TASKS’.
Procedure: Step 1:
List WHAT has to be done. Hint: try thinking of verbs ending in “...ing”, like
excavating or constructing.

Do not consider at this stage “who” is going to do what, concentrate on WHAT.
An activity or task is represented by a circle or rectangle, as illustrated below:
Arc Node
Activity or task
Step 2:
Decide on the ORDER in which it is to be completed. Some steps are obvious for
example:
The activity construct (wall) cannot be started until digging the foundation has been
completed, which in turn cannot be completed until the various site resources have
been ordered and delivered.
Therefore, there is a logical relationship between the start of one task and the
beginning of the next, hence the term logical diagram. One way of sequencing the
order of activities could be represented by the following:
plan-organise-excavate-concrete-construct-inspect
Writing this out as a logical network or in a PERT chart format is as following:
The activities are represented by rectangles and joined with arrows to show the
sequence or precedence: the logical relationships between them. Having completed
the network, the analysis can then begin. This is usually achieved by working out
the duration of each task and writing it into the network.
2. Activity–On–Arrow–Networks (AOA)
Generally, the Symbols used in Activity-on-Arrow Networks are as follows:
ARROW Represents an ACTIVITY or task (job or operation that requires
time or a resource; e.g., manpower - labour, tools, equipment,
etc).
Represents a DUMMY activity (often needed to express project
logic correctly or unambiguously).
CIRCLE Represents an EVENT (an instant of time before an activity
begins or at the end of an activity).
plan organise excavate concrete construct inspect

Each event circle is subdivided into 3 sectors and numbers inserted into them, of
which 2 are obtained in the 2 stages (forward and backward pass) of the time
analysis on the network. An example of an activity on arrow diagram is shown below.
2.1 Description of (AOA) Code
The critical path is determined by the shortest time in which a project can be
completed. This is usually determined by a sequence of activities.
 Critical Path Method = Critical Path Analysis (CPM = CPA)
 Total Project Time = TPT
 Total Float = TF
 Free Float = FF
 EET = Earliest Event Time
 EST = Earliest Starting Time
 EFT = Earliest Finishing Time
 LET = Latest Event Time
 LST = Latest Starting Time
 LFT = Latest Finishing Time
Identification Node
Label (number)
EET
(a) EST
(b) EFT
LET
(a) LST
(b) LFT
L
Alterative
Sequence

A small precedence network, prior to performing the time analysis would typically
look like the following example.
Example 1
Generally, networks are drawn from left to right. The start event, corresponding to the
beginning of the project will be at the left, and will only have arrows flowing out of it.
The end event, corresponding to the instant the project finishes, and will only have
arrows flowing in to the right hand side of the network, as illustrated in the AOA
Network.
The identification number is useful in large networks with many activities when any
activity can be simply defined by two numbers, which are the event nodes at the tail
and head of the activity arrow.
For example, the following activity could be represented as activity 21– 32:
Each activity represents a physical job, and therefore has a NAME and an associated
JOB DESCRIPTION but, particularly when carrying out computer analysis, a numeric
way of identifying activities is useful.
EVENTS may be numbered randomly but it is conventional to give the lowest
number, usually one (1) to the start event and continue through the network until the
end event (highest number). Therefore, each EVENT should be numbered so that
EndStart
21 32
3
4 6
2 5
1
7
1
Arrows only flow
from left to right

every activity has a lower tail event and a higher head event number or
node.
2.2 Activity-on-Arrow Notation
The way in which the arrows are drawn into and out of the events is determined by
the required logical sequence of the project activities. In a project any activity will, in
general, require others to be completed before it may start. Such requirements are
called the PRECEDENCE or logical relationships, as illustrated below.
Formula of AOA Analysis
 EFT = EST + Duration
 LST = LFT – Duration
 Total Float = D – A – Duration
 Free Float = C – A – Duration
One arrow is required for each activity. The tail of the arrow is the start of the activity.
The head of the arrow is the completion of the activity. Given that all networks must
show sequence, “nodes” are placed at the tail and head of each activity arrow.
To illustrate how the nodes are used to show sequence between activities, the
following examples will show several different schedule fragments of activity-on-
arrow networks.
Example 2
Activity Prior Activity
A None
Duration
1 2
A
B
C
D
“Biggest” “Smallest”
B is dependent on A and it must follow A,
and cannot start until A is finished.

