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.