1. Project and Production Management
Module 2
Project Planning
Prof Arun Kanda & Prof S.G. Deshmukh,
Department of Mechanical Engineering,
Indian Institute of Technology, Delhi

2. Module 2 Project Planning
1. Developing the Project Network
Work Break Down Structure
AOA & AON networks
Basic Scheduling for AOA networks
Critical Path
Floats
Basic Scheduling for AON networks
Critical path
4. Scheduling Probabilistic Activities
PERT assumptions
Probability Statements
5. Illustrative Examples
6. Self Evaluation Quiz
7. Problems for Practice
8. Further exploration

3. FORMATION OF PROJECT TEAM
Appointment of Project Manager
Selection of Project team members
Briefing meetings amongst team members
Broad consensus about scope of work and time frame
Development of work breakdown structure and allocation of responsibilities

4. WORK BREAKDOWN STRUCTURE
A breakdown of the total project task into components to establish
How work will be done?
How people will be organized?
How resources would be allocated?
How progress would be monitored?

5. ALTERNATIVE WAYS TO BREAKDOWN WORK

6. WORK BREAKDOWN STRUCTURE
Project
System I System II System N
Subsystem Subsystem Subsystem
Task Task
Subtask Subtask Subtask
Work package Work package

7. WORK BREAKDOWN STRUCTURE
Hardware orientation (Identification of basic work packages)
Agency orientation (Based on assignment of responsibility to different agencies)
Function oriented (e.g Design, Procurement, Construction and Commissioning)

8. WORK BREAKDOWN STRUCTURE (Continued)
Generally a WBS includes 6-7 levels. More or less may be needed for a situation.
All paths on a WBS do not go down to the same level.
WBS does not show sequencing of work.
A WBS should be developed before scheduling and resource allocation are done.

9. WORK BREAKDOWN STRUCTURE (Continued)
A WBS should be developed by individuals knowledgeable about the work. This means that levels will be developed by various groups and the the separate parts combined.
Break down a project only to a level sufficient to produce an estimate of the required accuracy.

10. ILLUSTRATIVE WORK BREAKDOWN STRUCTURE
Missile
Guidance Rocket Launching Warhead
control sys platform
Ballistic Propulsion Re entry
shell engine vehicle
I Stage Solid fuel II Stage

11. MEANS OF PROJECT REPESENTATION
Project name and description.
List of jobs that constitute the project.
Gantt or bar chart showing when activities take place.
Project network showing activities, their dependencies and their relation to the whole. (A-O-A and A-O-N representations)

12. WHY USE PROJECT NETWORKS ?
A convenient way to show activities and precedence in relation to the whole project.
Basis of project planning:
Responsibility allocation
Definition of subcontracting units
Role of different players
Basic scheduling and establishment of work time tables

13. WHY USE PROJECT NETWORKS -II ?
Critical path determination and selective management control
Deterministic vs probabilistic activity times
Resource planning for projects
Project crashing with time cost tradeoffs
Resource aggregation
Resource levelling
Limited resource allocation

14. WHY USE PROJECT NETWORKS - III ?
Project implementation:
Time table for implementation
Monitoring and reporting progress
Updation of schedules and resources
Coordination of work with different agencies
The project network is thus a common vehicle for planning, communicating and implementing the project right from inception.

15. EXAMPLE 1 Organizing a one day Seminar
Generate the list of jobs to be done:
1) Decide date ,budget, venue for seminar.
2) Identify speakers, participants.
3) Contact and finalize speakers.
4) Print seminar brochure.
5) Mail brochures to tentative participants
6) Estimate number of participants.

16. Organizing a one day seminar
7) Decide menu for lunch, tea & coffee
8) Arrange for catering
9) Arrange projection facilities at venue.
10) Receive guests at registration.
11) Conduct seminar as per brochure
12) See off guests.

17. EXAMPLE 1 Organizing a one day Seminar
Activity Predecessors
1) Decide date ,budget, venue for seminar. --
2) Identify speakers, participants
3) Contact and finalize speakers A2
4) Print seminar brochure A1, A3
5) Mail brochures to tentative participants A4
6) Estimate number of participants A5

18. Organizing a one day seminar
Activity Predecessors
7) Decide menu for lunch, tea & coffee A6
8) Arrange for catering A1,A7
9) Arrange projection facilities at venue. A6
10) Receive guests at registration A8, A9
11) Conduct seminar as per brochure A8, A9, A10
12) See off guests A11

