# Project Management ```MD 021 - Management and Operations
Managing Project Processes
Outline

Definition of a project

Network methods using deterministic estimates

Probabilistic estimates

Cost considerations
1
Definition of a project
A project is an interrelated set of activities that has a definite starting and
ending point and results in unique product or service.
Examples of projects include building construction, introducing a new product,
and redesigning the layout of a plant or office.
2
PERT and CPM Network Methods
Definitions
Activity - The smallest unit of work effort consuming both time and resources
that the project manager can schedule and control
Precedence relationship - 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 Using Network Models
First two steps:
Describe the project
a) Define project activities.
b) Determine precedence relationships.
Diagram the network
a) Nodes (circles) and arcs (arrows)
b) Activity-on-node (AON) network
 Nodes are activities and arcs show precedence relationships
 Activity-oriented
4
Project Management Example
Immediate
Activit
Description
Predecessor(s
y
)
A
--B
Select site and do site survey.
--C
Select equipment.
A
D
Prepare final construction plans and layout.
B
E
Bring utilities to the site.
B
F
Interview applicants and fill positions in nursing,
A
support staff, maintenance, and security.
G
Purchase and take delivery of equipment.
C
H
Construct the hospital.
D
I
Develop an information system.
A
J
Install the equipment.
E, G, H
K
Train nurses and support staff.
F, I, J
5
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]
6
Calculating Time Estimates
a) Optimistic time (a):
Shortest time during which an activity can be
completed.
b) Most likely time (m):
Best estimate of average time.
c) Pessimistic time (b):
Longest time an activity can take.
d) Activity’s time ( te ) and variance ( 2 ) with beta
distribution
te 
a  4m  b
6
2  (
ba 2
)
6
7
Calculating Probabilistic Estimates
Activity
Optimistic
( to )
A
B
C
D
E
F
G
H
I
J
K
11
7
5
8
14
6
25
36
10
1
5
Time estimates (weeks)
Most likely Pessimistic
(tm )
(t p )
12
8
10
9
25
9
36
40
13
2
6
13
15
15
16
30
18
41
45
28
15
7
8
Expected
time ( t e )
Variance
( 2 )
10
10
24
10
35
40
15
4
6
2.78
1.78
7.11
4.00
7.11
2.78
9.00
5.44
0.11
Analyzing Probabilities
Probabilities can be assessed using the z-transformation formula:
Z 
T  TE

T = specific time, TE = expected time (path mean),
 = standard deviation of path mean. Assuming the activity times are
independent, the path standard deviation
activity time variances.

is the square root of the sum of the
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.
9
Hospital Project Completion Probabilities
How likely is it that the hospital project will be completed in 72 weeks?
Path
A-F-K
A-I-K
A-C-G-J-K
B-D-H-J-K
B-E-J-K
z
72  Expected path duration
Path standard deviation
(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
10
Probability of
completion in 72 weeks
100%
100%
90%
81%
100%
Analyzing Costs in a Project
1. Direct costs and times
 normal time
 normal cost
 crash time
 crash cost
2. Cost assumptions: linear costs per unit of time
3. Indirect costs and penalty costs
11
Determining the Minimum-Cost Schedule
Step 1: Determine the project’s critical path(s).
Step 2: Find the cheapest activity or activities on the
critical path(s) to crash.
Step 3: 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.
12
Activit
y
A
B
C
D
E
F
G
H
I
J
K
Direct Cost and Time Data for the Hospital Project
Normal Normal Crash
Crash Max. time
Cost of
time
cost
time
cost
reduction crashing per
(wks)
(\$K)
(wks)
(\$K)
(wks)
week
12
9
10
10
24
10
35
40
15
4
6
Totals
\$12
50
4
16
120
10
500
1,200
40
10
30
\$1,992
11
7
5
8
14
6
25
35
10
1
5
13
64
7
20
200
16
530
1,260
52.5
13
34
\$2,209.5
13
1
2
5
2
10
4
10
5
5
3
1
\$1,000
7,000
600
2,000
8,000
1,500
3,000
12,000
2,500
1,000
4,000
Hospital Project Minimum-Cost Schedule
Assume:
Indirect cost = \$8,000/week
Penalty cost = \$20,000/week after Week 65
Critical path
B-D-H-J-K
Crash
activity
Project
duration
Crash cost
69 weeks
14
Indirect
cost change
Penalty
cost change
Total
cost change
```