Download - Project and Production Management
Project and Production Management
Module 2
Project Planning
Prof Arun Kanda & Prof S.G. Deshmukh, Department of Mechanical Engineering,Indian Institute of Technology, Delhi
Module 2 Project Planning
1. Developing the Project Network
1. Work Break Down Structure
2. AOA & AON networks2. Basic Scheduling for AOA
networks1. Critical Path2. Floats
3. Basic Scheduling for AON networks
1. Critical path2. Floats
4. Scheduling Probabilistic Activities
1. PERT assumptions2. Probability Statements
5. Illustrative Examples6. Self Evaluation Quiz7. Problems for Practice8. Further exploration
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
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?
ALTERNATIVE WAYS TO BREAKDOWN WORK
Task Task
System I System II System N
Subsystem Subsystem Subsystem
Project
Subtask Subtask Subtask
Work package Work package
WORK BREAKDOWN STRUCTURE
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)
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.
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.
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
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)
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
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
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.
EXAMPLE 1Organizing 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.
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.
EXAMPLE 1Organizing 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
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
DRAWING THE PROJECT NETWORK (A-O-A)
1 2 3 4 5 6 7 8 9 10 A2 A3 A4 A5 A6 A7 A8 A11 A12
A1
A10
A9
DEVELOPING THE PROJECT NETWORK (A-O-N)
A1 A4 A5 A6 A7 A8
A2 A3 A10
A9 A11 A12
5
3
21
EXAMPLE 2
Job Predecessorsa --b --c --d a,be b,c
4
a
b
c
d
e
EXAMPLE 3
Job Predecessorsa --b --c --d a,be a,cf a,b,c
1 2 5 6
3
4
a
b
c e
f
d
EXAMPLE 4
Job Predecessorsa --b ac ad ae b, c, d
1 2 5 6
3
4
ab
d
c e
DUMMIES FOR UNIQUENESS OF ACTIVITY REPRESENTATION
EXAMPLE 5
S T
DUMMIES FOR CREATION OF A SINGLE SOURCE AND SINK
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
EXAMPLE 6Inconsistent Network
2 3 4
5 6 7
1 8
A closed loop in a project network is a logical inconsistency.
EXAMPLE 7REDUNDANCY (A-O-N)
Job Predecessorsa --b ac --d a, b, ce df d
b e
***********
c f
a d
Redundancy a in the predecessor set for activity d could be removed thereby deleting arc a-d above
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.
PROJECT MANAGEMENT
Basic Scheduling with
A-O-A Networks
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
i j aactivity, a
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.
TIME ESTIMATES