19. DRAWING THE PROJECT NETWORK (A-O-A)
A A A A A A A A A12

20. DEVELOPING THE PROJECT NETWORK (A-O-N)
A A A A A A8
A A A12
A A A10

21. EXAMPLE 2 Job Predecessors a -- b -- c -- d a,b e b,c a d b e c 4 3 21 5 e c 4

22. EXAMPLE 3 Job Predecessors a -- b -- c -- d a,b e a,c f a,b,c 3 d b f c e 4

23. EXAMPLE 4 Job Predecessors a -- b a c a d a e b, c, d 3 b a c e d 4
DUMMIES FOR UNIQUENESS OF
ACTIVITY REPRESENTATION

24. EXAMPLE 5 S T
DUMMIES FOR CREATION OF
A SINGLE SOURCE AND SINK

25. THE ROLE OF DUMMIES IN PROJECT NETWORKS
Role of Dummy I II III
Network type
A-O-A yes yes yes
A-O-N no no yes
I Correct representation of precedence logic
II Uniqueness of activity representation
III Creation of single source/ sink

26. EXAMPLE 6 Inconsistent Network
A closed loop in a project network
is a logical inconsistency.

27. EXAMPLE 7 REDUNDANCY (A-O-N)
Job Predecessors a
b a c
d a, b, c
e d
f d
b e d a
***********
c f
Redundancy a in the predecessor set for activity d
could be removed thereby deleting arc a-d above

28. PREREQUISITES FOR A VALID PROJECT NETWORK
NECESSARY REQUIREMENT
The project network must not have any cycles or loops, since these represent logical inconsistencies in representation.
DESIRABLE FEATURES
The project network should have the minimum number of dummies and no redundancies since these unnecessarily clutter the network.

29. Basic Scheduling with A-O-A Networks
PROJECT MANAGEMENT
Basic Scheduling with
A-O-A Networks

30. ALTERNATIVE PROJECT REPRESENTATIONS
Activity on Arc
(A-O-A)
Arrow diagrams
Event oriented networks
Activity on Node
(A-O-N)
Precedence networks
Activity oriented networks
activity, a i j a

31. ACTIVITY DURATIONS Deterministic (as in CPM)
when previous experience yields fairly accurate estimates of activity duration, eg construction activity, market surveys.
Probabilistic (as in PERT)
when there is uncertainty in times, as for instance in R&D activities, new activities being carried out for the first time.

32. TIME ESTIMATES Deterministic times Probabilistic times
A single time estimate is used for each activity. This is taken from experts who have prior knowledge and experience of the activity.
Probabilistic times
Three time estimates (optimistic, most likely and pessimistic) are commonly used for each activity based on the consensus of the group.

33. EXAMPLE 1 Job Predecessors Duration (days) a -- 2 b -- 3 c a 1
d a, b
e d
f d
g c, e
h c, e
i f, g, h

34. PROJECT NETWORK FOR EXAMPLE 1 (A-O-A)h 4 1 a g 2 e 5 6 i b f 3 d 3 4 8

35. CRITICAL PATH The longest path in the network
Lower bound on the project duration
Selective control for management of project
Can be determined by
Enumeration of all paths in the network
Event based computations (A-O-A networks)
Activity based computations (A-O-N networks)

36. NODE NUMBERING FOR EXAMPLE 1 (A-O-A)c h 4 1 a g 2 e 5 6 i b f 3 d 3 4 8

37. PATH ENUMERATION Level 0 Level 1 Level 2 Level 3 Level 4 Level 5

38. FORWARD PASS Initialization: Ej= Max (Ei+ tij) for all i before node j
E1 = 0 (or the project start time S)
(This applies to all source nodes)
Ej= Max (Ei+ tij) for all i before node j
( Set B(j)) Ej j Ei
tij
B(j) i

39. FORWARD PASS EXAMPLE 1 (A-O-A)c h 2 6 5 4 1 a g 2 e 8 5 6 i 1 b f 3 d 3 7 3 4 4 8

40. BACKWARD PASS Initialization:
Ln (or the latest occurrence of all ending nodes)
= Project duration, T as determined in the forward pass
Li = Min (Lj-tij) over all successor nodes j of the node i being investigated, (set A(i))
A(i)
tij j i Lj Li

41. BACKWARD PASS EXAMPLE 1 (A-O-A)2 16 12 c h 2 6 5 4 1 21 a g 2 e 8 5 6 i 1 3 18 b 7 f 3 d 3 7 3 4 4 8

42. ACTIVITY SCHEDULE FROM EVENT TIMESEj Ei
tij j i Lj Li
Early start of activity ij = ES(ij) = Ei
Early finish of activity ij= EFij = ES(ij)+ tij
FORWARD
PASS
Late finish of activity ij = LF(ij) = Lj
Late start of activity ij = LS(ij) = LF(ij) -tij
BACKWARD
PASS