B A
A B
Example 3
A None
B None
C A and B
Example 4
A None
B A
C A
Example 5
A
B
C
C must follow both A and B, and cannot
start until both A and B are finished
A
B
E
D
C
B and C are dependent on A,
and as soon as A is finished
both B and C may start.
A B
C

C, D and E are ALL dependent on A and B.
None of activities C, D, E can start until both activities of A and B are finished, but as
soon as both A and B is finished then all three activities of C, D, and E may start.
Example 6
In general at any point in a network if one or more activities (A, B,…) meet at a
common source, the event, and if one or more activities (X, Y, …) leave this event
then this means that X, Y,…. are ALL dependent on ALL of A, B,…. Therefore:
X has all of A, B,… as its IMMEDIATE PREDECESSORS, and also…………….
Y has all of A, B,… as its IMMEDIATE PREDECESSORS, etc.
Immediate Predecessors, for a particular activity, are the LAST activities that must
be completed before the given activity can start. A table listing the immediate
predecessors for all activities in a project is called a precedence table, which needs
to be determined for any project before the corresponding network can be drawn.
2.4 Activity-on-Arrow Networks (dummy activities)
Sometimes dependency relationships require one or more DUMMY activities in order
to be represented correctly. A dummy activity is a simulated activity of sorts, one that
is of ZERO duration and is created for the sole purpose of demonstrating a specific
relationship and path of action on the arrow diagramming method.
Dummy activities are a useful tool to implement when the specific logical relationship
between two particular activities on the arrow diagramming method cannot
specifically be linked or conceptualised through simple use of arrows going from one
activity to another. In this case, the creation of a dummy activity, which serves
essentially as a form of a placeholder, can provide exceedingly valuable data.
A
B Y
X

Dummy activities should in no cases be allocated any duration of time in the planning
and/or scheduling or project activities and components. When they are illustrated in a
graphical format, dummy activities should be represented by the user of a dashed
line with an arrow head on one end, and may in some cases be represented by a
unique color.
Example 7
4 activities (A, B, C, D,…), with the following precedence requirements:
C is dependent on A only, ----------------- C also has A as its immediate processor.
D is dependent on both A and B, ------- D also have A and B as immediate
predecessors.
These relationships would be represented in an activity-on-arrow network as follows:
It would be INCORRECT to represent the activities in such a way as follows:
Example 8
5 activities (A, B, C, D, E…), with the following precedence requirements:
C is dependent on A only, ----------------- C also has A as its immediate processor.
D is dependent on B only, ---------------- D also has B as its immediate predecessors.
E is dependent on A and B, ------------- E also has A and B as immediate
predecessors.
These relationships would be represented in an activity-on-arrow network as follows:
C
D
A
B
A
B
C
D
CA
E

3. Time Analysis
When a network has been drawn using the correct logic for the precedence
relationships of the activities, the next step is to perform a time analysis on the
activities.
However, before a time analysis can be performed the project planner must obtain
reasonable time estimates for each activity. These times may be based on expert
knowledge or work study information, but must be realistic and as accurate as
possible if the subsequent time analysis is to be useful; that is, correctly performed.
The principle objective of a time analysis is to determine the EARIEST times that
each activity can start and finish. In particular, the earliest time that the last
activity can be finished by, in order to identify the earliest COMPLETION TIME of the
total project.
In addition, a time analysis will determine the later times in which each activity must
start and finish by, in order not to delay the completion time of the whole project. A
time analysis is therefore done in 2 stages:
1. FOREWARK PASS, in order to determine the earliest times, and
2. BACKWARD PASS, in order to determine the latest times.
When both forward and backward passes are completed the following 4 project times
can then be determined for each activity:
1. Earliest Start Time (EST)
2. Earliest Finish Time (EFT)
3. Latest Start Time (LST)
4. Latest Finish Time (LFT)
For some activities the EST and LST values will be the same, as will the EFT and
LFT values. These activities are called the critical path activities, and they will form
at least one continuous PATH through the network, hence the name “critical path
analysis”. It is the duration of this complete path, which determines the project
MINIMUM completion time.
Other, non-critical activities will have different values for EST, LST, EFT and LFT.
The difference between either set of values is called the TOTAL FLOAT (slack),
and its value is an indication of the flexibility with regards to scheduling the activity, or
in changing the length of the activity duration.

