LEC – 2

SCHEDULING METHODS AND

PROGRAMS
Schedule Methods

• Informal Methods
– Checklist
– To-do List
– Planner

• Formal Methods
– Bar Chart
– Network Diagram
• Arrow method (Activity on Arrow)
• Node method (Activity on Node) -> PDM
– PERT
– Linear Schedule
– BIM Schedule

2
Top Scheduling Computer
Programs
• Microsoft Project • Primavera P6
– Easy to learn – Handle everything
– Many project managers like it
– Extensive hardware
• ZOHO Projects requirements
– Web-based – Best for large
– Free for one project organizations
– Just Gantt charts

• FastTrack Schedule 9 • Workfront

– For both Mac and Windows – Web-based
– Effective resource – Easy to use interface
management tool

[http://www.brighthubpm.com/software-
reviews-tips/2492-the-top-five-project-
scheduling-software-programs/]
3
Introduction
Suppose that you meet with two friends and decide to
go on a hunting trip.
You must do specific activity such that the trip will be
at the right way. The following activity must be done.
Task of Friend 1 - Get the food – duration 2 hrs
Task of Friend 2 - Get the gears– duration 3 hrs
Task of yours - Get the jeep ready– duration 4 hrs

Who have floats?

Critical activity?
Options for friends?
Option with you?
Introduction

From chart you can see that the 3rd activity (preparing
the jeep) have the longest period of time any delay with
this activity leads to delay in the trip this activity is a
“critical activity”
Critical activity : An activity on the critical path any
delay on the start or finish of a critical activity will
result in a delay in the entire project

Critical path : The longest path in a network from start

to finish
BAR/ GANTT CHART
Bar Charts

Henry Gantt developed a method of relating

a list of activities to a timescale in a very
effective manner, by drawing bar charts
Bar Chart Basics

Definition
• Time-scaled line Example
graphic
representation of
project plan
• Bars – period of
activity time
• Info – project title,
location, activity
description and
duration
8
How to Create a Bar Chart
Steps
• Determine the project activities
• Estimate the duration of each Example
project activity and define the Weekly Schedule Example
start time, finish time, the Activity Week 1 Week 2 Week 3 Week 4
A
sequences of activities B
C

• Summarize the project

activities in a vertical column,
the Y-axis
• Time is represented
horizontally (x-axis)
Daily Schedule Example
• Draw in a bar for each activity Activity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
A
based on its start and finish B
C
time

9
How to Create a Bar Chart
Interrupted Activity
• Some activities are
interruptible Example
• Some days are not
workable such as holidays
and weekends
• Blank space or dashed
bars showing non-work
days

Daily Schedule Example - Interrupted Activities

Activity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A - Foundation
B - Ex. Framing & Siding
C - MEP & Finishes

10
Percent Complete (S-) Curves

Concept
• Cumulative percentage of Example
the estimated work
Weekly Schedule with S-curve
Activity Week 1 Week 2 Week 3 Week 4 % cost
• Percentage could be based 20% 100
on: A 90
80
– The ratio of monetary 25% 25% 70
value of each activity B 60
50
– The proportioned level 15% 15% 40
C 30
of effort (work hours or 20
work days) 10
Weekly 20% 25% 40% 15%
Cumulative 20% 45% 85% 100%

11
Update and Showing Progress

Concept
Example
• Rescheduling when
– Some activities
ahead or behind
– Changes
happening
• Showing progress
– As-built schedule
vs. as-planned
schedule

Example – Project ahead of schedule of behind?

12
Bar charts/ Gantt charts

 Commonly used for less number of activities with longer

durations
 Length of the bar represents the duration of the activity

13
Bar charts/ Gantt charts
•Bar charts can be
made more
elaborated to
include updated
information
•Bar chart is
commonly used as a
means of displaying
a network schedule
in a time-phased
fashion

14
 Bar charts/ Gantt charts
• If the project goes as per the schedule the bar chart alone
might be sufficient
• However the construction projects seldom goes according to
schedule
• You cannot tell exactly what effect a delay today will have on
the timings of future activities
– Activity D in previous diagram starting on 1/15.
– If B gets delayed by 1 week, what effect it has on D
• Perhaps D needs a machine that is being used by B
• Or perhaps D is scheduled to start on 1/15 because of
reasons unrelated to B & D and can proceed as
planned.
– Only the scheduler knows the exact reasons. 15
Bar charts/ Gantt charts
 Normally activities are listed in chronological order
 Any activity longer than 3 months should be sub-divided
into greater detail
 Bar charts should not contain more than 100 activities

16
 PBL
Figure 1 shows a double span bridge. Break the
construction works of the bridge down into activities.
The plan will be used for bidding purpose.

