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

EET

LET

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

End Start

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 Activity Prior Activity A None B None C A and B

Example 4

Activity Prior Activity 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

C

D

A

B

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 3 1 0 4 9 4

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

46 33

2

31

15

35

11

End 50

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 5 3

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)



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


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)




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

8 4



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


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)




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)




Total Float

Free Float

Independent Float

A

B

C

D

E

F

1

7

2

5

3

8

4

6

9

2

7

6

4

9

8 3

16

11

7 5 10



* 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)




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.

http://www.gantt-chart.biz/henry-laurence-gantt/



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 Task NameDuration Start Finish

1 1 1 day? 2/1/10 2/1/10

2 2 3 days 2/2/10 2/4/10

3 3 5 days 2/5/10 2/11/10

4 4 1 day? 2/12/10 2/12/10

5 5 4 days 2/8/10 2/11/10

6 6 1 day? 2/12/10 2/12/10

7 7 1 day? 2/15/10 2/15/10

8 8 3 days? 2/16/10 2/18/10

9 9 2 days? 2/19/10 2/22/10

10 10 4 days? 2/16/10 2/19/10

11 11 2 days? 2/20/10 2/23/10

12 12 1 day? 2/24/10 2/24/10

13 13 1 day? 2/25/10 2/25/10

14 14 1 day? 2/26/10 2/26/10

15 15 3 days? 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

Feb 1, '10 Feb 8, '10 Feb 15, '10 Feb 22, '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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