3.1 Forward Pass
The term forward pass refers specifically to the essential and critical construction
project management component in which the project team leader (along with the
project team in consultation) attempts to determine the early start and early finish
dates for all of the uncompleted segments of work for all network activities.
There are a number of reasons for the attempted early calculation of the early start
dates and early finish dates for the project, as well as the early start dates and the
early finish dates for all activities that are contained within the project as a whole.
Determination of the early start date and the early finish date allows for the earliest
possible allocation of the resources that may be needed for completion of the project
and the activities contained within. This refers primarily to the allocation of the project
team and the expenditure of their resources, as well as the allocation and
expenditures of man hours.
Generally, each event of the network is considered in sequence (a, b, c, d,…); if the
numbering convention described earlier has been adopted then the events are
considered in the order 1, 2, 3, 4,…. and so on.
At each event the forward pass determines the earliest time that each event can
be reached. An event may not be reached, or achieved until ALL of the incoming
activities are completed, because only then are the outgoing activities free to start
(calculated).
All times are measured relative to the start of the project --------------time ZERO.
After completion of the time analysis, relative times can be converted to absolute
times (calendar dates), provided information such as the start date of the project, the
length of the working week, etc., are previously known.
Example 9
Event Procedure:
2 31
0 4 94
4
5
6
4 9
8
15
EST (0 + 4) = 4
EST (4 + 5) = 9
EST (9 + 6) = 15
4
15
EST (4 + 4) = 8
Use the largest (EST) = 15 and NOT 8

Event 1: Enter 0 as the earliest time for event 1 and move to event 2.
Event 2: Only one activity (1–2) enters this event and its duration is 4. As soon
as it is finished event 2 is reached.
As it can start at the time 0 the earliest it can finish is (0+4) = 4.
Enter 4 as its earliest time for event 1 and move to event 3.
Event 3: Only one activity (2–3) enters this event, and as soon as it is finished
the event is reached. Activity (2–3) can start at the earliest time of 4,
and hence finishes at the earliest time of (4+5) = 9.
Enter 9 as the earliest time for event 3 and move on to event 4.
Event 4: Now 2 activities enter this event (2–4) and (3–4), both must be
considered. The event is not reached until both are finished. Activity (2–
4) can start at the earliest time 4, and can finish at the earliest time of
(4+4) = 8.
Activity (3–4) can only start at the earliest time of 9, and hence finish at
the earliest time of (9+6) = 15.
Therefore, the earliest time that BOTH activities can finish is the LARGEST of 8 and
15, so enter 15 as the earliest time for event 4 and move on to the next event 5, and
so on.
3.2 Summary: The Forward Pass
 Calculates ES and EF times
 Computes early event time for each node
 Move left to right on the diagram below
 Take the preceding activity early event time and add the duration
 If more than one activity precedes it then the largest value is recorded
 Write down trial values
 Note: the first node always has an early event time of 0
In General, in the forward pass, if any number of activities enters an event then
the earliest finish time for each activity is computed and then the “maximum of
these times is the earliest event time”, as illustrated in the follow example.
Example 10
3
11
18
83
26 26
Event Time
Duration
Use the maximum = 26
26

For any project the Forward Pass is completed when the earliest event time is
computed for the finial (end) event. This time will also be the minimum completion
for the project.
3.3 Backward Pass
This phase can only take place when the forwards pass has been completed, then
each activity is considered in the reverse order. The Backwards Pass
determines the “latest” times that each event must be reached by (achieved), in
order not to delay the project. The following example illustrates a simple network for
calculating the backward pass.
Example 11
The earliest completion of a project from the (forward pass) is 46. The final activities
of the project network are as follows:
Event 50: This is the END event for this project.
Enter 46 as the latest time for the event 50, and move on to the next
event 49: In general, enter the same value for the latest time for the end
event that was calculated (found) at the end of the forward pass.
Event 49: Only one activity (49–50) leaves this event and the duration is 11. In
order to be finished no later by 46 it must therefore start no later than
(46–11) = 35.
Enter 35 as the latest time event 49 and move to the next event 48.
49
48
46
31
35
4633
2
31
15
35
11
End50
Earliest completion time
from the forward pass is 46
Duration