19
20
21
Shortcomings of Bar Charts

• Bar charts begin to fail to provide valuable information when

projects become more complex
• A general criticism of bar charts is that they do
not show clear dependencies between activities
• Changes in the logical sequencing of activities in
a bar chart cannot be readily made
– Especially when many activities are involved
Shortcomings of Bar Charts

Bar chart shortcomings virtually disappear

when scheduling software is used
Most popular computer generated
schedules permit easy conversion between
precedence diagrams and bar charts
NETWORK SCHEDULE
WHAT IS NETWORK
Networks: A Definition

• Network: A graphical representation of the activities

(and events) comprising the project, in a logical
and chronological depiction
• Network diagrams are basically two types:
– arrow networks and
– node networks:
• Basic node networks
• Precedence networks

25
Arrow Networks

• Arrow network: A network on which activities are

represented by arrows between nodes (events)
• Also called:
– I-J Method (10-20 for activity A below),
– Activity on Arrow (AOA) Network or
– Arrow Diagramming Method (ADM)

A
10 20
5

26
 Arrow Networks:
Simple Example

Activity IPA*
A -
B A
C A
D B
E C, D

* IPA: Immediately Preceding Activities

27
Example Solution

B D
30
A E
10 20 40 50

28
Dummy activity (fictitious)

* Used to maintain unique numbering of activities.

* Used to complete logic, duration of “0”

* Used to depict correct dependencies.

January 20, 2025 29

 A

Divide node to correct

4 11
B
(a) Incorrect Representation

A
4 11
Dummy B
10
January 20, 2025
(b) Correct Representation 30
Example
Draw the arrow network for the project given next.

Activity IPA
A -
B A
C A
D B,C

January 20, 2025 31

Solution :
B

A
10 20 30 D 40
C
Improper solution

Activity IPA
A -
B A
C A
D B,C

32
January 20, 2025
Solution : B 30
Dummy

10 A 20 40 D 50
C
proper solution

Activity IPA
A -
B A
C A
D B,C
33
January 20, 2025
Example -
Draw the arrow network for the project given next.

Activity IPA
A -
B A
C A
D B
E B,C
F C

January 20, 2025 34

Solution :
B 30 D
Dummy 1

10 A 20 50 E 60
Dummy 2

C 40 F

Activity IPA
A -
B A
C A
D B
E B,C
F C

January 20, 2025 35

Example for Arrow Network
Activity IPA
A -
B -
C -
D A
E A,B
F A,B,C
G E,F
H D,G
I D,G
36
 Solution

A D
20
H
70
d1 d3
B E G
10 30 50 60 80

d2 I
C F
40

37
Removal of Redundant Dummies
Original Diagram Diagram after removal
of redundant dummies

(a) A B A B

(b) A B A B

C C

January 20, 2025 38

 Original Diagram Diagram after removal
of redundant dummies

(c) A C A C

B E B E

(d) A C A C

B E B E

January 20, 2025 39

 Activity Depends Upon Immediately Preceding
Activity (IPA)
A ----- -----
B A A
C A, B B

A B C

Redundant

Relationship

January 20, 2025 40

Removing Redundant Relationships:

Activity Description Depends Upon

A Site Clearing -----
B Removal of Trees -----
C Excavation for Foundations A
D Site Grading A, B, C
E Excavation for Utility Trenches A, B, C
F Placing formwork & Reinforcement B, C, J, M
G Installing sewer lines B, C, D, E, K
H Pouring concrete D, E, F, G, L
J Obtain formwork & reinforcing steel -----
K Obtain sewer lines -----
L Obtain concrete -----
M Steelworker availability -----

January 20, 2025 41

Removing Redundant Relationships:

42
Comments on Arrow
Networks
• An arrow represents an activity
• A node represents an event of starting and/or finishing an
activity or activities
• Arrow networks can only accommodate finish-start
relationships
• Dummy activities are required in Arrow Networks for logic or
identity
• Even though a network is not time-scaled, arrows go from
left to right since the “X-axis” is supposed to -loosely-
represent time
• Once the number of activities increase, it gets difficult and
complicated 43
 Node Networks