43. EARLY & LATE SCHEDULE FOR EXAMPLE 1
Job duration ES EF LS LF TF a b c d e f g h i

44. GANTT CHART SHOWING ACTIVITY SCHEDULE
b ^^^^^^ c
d ^^^^^^^^^
e ^^^^^^^^^^^^^ f
g ^^^^^^^^^^^^^^^^ h
i ^^^^^^^^

45. CRITICAL PATH EXAMPLE 1 (A-O-A)2 16 12 c h 2 6 5 4 1 21 a 12 3 18 g 2 e 8 5 6 i 1 3 18 b 7 f 3 21 d 3 7 3 4 4 8 7 18 3

46. EVENT SLACKS Ei Ej tij i j Li Lj Ei Li Ej Lj Slack on node i = Li - Ei
Slack on node j = Lj - Ej

47. ACTIVITY FLOATS Ei Ej tij Li Lj Ei Li Ej Lj
Total float = F1(ij) = Lj-Ei -tij
Safety float = F2(ij) = Lj- Li-tij
Free float = F3(ij) = Ej -Ei -tij
Independent float = F4(ij)
= Max (0, Ej -Li- tij)

48. FLOAT COMPUTATIONS Ei Ej tij Li Lj
Total float = LS - ES = LF-EF of activity
Safety float =
Total float - Slack on preceding node
Free float =
Total float - Slack on succeeding node
Independent float =
Max (0, Total float - Slack on preceding and succeeding nodes)

49. FLOATS FOR EXAMPLE 1 Job Total Safety Free Independent a 1 1 0 0c d e f g h i

50. INTERPRETATION OF FLOATS
An activity , in general, has both predecessors and successors. Each of the four kinds of float depends on how these accommodate the activity.
Predecessors Successors
activity

51. FLOAT INTERPRETATION SUCCESSORS Early Late Early Free Total
PREDECESSORS
Independent
Safety
Late

52. ANOMALIES ACTIVITY h FLOATS Total Safety Free Ind. 2 2 2 2 2 0 2 0 18 12 h 5 7 4 12 18 h 5 7 4 12 18 h 5 7 4 12 18 h 5 7 4 18 12

53. Basic Scheduling with A-O-N Networks
PROJECT MANAGEMENT
Basic Scheduling with
A-O-N Networks

54. ALTERNATIVE PROJECT REPRESENTATIONS
Activity on Arc
(A-O-A)
Arrow diagrams
Event oriented networks
Activity on Node
(A-O-N)
Precedence networks
Activity oriented networks
activity, a i j a

55. SCHEDULING WITH A-O-N NETWORKS
Basic scheduling computations can be done on both A-O-A or A-O-N networks.
A-O-N networks are simpler to draw, though they lack intuitive work flow interpretation of A-O-A networks.
There are no float anomalies in A-O-N networks.
A-O-N networks are becoming more popular, in computer packages,
Lead easily to PDM with expanded precedence relations FS , FF, SS, SF.

56. EXAMPLE Job Predecessors Duration (days) a -- 2 b -- 3 c a 1 d a, b 4
f d
g c, e
h c, e
i f, g, h

57. PROJECT NETWORK EXAMPLE (A-O-N)2 1 a c 6 g 4 4 5 i 3 d h e 3 b 8 f

58. FORWARD PASS (A-O-N Networks)
Initialization:
Early start(ES) for all beginning activities
= 0 (or the start date, S for the project)
Early finish (EF) for activity = ES+ duration
ES(j)= Max (EF all predecessors)
ES/EF
ES/ EF
ES/EF i1 j
ES/EF i2 ip

59. FORWARD PASS FOR EXAMPLE2 1 a c 6 g 4 4 5 i 3 d h e 3 b 8 f

60. BACKWARD PASS (A-O-N Networks)
Initialization
Project duration,T = Max (EF of ending jobs).
LF(all ending jobs) =T
LS = LF- Duration
LF = Min (LS of successors)
LS/LF
LS/LF
LS/LF
LS/LF

61. BACKWARD PASS FOR EXAMPLE
2 / 3
0 / 2
12 / 18 2 1 a c 6 g
3 / 7
18 / 21
7 / 12
12 / 16 4 4 5 i 3
0 / 3 d h e 3 b
7 / 15 8 f