Event 48: Two activities, (48–49) and (48–50) leave this event and BOTH must
be considered. Activity (48–49) must be finished no later than 35, and
hence must start no later than (35 – 2) = 33.
Activity (48–50) must be finished no later than 46, and hence must start
no later than (46 – 15) = 31.
Hence, the latest time that both activities must start by is the smallest
of 31 and 33 which is 31.
Therefore, 31 needs to be entered as the latest time for event 48, then
you can move on to the next event, which should be 47, etc.
Note: In general when working out the backward pass times, if any number of
activities leave an event then the latest start time for each SUCH activity is computed
and then the “minimum of these times is the latest event time”.
Example 12
In general, for any project the backward pass is completed when the latest event
time is computed for the first (start) event. This time should always be ZERO.
When both the Forward Pass and the Backward Pass have been competed then
the following times may be determined for each activity.
 Earliest Starting Time (EST)
 Earliest Finishing Time (EFT)
 Latest Start Time (LST)
 Latest Finishing Time (LFT)
Total Float (TF): The time by which an activity can expand, without affecting the
project completion time.
22
13
6
16
6
Minimum = latest event time

Free Float (FF): The time by which an activity can expand, without affecting
subsequent activities.
Independent Float: The time by which an activity can expand, without affecting any
other activity, either previous or subsequent.
Example 13
Results of Analysis
 EST = 4
 EFT = 4 + 5 = 9
 LST = 22 – 5 = 17
 LFT = 22
 TOTAL FLOAT = (22 – 4) – 5 = 13
o or (LST – EST) = (17 – 4) = 13
o or (LFT – EFT) = (22 – 9) = 13
 FREE FLOAT = (15 – 4) – 5 = 6
 INDEPENDENT FLOAT = (15 – 8) – 5 = 2
IN GENERAL, the computation would follow:
 EST = x
 EFT = x + t
 LST = Y – t
 LFT = Y
 TOTAL FLOAT = (Y – x) – t: or (LST – EST): or (LFT – EFT)
 FREE FLOAT = (y – x) – t
 INDEPENDENT FLOAT = (y – X) – t
8
4
5 22
15
X
x
t Y
y

However, if the independent float is a “NEGATIVE” number it is defined as ZERO?
NOTE:
Although there are 3 types of float defined here (above), generally the only float
(slack) that is used is TOTAL FLOAT. When calculating the float it is important to
place all the information (data) into a precedence table, so as to enable the
critical path to be visible at all times.
4. Critical Path Analysis
The next part of the analysis of the network is to find the CRITICAL PATH. By
definition the Critical Path is the shortest time path through the network. In small
and simple networks, it is easy to calculate the amount of float or slack available
for each task, but in a complicated network, it is not easy to 'see' which tasks have
float or slack, and which have none.
The main characteristics of a critical path analysis are defined in the following way:
4.1 Advantages of Critical Path (PA) Methods
 Reduce project completion time & idle times:
 Event times
 Save project cost: Identify critical path.
 Facilitate smoother planning: Identify critical path.
 Provide indicator to coordinate with other supplier and vendor (external
resources): Identify critical path.
1 2
A
3
5 53
B
Node numbers showing order of
activities in the left hand semi-circle
of each node
Arrows indicate
the order of the
tasks, the letter
above shows the
order, the time
period below the
arrow
The Critical Path
Latest Finish Time (LFT)
Earliest Start Time (EST)
Nodes show the start and finish of a task

 Reduce frequent troubleshooting and crisis management: Identify critical
path.
 Provide more time to make crucial technological decisions.
 Provides a means for viewing information on all work related activities (time,
duration, float, etc) when using a precedence table format.
4.2 Examples of Critical Path Analysis (no dummy activities)
ACTIVITY
NAME
IMMEDIATE
PREDECESSORS
TIME
DURATION
A NONE 2
B NONE 1
C A 2
B A 4
E B & C 4
F D 3
G D 5
H E & F 6
The activity on arrow network for the above project would look like the follow
diagram:
A time analysis (forward pass followed by a backward pass) is performed on the
network, as shown above, which then allows the following table to be developed
(drawn up).
Activity
Code
Number
Duration
Time
Earliest
start
time
(EST)
Earliest
Finish
Time
(EFT)
Latest
Start
Time
(LST)
Latest
Finish
Time
(LFT)
Total
Float
Free
Float
Independent
Float
A* (1-2) 2 0 2 0 2 0* 0 0
B (1-3) 1 0 1 4 5 4 3 3
1
0
0
3
5
4
2
2
2
4
6
6
5
9
9
6 15
15
B
A
D
E
G
H
C F
2
4
4
1
2 3
5
6
0
4
2
1
1
2
3
5
4
8
9
9
6
6
10
15
11