• A node network is a network where nodes

represent activities and arrows represent logic
relationships (dependencies)
• Also called activity on node (AON)
• Precedence diagrams (or networks) are an
advanced form for node networks

44
Example 1 Using Node
Networks

Activity IPA B D

A -
A E
B A
C A
C
D B
E C, D

45
Example 2 for Node Network

Activity IPA
A -
B -
C -
D A
E A,B
F A,B,C
G E,F
H D,G
I D,G
46
Solution of Example 2

A D H

PS B E G I
PF

C F

47
Lags and Leads
• A lag is defied as a minimum waiting period
between the finish (or start) of an activity and the
start (or finish) of its successor.
– A lead is a negative lag
– Think of a lag as (after) and a lead as (before)
– Arrow networks cannot accommodate lags

48
Tips for Proper Node
Network Drawing - 1
Improper Proper

A A
5 5

49
Tips for Proper Node
Network Drawing - 2
Improper Proper

A A
5 5

B B
3 3

50
Tips for Proper Node
Network Drawing - 3
Improper Proper

A A
5 5

B
B
3
3

51
Tips for Proper Node
Network Drawing - 4
Improper Proper

A
A 5
5
B
or 3

A
B
5
3

B
3

52
Tips for Proper Node
Network Drawing - 5
Improper Proper

A C A C
5 4 5 4

B D B D
3 7 3 7

53
Tips for Proper Node
Network Drawing - 6
Starting a network diagram
Improper Proper

A A
5 5

B B
PS
3 3

C C
4 4

54
Tips for Proper Node
Network Drawing - 7
Ending a network diagram
Improper Proper

X
X
5
5

Y Y
3 3 PF

Z Z
4 4

55
Arrow versus Node
Diagrams

• Advantages of node diagrams:

1. Node networks are easier to draw
2. Node networks do not require dummy activities
3. Node networks can accommodate lags between activities
without the addition of more activities
4. Node diagrams can accommodate all four types of relationships:
finish-to-start, start to start, finish to finish, and start to finish

• Advantage of arrow diagrams: representing activities

and events

56
Networks and Bar Charts

• Logic networks made bar charts obsolete as a

scheduling method.
• However, bar charts serves now an important role
in scheduling: reporting CPM-based schedule.
– Most industry personnel, especially field people, prefer
bar charts over networks for their simplicity

57
Time-Scaled Logic Diagrams

• It was thought of a method that combines the main

advantage of bar charts (time-scaled) with the main
advantage of networks (show logic) in one method
• The main problem is the amount of lines and their
intersections
• A partial solution is to show binding (driving)
relationships only

58
Practice Quiz

• True or False:
1. A node in an arrow diagram represents an event
2. An arrow in an arrow diagram represents an event
3. A node in a node diagram represents an event
4. An arrow in a node diagram represents a logic relationship
5. A milestone is a term used by scheduling software to indicate an
important event
6. One of the major advantages of networks over bar charts is ability to
depict logic

60
 Critical Path Method (CPM)

Activity Event Times Critical Path

• Early start (ES) • The sequential
combination of
• Early Finish (EF) activities and
• Late Start (LS) relationships from
project start to finish
• Late Finish (LF) that requires the
• Lag – waiting period longest time to
complete.

61
 PDM Basic

Concept Special Notes

• PDM is an AON • PDM with only FS is
network that allows for AON – many times
the use of four types AON and PDM are
of relationships exchangeable
(sequences):
– Finish to Start (FS) • Two activities can
– Start to Start (SS) have more than one
– Finish to Finish (FF) relationship – called
– Start to Finish (SF) multiple relationships

62
 Float/Slack

Total Float (TF) Free Float (FF)

• The maximum amount • The amount by which
of time by which an that activity can be
activity can be delayed without
delayed without delaying the early start
delaying the entire of any following
project. activity or affecting
any other activity in
• The total float is the network.
shared by activities on
the same path. • Free float is not
shared 63
PDM Calculation

Forward Pass Backward Pass

• From beginning to end • From end to beginning
and largest value is used
• Use calculated early
• Use 0 for the early start of finish time as late finish
first activity for the last activity
• EF = ES + Duration (D) • LS = LF – D
• ES = early event time or • LF = late event time or
ES j = max (EF i+lag) LF i = min(LSj-lag)

64
Float Calculation

Float Formula Critical Path

• TF = LF – D – ES • Critical activities:
– Start Float (SF) = LS – ES – ES = LS and EF = LF
– Finish Float (FNF) = LF – EF
– TF = 0
• FF = min(ES of next activity –Lag) –
EF • Critical path:
– If more than one activity exits – Connecting all the critical
the node, use the smallest activities through the
calculated value of the FF network

65
 Independent float (Ind. F): we may define it as the
maximum amount of time an activity can be delayed
without delaying the early start of the succeeding
activities and without being affected by the allowable
delay of the preceding activities.

