Project Management
MD707 Operations Management
Professor Joy Field
Definition of a Project

A project is an interrelated set of activities that has a
definite starting and ending point within a limited time
frame and results in a unique product or service.

Examples of projects include building construction,
introducing a new product, and software development.
2
Some Terminology …

Activity


Precedence relationship


The smallest unit of work effort consuming both time and
resources that the project manager can schedule and control
A sequencing constraint between interrelated activities by which
one activity cannot start until a preceding activity has been
completed
Schedule

A plan that sets priorities, determines start and finish times, and
allocates resources to accomplish the activities
3
Project Management Approaches
Predictive
(e.g. CPM, waterfall, stage
gate)
Adaptive
(e.g. agile)
Activities
Low uncertainty
High uncertainty
Precedence
relationships
Low uncertainty
High uncertainty
Activity duration
Low or high uncertainty
High uncertainty
4
Project Management Using Network Models
First two steps:

Describe the project



Define project activities
Determine precedence relationships
Diagram the network


Nodes (circles) and arcs (arrows)
Activity-on-node (AON) network - Nodes are activities and arcs
show precedence relationships
5
Project Management Example
St. John’s Hospital
Activity
A
B
C
D
E
F
G
H
I
J
K
Immediate
Predecessor(s)
Select administrative and medical staff.
--Select site and do site survey.
--Select equipment.
A
Prepare final construction plans and layout.
B
Bring utilities to the site.
B
Interview applicants and fill positions in nursing,
A
support staff, maintenance, and security.
Purchase and take delivery of equipment.
C
Construct the hospital.
D
Develop an information system.
A
Install the equipment.
E, G, H
Train nurses and support staff.
F, I, J
Description
6
AON Network for St. John’s Hospital Project
I
A
Start
B
F
K
C
G
D
H
Finish
J
E
7
Determining the Critical Path
Activity
A
B
C
D
E
F
G
H
I
J
K
Time (weeks)
12
9
10
10
24
10
35
40
15
4
6
Path
Length (weeks)
A-F-K
28
A-I-K
33
A-C-G-J-K
67
B-D-H-J-K
69*
B-E-J-K
43
*critical path = longest path through the network
8
Network Time Calculations

Earliest finish time (EF) for an activity
 EF = ES + t

Earliest start time (ES) for an activity
 ES = Max [EF times of all immediately preceding activities]

Latest start time (LS) for an activity
 LS = LF – t

Latest finish time (LF) for an activity
 LF = Min[LS times for all immediately following activities]
9
Calculating Activity Slacks
Activity slack: LS-ES or LF-EF, Critical path in bold
Activity
A
B
C
D
E
F
G
H
I
J
K
LF
14
9
24
19
59
63
59
59
63
63
69
EF
12
9
22
19
33
22
57
59
27
63
69
Slack
2
0
2
0
26
41
2
0
36
0
0
10
Calculating Time Estimates

Optimistic time (t o)


Most likely time (t m )


Best estimate of average time
Pessimistic time ( t p )


Shortest time during which an activity can be completed
Longest time an activity can take
Activity’s expected time (t e) and variance (  2 ) with beta
distribution
te 
t o  4t m  t p
6
2  (
t p  to
6
)2 
(t p  t o ) 2
36
11
Calculating Probabilistic Estimates
St. John’s Hospital Example
Activity
A
Time estimates (weeks)
Optimistic Most likely Pessimistic
( )
( )
( )
11
12
13
Expected
time ( )
Variance
( )
B
7
8
15
C
5
10
15
10
2.78
D
8
9
16
10
1.78
E
14
25
30
24
7.11
F
6
9
18
10
4.00
G
25
36
41
35
7.11
H
36
40
45
40
2.78
I
10
13
28
15
9.00
J
1
2
15
4
5.44
K
5
6
7
6
0.11
12
Analyzing Probabilities

Probabilities can be assessed using the z-transformation
formula
Specified time - Path mean
z
Path standard deviation

Assuming the activity times are independent, the path standard
deviation is the square root of the sum of the activity time variances.
To determine the probability of completing a project in a
specified amount of time



Calculate the probability of each of the paths being completed in that
amount of time based on the value of z. For any value of z that is
greater than 3, the probability that the corresponding path will be
completed in that amount of time can be considered to be 100%.
If all paths are independent, then the probability of completing a project
in the specified amount of time is the product of the individual path
probabilities.
13
Hospital Project Completion Time Probabilities
How likely is it that the hospital project will be completed in 72
weeks?
Probability of
completion in 72 weeks
Path
A-F-K
A-I-K
A-C-G-J-K
B-D-H-J-K
B-E-J-K
(72 – 28)/2.05 = 21.5
(72 – 33)/3.04 = 12.8
(72 – 67)/3.94 = 1.27
(72 – 69)/3.45 = 0.87
(72 – 43)/3.80 = 7.6
100%
100%
90%
81%
100%
14
Analyzing Costs in a Project

Direct costs and time





Cost assumptions


Normal time
Normal cost
Crash time
Crash cost
Linear costs per unit of time (The problems in your textbook do
not necessarily make this assumption.)
Indirect costs and penalty costs
15
Determining the Minimum-Cost Schedule

Step 1


Step 2


Find the least expensive activity or activities on the critical path(s) to
crash.
Step 3


Determine the project’s critical path(s).
Reduce the time for this activity until the first of (a) it cannot be further
reduced, (b) another path becomes critical, or (c) the increase in direct
costs exceeds the savings that result from shortening the project. If more
than one path is critical, the time for an activity on each path may have
to be reduced simultaneously.
Step 4

Repeat this procedure until the increase in direct costs is less than the
savings generated by shortening the project.
16
Direct Cost and Time Data for Hospital Project
Activity
A
B
C
D
E
F
G
H
I
J
K
Normal
time
(wks)
12
9
10
10
24
10
35
40
15
4
6
Totals
Normal
cost
($K)
$12
50
4
16
120
10
500
1,200
40
10
30
$1,992
Crash
time
(wks)
11
7
5
8
14
6
25
35
10
1
5
Crash Max. time Cost of
cost
reduction crashing
($K)
(wks)
per week
$13
1
$1,000
64
2
7,000
7
5
600
20
2
2,000
200
10
8,000
16
4
1,500
530
10
3,000
1,260
5
12,000
52.5
5
2,500
13
3
1,000
34
1
4,000
$2,209.5
17
Hospital Project Minimum-Cost Schedule
Assume:
Indirect cost = $8,000/week, Penalty cost = $20,000 per week after Week 65
Critical
path
B-D-H-J-K
Crash
activity
Project
duration
Crash cost
Indirect
cost
change
Penalty
cost
change
Total
cost
change
69 weeks
18