C (2-3) 2 2 4 3 5 1 0 0
D* (2-4) 4 2 6 2 6 0* 0 0
E (3-5) 4 4 8 5 9 1 1 0
F* (4-5) 3 6 9 6 9 0* 0 0
G (4-6) 5 6 11 10 15 4 4 4
H* (5-6) 6 9 15 9 15 0* 0 0
* denotes critical activities AND there is one critical path: A, D, F, H.
4.3 Examples of Critical Path Analysis (with dummy activities)
ACTIVITY
NAME
IMMEDIATE
PREDECESSORS
TIME
DURATION
A NONE 2
B NONE 1
C NONE 4
D A & C 4
E B 2
F C 3
G A & E 2
H D, F & G 1
The activity on arrow network requires Dummy Activities as follows:
A time analysis (forward pass followed by a backward pass) is performed in the usual
way, as shown above, taking all dummy durations as ZERO, which then allows the
following table to be developed (drawn up).
Activity
Code
Number
Duration
Time
Earliest
start
time
(EST)
Earliest
Finish
Time
(EFT)
Latest
Start
Time
(LST)
Latest
Finish
Time
(LFT)
Total
Float
Free
Float
Independent
Float
A (1-3) 2 0 2 2 4 2 0 0
B (1-2) 1 0 1 3 4 3 0 0
C* (1-4) 4 0 4 0 4 0* 0 0
1
0
0
4
4
4
2
4
1
5
6
3
7
8
8
8 9
9
C
B
E
6 15
15
F
G
A D
1
2
3
4
2
2
4 1
3
0
1
4
2
4
2
5
4
2
7
4
8
5
6
9
3 4
2
6 4
4
H
4
3
2
84

D* (6-7) 4 4 8 4 8 0* 0 0
E (2-5) 2 1 3 4 6 3 2 0
F (4-7) 3 4 7 5 8 1 1 1
G (4-7) 2 3 5 6 8 3 3 0
H* (7-8) 1 8 9 8 9 0* 0 0
* denotes critical activities AND there is one critical path: C, D, & H.
5. Activity on Node Method
Activity–ON–Node (AON) is an activity sequencing tool, also known as Precedence
Diagramming Method (PDM). Activity sequence diagrams use boxes or rectangles
to represent the activities which are called as nodes. The nodes are connected with
other nodes by arrows that show all dependencies between the connected activities,
which then make up the network precedence diagram.
The activity on node diagrams allows you to be more specific about your start and
finish times, and how much time can be allocated to each activity. It also allows you
to build in how much ‘give’ there could be for each activity.
5.1 Activity on Node Networks
Symbols used in activity on name networks include:
NODE: or rectangle box to represent an activity.
ARROW: to represent precedence relationships.
Each activity node is subdivided into sectors and numbers inserted into them as
follows:
Earliest Start Time (EST) Latest Start Time (LST)
Duration Total Float
5.2 Formula of AON Analysis
 EFT = EST + Duration
 LST = LFT – Duration
 LFT = LST + Duration
 Total Float = Latest Start Time – Earliest Start Time
 Node of AON
 No free float
NAME
EST LST
NAME, LABEL, RESOURSE
Duration Total Float

The values of EST and LST; that is, the total float are obtained in the Time Analysis,
which is performed in 2 stages (Forward Pass and backward Pass), as in the
“Activity-On-Arrow Method”.
Important Note: It is also conventional to have a START and END node on each
network, each having ZERO duration. These 2 activity nodes are, in effect, dummy
activities, and apart from these special node cases, NO DUMMY ACTIVITIES are
required.
5.3 Example of Activity on None Network
ACTIVITY
NAME
IMMEDIATE
PREDECESSORS
TIME
DURATION
A NONE 2
B NONE 1
C NONE 4
D A & C 4
E B 2
F C 3
G A & E 2
H D, F & G 1
The Activity-on-Node network for this project described above is as follows:
Activity
Code
Number
Duration
Time
Earliest
start
time
(EST)
Earliest
Finish
Time
(EFT)
Latest
Start
Time
(LST)
Latest
Finish
Time
(LFT)
Total
Float
Free
Float
Independent
Float
4 4
D*
4 0
0 3
B
1 3
0 0
C*
4 0
0 2
A
2 2
0 0
START
0 0
8 8
H*
1 0
9 9
END
0 0
3 6
G
2 3
1 4
E
2 3
4 5
F
3 1