Ind. Fi = min(ESi+1) – max(LFi-1) – Duri

 Independent Float
 Free float is calculated so as to not affect the succeeding activities, but it
may be affected by the preceding activities.
 For example, if activity B is delayed (within its total float), this amount will
be taken away from the total float and the free float of activity E.
 Let B start on day 8 and finish on day 15 (using its entire total float).
Activity E will then start on day 15 and finish on day 21.
 This leaves activity E with only 6 days of total float, one of which is free
float.
 Independent Float
 Independent float (Ind. F) of an activity is not shared or affected by any
other activity. Independent float is calculated as follows:

 This equation may result in negative numbers, which should be

interpreted as zero independent float.
 Change ES of activity (i) to LF of activity (i-1). Check new ES of
activity (i+1). The difference between both ES of act (i+1) is indep
float.
 Independent float is part of free float, so make sure that Ind. F ≤ FF.
 Independent float is the only float that can be considered truly an
activity float, that is, not shared with any other activity, predecessor or
successor.
 Interfering float and independent float are not used in construction
scheduling or even calculated by commercially available software-
scheduling programs. They are sometimes used, although rarely, in
delay-claims resolution.
Interfering Float

• Interfering float (Int. F) is the maximum amount of time an activity may

be delayed without delaying the entire project but causing a delay to the
succeeding activities. It is the part of the total float that remains after
free float is deducted. Only shows the amount of delay to the ES of
succeeding activity if full TF is consumed by the preceding activity
• Increase the ES of activity to the TF. See how much ES of
succeeding activity will change

Int. F = TF – FF

7
Hang Wallpaper ?
69
CPM Calculations: Example
2

Activity Duration IPA

A 5 -
B 7 A
C 4 A
D 5 B
E 6 B,C
F 3 C
G 8 D,E
H 5 E
I 4 E,F
J 1 G,H,I
70
CPM Calculations:
Example 2 Graphic
Solution 1
12, 17 18, 26
D G
5, 12 5 8
B
7 13, 18 18, 26
26, 27
5, 12 3 J
0, 5 12, 18 18, 23
1
A E H
5 6 5 26, 27
4
0, 5 12, 18 21, 26 18, 22
3 I
5, 9 4
10
C 9, 12
4 F 22, 26
3
8, 12
19, 22

71
Free Float

• Free Float, FF: The maximum amount of time an activity

can be delayed without delaying the ES of the succeeding
activity(s)
– FFi = min(ESi+1) – EFi
– FFB = min(8, 12) – 8 = 0
– FF ≤ TF

8, 15
E
2,8 7
B 10,17
6
4,10
12, 17
F
5

72
Free Float Calculation
in Our Example:
Activities C, F, I
12, 18 18, 23 26, 27
E H J
6 5 1

12, 18 21, 26 18, 22 26, 27

I
5, 9 4
C 9, 12
4 F 22, 26
3
8, 12
19, 22

73
CPM Calculations:
Example 2 Tabular
Solution
Activity ES EF LS LF TF FF
A 0 5 0 5 0 0
B 5 12 5 12 0 0
C 5 9 8 12 3 0
D 12 17 13 18 1 1
E 12 18 12 18 0 0
F 9 12 19 22 10 6
G 18 26 18 26 0 0
H 18 23 21 26 3 3
I 18 22 22 26 4 4
J 26 27 26 27 0 0

Constr. Project Sched. & Control - S. Mubarak - Part 4 74

 PDM Diagram
 PDM diagram before forward pass
 PDM Diagram
 PDM diagram after forward pass
 PDM Diagram
 Restricted
Start PDMfloat diagram after backward pass
Finish Restricted Float

Is this correct??
AOA: ES, LS, LS, LF, TF, FF

EF
(ES, EF)
(LS, LF)
LF
Why Critical Path Method
(CPM)?
• Think
• Read
• Search
Then you can figure out…

79
Make a Comparison
You tell me their Pros &
Cons
Bar Chart
VS.

AOA
VS.

AON
vs.

PDM

80