Supply Chain Management
Module 6: Project Management
Dr. A. Gill 1
Learning Objectives
On completion of this material you should know:
 What is a project, project hierarchy, project life cycle and
work breakdown structure
 PERT
 CPM
 Gantt Chart
 Determine slack & critical path
 Compute project completion probabilities
Dr. A. Gill 2
Standish Report on Projects
Failed
Successful
Challenged
31% projects successful; 51% Challenged; 18% failed
Dr. A. Gill 3
Project Definition
A temporary endeavor undertaken to create a product,
service or facility, in which human, machines, materials
and financial resources are organized to undertake a
unique scope of work, of given specifications, within
constraints of time and cost, to deliver a beneficial
change defined by quantitative and qualitative objectives.
Dr. A. Gill 4
Project Features
 Has a definite start and finish.
 Passes through a life cycle of phases.
 Has a budget with a cash flow.
 Draws resources from different depts.
 Single point of responsibility
 Team roles change or terminate over time.
Dr. A. Gill 5
Project Manager

Project manager is a single point of responsibility who
integrates, coordinates and controls all activities to
complete a project.

Technical vs Generalist Project Manager
Dr. A. Gill 6
Major Projects
 Microsoft Windows Project:
 hundreds of programmers
 millions of lines of code
 millions of dollars cost
 Ford Redesign of Mustang Project:
 450 member project team
 Cost $700-million
 25% faster and 30% cheaper than comparable
projects at Ford
Dr. A. Gill 7
Project Management Software
 CA Super Project
 Harvard Total Manager
 MS Project
 Sure Track Project Manager
 Time Line
Dr. A. Gill 8
Hierarchy for Project Components
Activity
Task
= f(activity)
Project
= f(task)
Program
= f(project)
System
= f(program)
Dr. A. Gill 9
Project Division

Companies sub-divide the projects into smaller units (‘divide
and conquer’ policy) in order to have a better control.

Project life cycle (PLC) and work breakdown structure (WBS)
sub-divide a project into manageable pieces.

WBS is a hierarchical sub-division of scope of work, PLC
sub-divides the scope of work into sequential time phases.
Dr. A. Gill 10
Work Breakdown Structure
Project
Level 1
Level 2
Level 3
Level 4
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Project Life Cycle Phases

Concept and Initiation

Design and Development


Implementation or Construction
Commissioning or Handover
Dr. A. Gill 12
Project Scheduling