A 2 0 2 2 4 2 0 0
B 1 0 1 3 4 3 0 0
C* 4 0 4 0 4 0* 0 0
D* 4 4 8 4 8 0* 0 0
E 2 1 3 4 6 3 2 0
F 3 4 7 5 8 1 1 1
G 2 3 5 6 8 3 3 0
H* 1 8 9 8 9 0* 0 0
5.4 Class Studies Exercise 1: Critical Path Analysis (Time Analysis)
1. Using the activity precedence network shown below, perform a time analysis
(forward pass and backward pass) and determine the projects duration and
critical path, and show all results in a table format.
Activity
Code
Number
Duration
Time
Earliest
start
time
(EST)
Earliest
Finish
Time
(EFT)
Latest
Start
Time
(LST)
Latest
Finish
Time
(LFT)
Total
Float
Free
Float
Independent
Float
A
B
C
D
E
F
1
72
5
3
8
4
6
9
2
7
6
4
9
8 3
16
11
7 510

* denotes critical activities AND there is?
5.5 Class Exercise 2: Critical Path Analysis (Time Analysis)
2. Using the activity precedence network shown below, perform a time analysis
(forward pass and backward pass) and determine the projects duration and
critical path, and show all results in a table format.
Activity
Code
Number
Duration
Time
Earliest
start
time
(EST)
Earliest
Finish
Time
(EFT)
Latest
Start
Time
(LST)
Latest
Finish
Time
(LFT)
Total
Float
Free
Float
Independent
Float
A
B
C
G
H
I
J
K
L
1
0
0
4
2
3
5
4
5
6
7
8
11
10
10

D
E
F
G
H
* denotes critical activities AND there is?
5. 6 Project Planning Crash Action
Identifying the critical paths helps ensure that resources are allocated to best effect.
You may find that you need to complete a project earlier than your Critical Path
Analysis says is possible. In this case you need to re-plan your project.
There are a number of options available, although you will need to assess the impact
of each option on the project’s cost, quality, and time required to complete it. For
example, you could increase resource available for each project activity to bring
down time spent on each but the impact of some of this would be insignificant and a
more efficient way of doing this would be to look only at activities on the critical path.
As an example, it may be necessary to complete one of the previous project
networks, such as class exercise 2 in 21 days rather than 23 days. As an example
(only), you could look at using blocks instead of bricks in activity 2 to 3 or increase
the labour in activity 2 to 4. This could shorten the project by two days, but might
raise the project cost – doubling resources at any stage may only improve
productivity by, say 50%, as additional time may need to be spent getting the team
members up to speed on what is required, coordinating tasks split between them,
integrating their contributions, etc.
In some situations, shortening the original critical path of a project can lead to a
different series of activities becoming the critical path. For example, if activity 1 to 3
were reduced to 2 days, activity 2 to 5 could come onto the critical path.
Therefore, Crash Action occurs when the critical path of a set duration has to be
reduced. Sometimes customers will pay extra to have the time frame shortened. The
Project manger then determines the appropriate crash action such as:
 Hiring extra labour
 Hiring extra equipment
 Working overtime (weekends)
 Working at night
 Using different methods or technology

In order to reach the optimum cost-time solution, the first thing to do is to crash all the
critical activities. When this is done, the original critical path becomes shorter (that is,
a new critical path is established).
As with Gantt Charts, in practice project managers use software tools like Microsoft
Project to create CPA Charts. Not only do these tools make networks/charts easier to
draw, they also make modification of plans easier, and provide facilities for
monitoring progress against plans.
The following section focuses on Gantt chart and how to design (develop) a chart to
plan and monitor the time duration of a project.
6.0 Project Planning with Gantt Charts
Introduction
Henry Gantt (1861-1919), a mechanical engineer,
management consultant, and industrial advisor
developed Gantt charts in the 1910's. Not as
commonplace as they are today, Gantt charts
were innovative and new during the 1920's, where
Gant charts were used on large construction
projects like the Hoover Dam started in 1931 and
the Eisenhower National Defence Interstate
Highway System started in 1956.
In the early 20th century Henry Gantt developed a simple graphical method of
scheduling activities now called the Gantt chart or more popularly the common Bar
Chart. Bar charts can be generated by a variety of software programs including
Microsoft's Excel and Microsoft Project.
Planning and Scheduling Complex Projects are generally difficult at the best of times
that is why construction project managers generally employ analysis techniques to
help in determining the actual duration of a project. Gantt Charts are one of these
techniques that are useful tools for analysing, planning and scheduling complex
projects.
A Gantt chart is a graphical scheduling tool (visual representation) of the sequence
of construction events for the planning and control of a project. In its most basic form,
a Gantt chart is a bar chart that plots the tasks of a project versus time. It then
displays the corresponding data to a schedule, such as that produced by the critical
path method (CPM) procedure or one that is input directly to the procedure, and it
offers several options and statements for modifying the chart to your needs.