• Deterministic 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.
EXAMPLE 1
Job Predecessors Duration (days)
a -- 2
b -- 3
c a 1
d a, b 4
e d 5
f d 8
g c, e 6
h c, e 4
i f, g, h 3
PROJECT NETWORK FOR EXAMPLE 1 (A-O-A)
a
b
c
d
e
f
g
h
i2
3
1
4
5
8
6
4
3
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)
NODE NUMBERING FOR EXAMPLE 1 (A-O-A)
a
b
c
d
e
f
g
h
i2
3
1
4
5
8
6
4
3
PATH ENUMERATION
Level 0
Level 1
Level 2
Level 3
Level 4 Level 5
Level 6
Level 7
FORWARD PASS
• Initialization:E1 = 0 (or the project start time S)
(This applies to all source nodes)
• Ej= Max (Ei+ tij) for all i before node j
j
iB(j) tijEi
Ej( Set B(j))
FORWARD PASSEXAMPLE 1 (A-O-A)
1
2 5 6
3 4 7
8a
b
c
d
e
f
g
h
i2
3
1
4
5
8
6
4
3
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))
i jLj
Li
tij A(i)
BACKWARD PASS EXAMPLE 1 (A-O-A)
1
2 5 6
3 4 7
8a
b
c
d
e
f
g
h
i2
3
1
4
5
8
6
4
3
0
2
3
12
7
16
18
21
ACTIVITY SCHEDULE FROM EVENT TIMES
i jtijEi
Li
Ej
Lj
Early start of activity ij = ES(ij) = EiEarly finish of activity ij= EFij = ES(ij)+ tij
Late finish of activity ij = LF(ij) = LjLate start of activity ij = LS(ij) = LF(ij) -tij
FORWARDPASS
BACKWARDPASS
EARLY & LATE SCHEDULE FOR EXAMPLE 1
Job duration ES EF LS LF TF
a 2 0 2 1 3 1
b 3 0 3 0 3 0
c 1 2 3 11 12 9
d 4 3 7 3 7 0
e 5 7 12 7 12 0
f 8 7 15 10 18 3
g 6 12 18 12 18 0
h 4 12 16 14 18 2
i 3 18 21 18 21 0
GANTT CHART SHOWING ACTIVITY SCHEDULE
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
a
b ^^^^^^
c
d ^^^^^^^^^
e ^^^^^^^^^^^^^
f
g ^^^^^^^^^^^^^^^^
h
i ^^^^^^^^
CRITICAL PATH EXAMPLE 1 (A-O-A)
1
2 5 6
3 4 7
8a
b
c
d
e
f
g
h
i2
3
1
4
5
8
6
4
3
0
2
3
12
7
16
18
21
0
3
3 7 18
21
1812
EVENT SLACKS
i j
Ei
Li
Ej
Lj
Ei Li Ej Lj
tij
Slack on node i = Li - EiSlack on node j = Lj - Ej
ACTIVITY FLOATS
i j
Ei
Li
Ej
Lj
Ei Li Ej Lj
tij
Total float = F1(ij) = Lj-Ei -tijSafety float = F2(ij) = Lj- Li-tij Free float = F3(ij) = Ej -Ei -tij Independent float = F4(ij) = Max (0, Ej -Li- tij)
FLOAT COMPUTATIONS
Ei
Li
Ej
Lj
tij
Total float = LS - ES = LF-EF of activitySafety 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)
FLOATS FOR EXAMPLE 1
Job Total Safety Free Independent
a 1 1 0 0b 0 0 0 0c 9 8 9 8d 0 0 0 0e 0 0 0 0f 3 3 3 3g 0 0 0 0 h 2 2 0 0i 0 0 0 0
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.
activity
Predecessors Successors
FLOAT INTERPRETATION
Free Total
Independent Safety
Early Late
Early
Late
SUCCESSORS
PREDECESSORS
ANOMALIES
ACTIVITY h FLOATSTotal Safety Free
Ind.• 2 2 2 2
• 2 0 2 0
• 2 2 0 0
• 2 0 0 0
5 7
5 7
5 7
5 7
h
h
h
h
4
4
4
4
12 18
12 18
12 18
12 18
12 18
PROJECT MANAGEMENT
Basic Scheduling with
A-O-N Networks
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
i j aactivity, a
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.