CPM: Critical Path Method. Activity times are known &
constant. Developed in 1950’s by DuPont for chemical
plants.
PERT: Project Evaluation and Review Technique. 1950’s US
& British Navy for Polaris missile. PERT was basically given
to handle probabilistic (uncertain) activity times.
Today, computerized programs combine the best features of
both of these two approaches.
Dr. A. Gill 13
 A project manager must know:
 The total time to complete the project?
 Scheduled start/finish time for each activity?
 Which activities are critical and must be completed within
time to keep the project on schedule?
 How long the non-critical activities may be delayed so that
the project is still completed on schedule?
Dr. A. Gill 14
CPM: Precedence Table: Apartment Building Construction
Activity Description
Immediate
Predecessor
Activity
Time
(wks)
A
Prepare drawings
---
5
B
Find new tenants
---
6
C
Develop brochure
A
4
D
Select contractor
A
3
E
Building permit proposal
A
1
F
Approval of building permit
E
4
G
Perform construction
D, F
14
H
Sign contracts with tenants
B, C
12
I
Tenants move in
G, H
2
Total
51
Dr. A. Gill 15
Precedence diagram:
(E) Prepare
permit
(A)
Drawings
Start
(D) Select
contractor
(F) Get
permit
(G)
construction
(C)
Brochure
(B) New
tenants
(I) Move
ins
(H)
Contracts
Finish
Dr. A. Gill 16
Some Definitions
 Path: is a sequence of connected nodes that leading from
start node to finish node. (e.g. A-E-F-G-I).
 All paths in a network must be completed to finish the
project. Therefore, the path with longest time will
determine the project completion time as other paths will
take less time.
 Critical Path: The path that takes longest time is called
critical path. If activities on the longest path are delayed,
the entire project is delayed.
 Critical Activities: Activities lying on critical (longest)
path are called critical activities.
Dr. A. Gill 17
Finding Project Completion Time:
 To find the project completion time, we need to find the
critical path and its completion time,
 To find the critical path, we need to find the earliest start
time, earliest finish time, latest start time and latest
finish time of each activity on the network.
Dr. A. Gill 18
 Earliest Start Time (ES):
Earliest time an activity may begin.
 ES = Max { earliest finish times (EF’s) of predecessors}
 Earliest Finish Time (EF):
Earliest time an activity may be completed.
 EF = ES + t, where t is the activity duration time.
 Forward Pass:
The process of finding first ES, then EF going from start
node to finish node is called forward pass.
Dr. A. Gill 19
 Latest Finish Time (LF):
Latest time an activity may be completed without increasing the
project completion time.
 LF = Min { latest start times (LS’s) of following activities
 Latest Start Time (LS):
Latest time an activity may begin without increasing the project
completion time.
 LS = LF - t, where t is the activity duration time.
 Backward Pass:
The process of finding first LF, then LS going from final node to
start node is called backward pass.
Dr. A. Gill 20
Forward Pass:
For each node, first find ES, then find EF
First find ES=Max {EF of previous nodes}
ES of first node = 0
Then find
EF=ES+ t
Backward Pass:
For each node, first find LF, then find LS
First find LF=Min {LS of following nodes}
LF of last node = EF
Then find
LS=LF- t
Node labels:
Node
ES
EF
A
0
5
time
LS
LF
5
0
5
Dr. A. Gill 21
Forward pass
E
5
6
F
1
A
0
5
5
8
G
3
10
24
14
C
Start
10
4
D
5
6
5
9
I
4
26
2
H
B
24
0
6
12
9
21
Finish
6
Project network diagram
Dr. A. Gill 22
Backward pass
E
5
6
F
6
10
1
5
6
4
6
10
G
10
24
14
10
24
A
0
5
D
5
8
5
0
5
3
7
10
C
5
9
4
8
12
Start
B
0
6
6
6
12
H
9
21
12
12
24
I
24
26
2
24
26
Finish
Project network diagram
Dr. A. Gill 23
 Slack or Float:
Length of time an activity may be delayed without delaying
the project.
 Slack = LS-ES = LF - EF for an activity.
 Critical Activities:
Activities with zero slack, if delayed will delay the entire
project and are therefore called critical activities.
 Critical Path:
A path connecting critical activities is critical path.
Dr. A. Gill 24
S=0
S=0
S=0
E
5
6
F
6
10
1
5
6
4
6
10
G
10
24
14
10
24
A
0
5
D
5
8
5
0
5
3
7
10
C
Start
5
4
S=2
S=0
9
8
12
B
0
6
6
6
12
S=0
S=3
H
9
21
12
12
24
I
24
26
2
24
26
Finish
S=3
S=6
Project network diagram
Dr. A. Gill 25
 A project manager must know:
 Question 1. How long the project takes to complete?
EF, LF of I = 26 weeks
 Question 2. What are schedules start and finish times for
each activity? ES, EF, LS, LF
 Question 3. Which activities are critical and must be
completed on schedule? A, E, F, G, I
 Question 4. How long the non-critical activities may be
delayed so that the project is not delayed? slacks.
Dr. A. Gill 26
Gantt Charts
Prepare a Gantt chart for the apartment construction
example we solved in the class.
Dr. A. Gill 27
Project Scheduling (Uncertain activity times)
For common projects (e.g. construction industry), managers can
provide accurate data from experience. But for new projects,
activity times are uncertain, but they can be described by an
optimistic time, most probable time and a pessimistic time.
 Optimistic time,
a = Minimum activity time if everything
progresses ideally (optimally).
 Most
probable time, m = Most probable guess of activity
time under normal conditions.
 Pessimistic
time, b = Max activity time if delays are
encountered.
Dr. A. Gill 28
Precedence Table: R&D project for cordless vacuum cleaners
Activity Description
Immediate
Predecessor
A
Product design
---
B
Plan market research
---
C
Routing sheet
A
D
Prototype model
A
E
Marketing brochure
A
F
Cost estimates
C
G
Product testing
D
H
Do market survey
I
Forecast report
J
Final report
B, E
H
F, G, I
Dr. A. Gill 29
Time Estimates
Activity Optimistic Most Probable Pessimistic
(a)
(m)
(b)
A
4
5
12
B
1
1.5
5
C
2
3
4
D
3
4
11
E
2
3
4
F
1.5
2
2.5
G
1.5
3
4.5
H
2.5
3.5
7.5
I
1.5
2
2.5
J
1
2
3
Dr. A. Gill 30
 With three estimates i.e. optimistic, most probabilistic and
pessimistic times, the activity times follow a beta
distribution, which looks like a positively skewed normal
distribution. We use expected value of this distribution as
activity time for calculations.
a  4m  b
t exp 
6
0
a
m
texp
b
Activity time in weeks
Dr. A. Gill 31
 Since texp is just an expected time (not exact time), we
need to consider its dispersion or variation around
2
expected value.
2
ba
variance 
Activity
texp
variance
A
6
1.78
B
2
0.44
C
3
0.11
D
5
1.78
E
3
0.11
F
2
0.03
G
3
0.25
H
4
0.69
I
2
0.03
J
2
0.11