Gantt charts allow you to consider how long a project should take, determine the
resources needed and lay out the order or sequence in which work tasks need to be
carried out. They are also very useful in managing the dependencies between the
tasks. When a project is under way, Gantt charts are useful for monitoring its
progress. You can immediately see what should have been achieved at a point in
time, and can therefore take remedial action to bring the project back on course. This
can be essential for the successful and profitable implementation of the project.
6.1 Reason for using a Gantt Chart
The main reasons for using a Gantt chart are listed below:
 Help you to plan out the tasks that need to be completed.
 Give you a basis for scheduling when these tasks will be carried out.
 Allow you to plan the allocation of resources needed to complete the project,
and
 Help you to work out the critical path for a project where you must complete it
by a particular date.
When a project is under way, Gantt Charts help you to monitor whether the project is
on schedule. If it is not, it allows you to pinpoint the remedial action necessary to put
it back on schedule.
They can effectively visualise tasks, time required to complete tasks, and statuses of
achievements of tasks. In addition, in order to draw a Gantt chart, tasks need to be
identified, and a process model, such as the scheduling and required manpower,
must be clarified.
Thus, drawing Gantt charts help re-organise and clarify the process model.
Therefore, Gantt Charts are a highly effective tool in construction, and business
process management, which aims to improve and manage business process.
6.2 Sequential and parallel activities:
An essential concept behind project planning and Critical Path Analysis is that some
activities are dependent on other activities being completed first. As a small-minded
example, it is not a good idea to start building a bridge before you have designed it!

These dependent activities need to be completed in a sequence, with each stage
being more-or-less completed before the next activity can begin. We can call
dependent activities 'sequential' or 'linear' tasks. Other activities are not dependent
on completion of any other tasks. These may be done at any time before or after a
particular stage is reached. These are nondependent or 'parallel' tasks.
6.3 Drawing a Gantt Chart
The figures below show a variety of different Gantt charts used to plan a building
process of sort. Thirteen weeks are indicated on the first bar chart timeline, 5 weeks
on the second and so on.
There are milestone events on the third chart, presentations of plans for the project
and for the new process developed in the study. The rest of the tasks are activities
that stretch over periods of time. To draw up a Gantt diagram (Gant diagram), the
follow steps should be used:
Step 1: List all activities in the plan
For each task, show the earliest possible start date, how long you estimate the length
of time it should take, and whether it is parallel or sequential. If tasks are sequential,
show which stages they depend on. Head up a sheet of graph paper (using pencil
and a ruler) with the days, weeks or months through to task completion on the top x-
axis. The y-axis can be used to itemise each task in its order (A, B, C,...).
You may also want to use a spreadsheet for this instead of graph paper if you prefer.
You will end up with a task list similar to the ones shown here in these Gantt chart
figures. These examples show the task list for a basic construction project.

Step 2: Plot the Tasks onto a Plan
List the tasks in days or weeks through to task completion in the first column on the
left hand side of the page, the y-axis. To draw up a rough first draft of the Gantt
chart; plot each task on the plan, showing it starting on the earliest possible date.
Schedule them in such a way that sequential actions are carried out in the required
sequence. Ensure that dependent activities do not start until the activities they
depend on have been completed. Draw each task as a horizontal bar, with the length
of the bar being the length of time you estimate the task will take. Above each task
bar, mark the estimated time taken to complete the task. At this stage there is no
need to include scheduling; all you are doing is setting up the first draft.