62. EARLY & LATE SCHEDULE FOR EXAMPLE
Job duration ES EF LS LF TF a b c d e f g h i

63. CRITICAL PATH FOR EXAMPLE
2 / 3
0 / 2
12 / 18 2 1 a c 6 g
1 / 3
12 /18
11 / 12
3 / 7
18 / 21
7 / 12
12 / 16 4 4 5 i 3
0 / 3 d h e 3 b
3 / 7
7 / 12
18 /21
14 / 18
7 / 15
0 / 3 8 f
10 / 18

64. CRITICAL PATH FOR EXAMPLE2 1 a c 6 g 4 4 5 i 3 d h e 3 b 8 f

65. GANTT CHART SHOWING ACTIVITY SCHEDULE
a *** ]
b ^^^^^^
c ** ]
d ^^^^^^^^^
e ^^^^^^^^^^^^^
f ****************** ]
g ^^^^^^^^^^^^^^^
h ********** ]
i ^^^^^^^^^

66. INTERPRETATION OF FLOATS
An activity , in general, has both predecessors and successors. Each of the four kinds of float depends on how these accommodate the activity.
Predecessors Successors
activity

67. FLOAT INTERPRETATION SUCCESSORS Early Late Early Free Total
PREDECESSORS
Late Independent Safety

68. COMPUTATION OF FLOATS ES/EF i1 k1 LS/LF ES/EF ES/EF i2 k2 j LS/LFim kn
LS/LF
Slack on preceding node= Max (LF of predecessors) -ES
Slack on succeeding node = LF- Min (ES of successors)
(in the corresponding A-O-A representation)

69. FLOATS FOR EXAMPLE Job Total Safety Free Independent a 1 1 0 0c d e f g h i

70. FLOAT COMPUTATIONS FOR ACTIVITY a
Total Float = LS - ES = LF - EF =1
Safety float = Total Float - [Max (LF of predecessors)-ES]
= (0 - 0) = 1
Free float = Total Float -[LF -Min(ES of successors)]
= (3-2) = 0
Independent float = Total float - both the latter terms
= 1 - (0+1) = 0
0 / 2
2 / 3 c a
3 / 7
1 / 3 d

71. FLOAT COMPUTATIONS FOR ACTIVITY c
Total Float = LS - ES = LF - EF =9
Safety float = Total Float - [Max (LF of predecessors)-ES]
= (3 -2) = 8
Free float = Total Float -[LF -Min(ES of successors)]
= (12-12) = 9
Independent float = Total float - both the latter terms
= 9 - (1+0) = 8
12 / 18
2 / 3 c g a
11 / 12
1 / 3
12 / 16 h

72. FLOAT COMPUTATIONS FOR ACTIVITY f
Total Float = LS - ES = LF - EF =3
Safety float = Total Float - [Max (LF of predecessors)-ES]
= (7 -7) = 3
Free float = Total Float -[LF -Min(ES of successors)]
= ( ) = 3
Independent float = Total float - both the latter terms
= 3 - (0+0) = 3
18 / 21
7 / 15 d f i
10 / 18
3 / 7

73. FLOAT COMPUTATIONS FOR ACTIVITY h
Total Float = LS - ES = LF - EF =2
Safety float = Total Float - [Max (LF of predecessors)-ES]
= ( ) = 2
Free float = Total Float -[LF -Min(ES of successors)]
= ( ) = 2
Independent float = Total float - both the latter terms
= 2 - (0+0) = 2 c
18 / 21
12 / 16
11 / 12 e h i
14 / 18
7 / 12

74. PRECEDENCE DIAGRAMMMING METHODS
Generalized precedence relations
Start to Start (SS)
Finish to Finish (FF)
Start to Finish (SF)
Finish to Start (FS)
Permit partial or complete overlap of activities

75. START TO START LAG (SS) v1 v2 u1 u2

76. FINISH TO FINISH LAG (FF)v1 v2 u1 u2

77. START TO FINISH LAG (SF)v1 v2 u1 u2

78. FINISH TO START LAG (FS)v u

79. PDM EXAMPLE COMPUTATIONS
SF 4
SS 3
FS 4 B 8 D 6
FS 0
FF 5
FS 0 A 10 E 12 F 14 G 2
SS 3
SS 2
FF 5 C 20
FF 2
SS 10

80. Project Scheduling with Probabilistic Activity Times
PROJECT MANAGEMENT
Project Scheduling with Probabilistic Activity Times