6


Dr. A. Gill 32
S=4
S=0
A
0
6
6
0
6
Start
Finish
S=4
C
6
9
F
9
11
3
10
13
2
13
15
S=1
S=0
S=1
J
15
17
2
15
17
D
6
11
G
11
14
5
7
12
3
12
15
E
6
9
H
9
13
I
13
15
3
6
9
4
9
13
2
13
15
S=0
S=0
B
0
2
2
7
9
S=0
S=7
Project network diagram
Dr. A. Gill 33
 The critical path is A→E→H→I→J . The project can be
completed with an expected time of 17 weeks i.e.
E(T)= tA + tE + tH + tI + tJ = 17 weeks
 Small variation in non-critical activities times may not affect
project completion time as the available slack (allowed
delay) will absorb this variation.
 Small variation in critical activities times is likely to affect
project completion time as shown in following diagram:
Start
A
6
E
H
3
4
I
Finish
J
2
2
Dr. A. Gill 34
 Numbers used for activity times are expected numbers.
 To find that probability, we need variance of the project
completion time, which is sum of variances of critical
activities:
 T   A  E  H  I  J
2
2
Standard Deviation,
2
T
2

2
T 2 
2
 2.72
2.72
 1.65
Dr. A. Gill 35
Completion time distribution
 = 1.65
t or m =17
exp
Dr. A. Gill 36
What is the probability that project will be finished within 20
weeks i.e. P(X ≤ 20)?
 = 1.65
Step 1: Find Z-score for X=20,
z = (x-m)/ = 1.82
P(x ≤ 20)
m =17
z=0
20
z=1.82
Dr. A. Gill 37
Step 2: Find area to the left of z=1.82 from normal
distribution tables. Area=0.9656
 = 1.65
Normal Probability Table (Portion)
Z
.00
.01
.02
0.0 .5000 .5040 .50798
:
:
:
:
P(x ≤ 20)
1.8 .9641 .9649 .9656
1.9 .9713 .9719 .9726
m =17
z=0
20
z=1.82
There are 96.56% chances that the project will be
completed in 20 weeks or less.
=NORM.S.DIST(1.82,1)
Dr. A. Gill 38
Exercise:
(1) What is the probability that the project will take more
than 20 weeks to complete.
(2) What is the probability that the project will take less
than 14 weeks to complete.
(3) What is the probability that the project will be
completed between week # 14 and week# 20?
(4) The project manager has to quote a completion date to
the client. He wants to be 98% sure that he can complete
the project before this date. What date he should quote?
Dr. A. Gill 39