Step 3: Schedule the Tasks or Activities
Now on a fresh sheet redraw the Gantt chart to schedule actions and tasks.
Schedule these in such a way that sequential actions are carried out in the desired
sequence e.g. dig holes, lay foundations, begin construction. Ensure that these
dependent activities do not start until the activities they depend on have been fully
completed.
Where possible schedule all parallel tasks so that they do not interfere with
sequential actions on the critical path. While scheduling, ensure that you make best
use of the time and resources you have available. Do not over-commit resources and
allow some time in the schedule for holdups, overruns, quality rejections, failures in
delivery, weather conditions, waste etc.
Once the Gantt chart is drawn, you can see how long it will take to complete your
project. The key steps to be carried out to ensure successful completion of the
project should be clearly visible.
ID TaskNameDuration Start Finish
1 1 1day? 2/1/10 2/1/10
2 2 3days 2/2/10 2/4/10
3 3 5days 2/5/10 2/11/10
4 4 1day? 2/12/10 2/12/10
5 5 4days 2/8/10 2/11/10
6 6 1day? 2/12/10 2/12/10
7 7 1day? 2/15/10 2/15/10
8 8 3days? 2/16/10 2/18/10
9 9 2days? 2/19/10 2/22/10
10 10 4days? 2/16/10 2/19/10
11 11 2days? 2/20/10 2/23/10
12 12 1day? 2/24/10 2/24/10
13 13 1day? 2/25/10 2/25/10
14 14 1day? 2/26/10 2/26/10
15 15 3days? 3/1/10 3/3/10
M T W T F S S M T W T F S S M T W T F S S M T W T F S S
Feb1, '10 Feb8, '10 Feb15,'10 Feb22,'10

6.4 Gantt Chart Considerations
In practice professional construction project managers use sophisticated software
like Microsoft Project, illustrated below, and Microsoft Excel or Primavera to create
Gantt charts. Not only do these packages make the drawing of Gantt charts easier,
they also make subsequent modification of plans easier and provide facilities for
monitoring progress against plans. Tables and spreadsheets can also be used to
create simple and easy to change charts without Microsoft Project. Spreadsheets
with coloured bars are most useful for the simplest projects and help with defining the
overall completion time. A summary of useful tips include the following:
 Sometimes Gantt charts are drawn with additional columns showing details
such as the amount of time the task is expected to take, resources or skill level
needed or person responsible.
 Beware of identifying reviews or approvals as events unless they really will
take place at a specific time, such as a meeting. Reviews and approvals often
can take days or weeks.
 The process of constructing the Gantt chart forces group members to think
clearly about what must be done to accomplish their goal. Keeping the chart
updated as the project proceeds helps manage the project and head off
schedule problems.
 It can be useful to indicate the critical points on the chart with bold or coloured
outlines of the bars.
 Computer software can simplify constructing and updating a Gantt chart.

Further examples of Gantt Charts

7. PERT (Program Evaluation and Review Technique)
PERT is a variation on Critical Path Analysis that takes a slightly more sceptical view
of time estimates made for each project stage. PERT was developed to deal with
projects where some, or all, of the activities has uncertain or variable durations,
particularly in research and development projects. Any such activity will have some
statistical distribution to represent the variable duration. In particular this was thought
to be best represented by a “beta – distribution” which typically has a positive
skewed distribution and only allows non-negative (positive) values of the variable. An
example illustrated the distribution is shown on the graph below.
Prob. Density
0 a m b
With PERT each variable activity will be given 3 estimates of time duration:
I. Best or Optimistic = a
II. Most likely or Realistic = m
III. Worst or Pessimistic = b
To use it, estimate the shortest possible time each activity will take, the most likely
length of time, and the longest time that might be taken if the activity takes longer
than expected. Use the formula below to calculate the time to use for each project
stage:
Shortest time + 4 x likely time + longest time (a + 4m + b)
6 6
This helps to bias time estimates away from the unrealistically short time-scales
normally assumed.
Key Points:
Critical Path Analysis is an effective and powerful method of assessing:
 What tasks must be carried out.
 Where parallel activity can be performed.
 The shortest time in which you can complete a project.
 Resources needed to execute a project.
 The sequence of activities, scheduling and timings involved.
 Task priorities – the most efficient way of shortening time on urgent projects.
An effective Critical Path Analysis can make the difference between success and
failure on complex projects. It can be very useful for assessing the importance of
problems faced during the implementation of the plan. PERT is a variant of Critical
Path Analysis that takes a more sceptical view of the time needed to complete each
project stage. A more details description of PERT will be covered in the next section.
It can be assumed that these 3 estimates form
part of the beta- distribution and correspond to
the position shown on the above diagram.
Activity Duration

8. PERT (Program Evaluation and Review Technique) Working Examples
See next chapter (Network Analysis and Project Delay Techniques

Network Anaysis_ critical path methods

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