81. UNCERTAIN ACTIVITY DURATIONS
For each activity in the project three time estimates are obtained
Optimistic time, a
Most likely time, m
Pessimistic time, b

82. PERT TIME ESTIMATES Mean of activity duration = (a + 4m + b) / 6
Variance of activity duration =
{ (b - a) / 6}2
Standard deviation of activity duration =
Sq. root of variance =
(b - a ) / 6

83. BETA DISTRIBUTION f(t) = K(t-a)c (b - t)d , a <= t <=b
a m b
f(t) = K(t-a)c (b - t)d , a <= t <=b
= 0, otherwise
[ a,b are the location parameters
c,d are the shape parameters ]

84. WHY CHOOSE BETA ?
The beta distribution is bounded on both sides with non-negative intercepts.
It is a uni-modal distribution.
Permits flexibility of shapes by suitable choice of location and shape parameters.
Intuitive appeal.
Easy approximations to mean and variance.

85. OTHER POSSIBLE DISTRIBUTIONS
UNIFORM
TRIANGULAR
EXPONENTIAL
NORMAL
DISCRETE
OTHERS ...

86. UNIFORM DISTRIBUTION 1/ (b-a) a b Mean = (a + b) / 2
Variance = (b - a)2 / 12

87. TRIANGULAR DISTRIBUTION
2/ (b-a)
a m b
Mean = (a + m + b) / 3
Variance = {(b -a)2 + (b - m)2 + (m -a)2}/36
= (a2 + m2 + b2 - am - ab - mb)/18

88. EXPONENTIAL DISTRIBUTIONm
f(t) = me -mt
Mean = 1/m
Variance = 1/m2

89. NORMAL DISTRIBUTION
N (mu, sigma 2) mu
Mean = mu
Variance = sigma 2

90. DISCRETE DISTRIBUTIONp2 pn p1 p3
- - -
t t t tn
Mean = p1 t1 + p2 t pn tn
Variance = p1 t12 + p2 t pn tn2
- (Mean) 2

91. BASIC PERT PROCEDURE - I
Compute mean and variance of all jobs.
Conduct forward and backward pass on the project network with expected times of all activities.
Identify the Critical Path.
Obtain variance of critical path by adding variance of activities.

92. BASIC PERT PROCEDURE - II
Obtain the distribution of the Project Duration.
Make probability statements about the project
Chances of meeting the target date.
Probability of exceeding a given ceiling date.
Probability that the project duration is confined to an interval of time.

93. AN EXAMPLE Job Predecessors Time estimates Mean Variance a m b A B
C A
D A
E A
F B,C
G D,F
H D,F
I E,H

94. SAMPLE NETWORK (A-O-A)2 5 A
8.33 I
4.33 D
7.66 1 H 4 6 6 C 8 B G
6.33
15.33 F 4 3 6

95. FORWARD & BACKWARD PASSE 2 5 A
8.33 I
4.33 D
7.66 1 H 4 6 6 C 8 B G
6.33
15.33 F 4 3 6

96. CRITICAL PATH
4.33
20.33 E 2 5 A
8.33 I 24
4.33
31.66
4.33 D
7.66 1 H 4 6 6 C 8 B G
31.66
16.33
10.33
6.33
15.33 F 4 3 6
10.33
16.33

97. DISTRIBUTION OF THE PROJECT DURATION
Project duration follows a Normal Distribution with
Mean = Variance = 6 = (2.45)2

98. CONFIDENCE INTERVALS Chances that the project is completed within
mean +/- 1 sigma 68% ( )
mean +/- 2 sigma 95% ( )
mean +/_ 3 sigma 99% ( )

99. PROBABILITY STATEMENTS - I
Probability of meeting a Target Date,
say 36 days
Z (Standard normal deviate) =
( )/2.45 = 4.34/2.45 = 1.77
Area from normal tables =

100. PROBABILITY STATEMENTS - II
Probability of exceeding a ceiling, say
28 days
Z (Standard normal deviate) =
( )/2.45 = -3.66/2.45 =
Area from normal tables =

101. PROBABILITY STATEMENTS - III
Probability of duration lying in an interval, say 28 to 36 days
Area from normal tables = =

102. STANDARD PERT ASSUMPTIONS
1. The activities are independent
2 The critical path contains a large no. of activities so that we can invoke the Central Limit Theorem.
3 .All activities not on the critical path are ignored.
4. Activity times follow a Beta distribution.
5. The mean and variance of the activities are given by (a+4m+b)/6 and [(b-a)/6]2.