EXAMPLE Job Predecessors Duration (days)a -- 2b -- 3c a 1d a, b 4e d 5 f d 8 g c, e 6h c, e 4i f, g, h 3
PROJECT NETWORKEXAMPLE (A-O-N)
a c g
bd e h i
f
2 1 6
34
8
345
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)
i1
i2j
ip
ES/ EFES/EFES/EF
ES/EF
FORWARD PASS FOR EXAMPLE
a c g
bd e h i
f
2 1 6
34
8
345
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
BACKWARD PASSFOR EXAMPLE
a c g
bd e h i
f
2 1 6
34
8
345
0 / 2
0 / 3
2 / 3
3 / 7 7 / 12
12 / 18
12 / 16
7 / 15
18 / 21
EARLY & LATE SCHEDULE FOR EXAMPLE
Job duration ES EF LS LF TF
a 2 0 2 1 3 1
b 3 0 3 0 3 0
c 1 2 3 11 12 9
d 4 3 7 3 7 0
e 5 7 12 7 12 0
f 8 7 15 10 18 3
g 6 12 18 12 18 0
h 4 12 16 14 18 2
i 3 18 21 18 21 0
CRITICAL PATHFOR EXAMPLE
a c g
bd e h i
f
2 1 6
34
8
345
0 / 2
0 / 3
2 / 3
3 / 7 7 / 12
12 / 18
12 / 16
7 / 15
18 / 21
18 /21
10 / 18
14 / 18
12 /1811 / 12
7 / 12 3 / 7
1 / 3
0 / 3
CRITICAL PATH FOR EXAMPLE
a c g
bd e h i
f
2 1 6
34
8
345
GANTT CHART SHOWING ACTIVITY SCHEDULE
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
a *** ]
b ^^^^^^
c ** ]
d ^^^^^^^^^
e ^^^^^^^^^^^^^
f ****************** ]
g ^^^^^^^^^^^^^^^
h ********** ]
i ^^^^^^^^^
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.
activity
Predecessors Successors
FLOAT INTERPRETATION
SUCCESSORS
Early Late
Early Free Total
PREDECESSORS
Late Independent Safety
COMPUTATION OF FLOATS
j
k1
k2
i1
i2 ES/EF
LS/LF
LS/LF
LS/LF
ES/EF
ES/EF
ES/EF
Slack on preceding node= Max (LF of predecessors) -ESSlack on succeeding node = LF- Min (ES of successors) (in the corresponding A-O-A representation)
imLS/LF kn
FLOATS FOR EXAMPLE
Job Total Safety Free Independent
a 1 1 0 0b 0 0 0 0c 9 8 9 8d 0 0 0 0e 0 0 0 0f 3 3 3 3g 0 0 0 0 h 2 2 0 0i 0 0 0 0
FLOAT COMPUTATIONS FOR ACTIVITY a
Total Float = LS - ES = LF - EF =1Safety float = Total Float - [Max (LF of predecessors)-ES] = 1- (0 - 0) = 1Free float = Total Float -[LF -Min(ES of successors)] = 1 - (3-2) = 0Independent float = Total float - both the latter terms = 1 - (0+1) = 0
a c
d
0 / 2
1 / 3
2 / 3
3 / 7
FLOAT COMPUTATIONS FOR ACTIVITY c
Total Float = LS - ES = LF - EF =9Safety float = Total Float - [Max (LF of predecessors)-ES] = 9- (3 -2) = 8Free float = Total Float -[LF -Min(ES of successors)] = 9 - (12-12) = 9Independent float = Total float - both the latter terms = 9 - (1+0) = 8
a c g
h
2 / 3
11 / 12
12 / 18
12 / 161 / 3
FLOAT COMPUTATIONS FOR ACTIVITY f
Total Float = LS - ES = LF - EF =3Safety float = Total Float - [Max (LF of predecessors)-ES] = 3- (7 -7) = 3Free float = Total Float -[LF -Min(ES of successors)] = 3 - (18 - 18) = 3Independent float = Total float - both the latter terms = 3 - (0+0) = 3
d f i7 / 15
10 / 18
18 / 21
3 / 7
Total Float = LS - ES = LF - EF =2Safety float = Total Float - [Max (LF of predecessors)-ES] = 2- (12 - 12) = 2Free float = Total Float -[LF -Min(ES of successors)] = 2 - (18 - 18) = 2Independent float = Total float - both the latter terms = 2 - (0+0) = 2
FLOAT COMPUTATIONS FOR ACTIVITY h
c
e h i12 / 16
14 / 18
18 / 2111 / 12
7 / 12
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
START TO START LAG (SS)
u1
v1
u2
v2
FINISH TO FINISH LAG (FF)
u1
v1
u2
v2
START TO FINISH LAG (SF)
u1
v1
u2
v2
FINISH TO START LAG (FS)
u v
PDM EXAMPLE COMPUTATIONS
A10
E12
F14
G2
C20
B 8
D6
SS 3
FF 2 SS 10
FS 0
SS 2FF 5
FS 0
SF 4
FF 5
FS 4
SS 3
PROJECT MANAGEMENT
Project Scheduling with Probabilistic Activity
Times
UNCERTAIN ACTIVITY DURATIONS
• For each activity in the project three time estimates are obtained–Optimistic time, a
–Most likely time, m
–Pessimistic time, b
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
BETA DISTRIBUTION
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 ]
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.
OTHER POSSIBLE DISTRIBUTIONS
• UNIFORM• TRIANGULAR• EXPONENTIAL• NORMAL• DISCRETE• OTHERS ...
UNIFORM DISTRIBUTION
a b
1/ (b-a)
Mean = (a + b) / 2 Variance = (b - a)2 / 12
TRIANGULAR DISTRIBUTION
a m b
Mean = (a + m + b) / 3Variance = {(b -a)2 + (b - m)2 + (m -a)2}/36 = (a2 + m2 + b2 - am - ab - mb)/18
2/ (b-a)
EXPONENTIAL DISTRIBUTION
f(t) = me -mt
m
Mean = 1/mVariance = 1/m2
NORMAL DISTRIBUTION
Mean = muVariance = sigma 2
mu
N (mu, sigma 2)
DISCRETE DISTRIBUTION
p1
p2
p3
pn
- - -
t1 t2 t3 tn
Mean = p1 t1 + p2 t2 + ... + pn tn
Variance = p1 t12 + p2 t2
2 + pn tn2
- (Mean) 2
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.
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.
AN EXAMPLE
Job Predecessors Time estimates Mean Variance
a m b ------------------------------------------------------------------------------------------A -- 2 4 8 4.33 1
B -- 4 6 10 6.33 1
C A 6 6 6 6.00 0
D A 2 8 14 8.00 4
E A 6 8 12 8.33 1
F B,C 3 6 9 6.00 1
G D,F 8 16 20 15.33 4
H D,F 4 4 4 4.00 0
I E,H 4 8 10 7.66 1
SAMPLE NETWORK (A-O-A)
1
2 5
6
43
A
B C
D
E
F
H
I
G
4.33
6.33
6
6
8
8.33
47.66
15.33
FORWARD & BACKWARD PASS
1
2 5
6
43
A
B C
D
E
F
H
I
G
4.33
6.33
6
6
8
8.33
47.66
15.33
1
2 5
6
43
A
B C
D
E
F
H
I
G
4.33
6.33
6
6
8
8.33
47.66
15.33
CRITICAL PATH
0
4.33 20.33
31.66
16.3310.33
10.33 16.33
31.66
244.33
0
DISTRIBUTION OF THE PROJECT DURATION
• Project duration follows a Normal Distribution withMean = 31.66 Variance = 6 = (2.45)2
-3 -2 -1 0 1 2 3
24.31 31.66 39.01
CONFIDENCE INTERVALS
• Chances that the project is completed within
• mean +/- 1 sigma 68% (29.41 --34.11)
• mean +/- 2 sigma 95% (26.76 -- 36.56)
• mean +/_ 3 sigma 99% (24.31 -- 39.01)
PROBABILITY STATEMENTS - I
• Probability of meeting a Target Date,
say 36 days
• Z (Standard normal deviate) =
(36 - 31.66)/2.45 = 4.34/2.45 = 1.77
• Area from normal tables = 0.9616
PROBABILITYSTATEMENTS - II
• Probability of exceeding a ceiling, say
28 days
• Z (Standard normal deviate) =
(28 - 31.66)/2.45 = -3.66/2.45 = - 1.49
• Area from normal tables = 0.0681
PROBABILITYSTATEMENTS - III
• Probability of duration lying in an interval, say 28 to 36 days
• Area from normal tables =0.9616 - 0.0681
= 0.8935
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.