CHAPTER VIII
CPM-PERT
Instructor : Lect.Volkan ÇETİNKAYA
“A project is a series of activities directed
to accomplishment of a desired
objective.”
Plan your work first…...then
work your plan!
 PERT: (Project Evaluation and Review
Technique
 CPM: (Critical Path Method)
 Building, Airport, Roadway and similar
construction projects.
 Loading of new computer systems.
 Design of new products.
 Ship Constructing
 When will the project finish?
 Which critical activities are there?And not?
 What’s the probability of finishing the project in a definite
term?
 Where is the project?Going on accurately?
 Is the project under or below the budget?
 Are there adequate resources for the completion of project?
 If it is planned to complete the project before planned time,
How can it be done by least cost?
 CPM: For certain activities , it may be possible to
decrease their completion times by spending more
money.How does this affect the overall completion
time of the project.
 PERT: It has probability, It is for a particular activity
the most likely completion time is 4 weeks but it
could be anywhere between 3 weeks and 8 weeks.
 CPM: In CPM activities are shown as a network of
precedence relationships using activity-on-node network
construction.
 Single estimate of activity time
 Deterministic activity times
 Used in Production management-for the jobs of repetitive in
nature where the activity time estimates can be predicted
with considerable certainty due to existance of past
experience
 CPM’de faaliyetlerin süreleri kesin olarak
bilinmektedir.
 PERT’te faaliyetlerin süre ve maliyetleri kesin
olarak bilinmemekte, bu veriler rassal
değişkenler olarak atanmaktadır. Dolayısıyla
elde edilen kritik yol bir “olasılık kritik yolu”dur.
 PERT: In PERT activities are shown as a network of
precedence relationships using activity-on-arrow
network construction.
 Multiple estimate of activity time
 Probabalistic activity times
 Used in Project Management-for non-repetitive
jobs(research and development works) where the time
and cost estimates tend to be quite uncertain.
Advantages
Limitations
- Gantt charts are quite commonly
- Do not clearly indicate details
regarding the progress of activities
used. They provide an easy graphical
representation of when activities
(might) take place.
- Do not give a clear indication of
interrelation ship between the
separate activities
 Arrows: An arrow leads from tail to head directionally.It
indicates ACTIVITY, a time consuming effort that is
required to perform a part of the work.
 Nodes: A node is represented by a circle. It indicates
EVENT, a point in time where one or more activities start
and/or finish.
 Describe the project and important activities.
 Describe the relationships among facilities.
 Draw the project network.
 Determine time and cost of all activities.
 Compute the longest way(critical path) of the network.
 Use the network to plan, to schedule follow and control
the project.
 A new founded company wants to design a product.
Below the activities , priority relationships and
activity durations were given. Draw the project
network.
Activity
Predecessor
Duration
A: Construction of production lines
-
8
B:Purchasing
-
11
C: Production of semi finished product-1
A
10
D: Production of semi finished product-2
B
7
E: testing of semi finished product-2
D
13
C,E
15
F: Assembly
 □j = Earliest occurence time of event ‘j’
 ∆j = Latest occurence time of event ‘j’
 Dij = Duration of activity
 Forward Pass: (Earliest Occurence Times) The computations
start at node 1 and advance recursively to end node n .
 Backward Pass : (Latest Occurence Times) Following the
completion of the forward pass , the backward pass
computations starts at node n and end at node 1.
 An activity(i,j) will be critical if it satisfies these 3 conditions.
 □i = ∆i
 □j = ∆j
 ∆j - ∆i = □j - □i = Dij
 Time Schedule for Example 3
 Draw the project network
 Compute the critical path according to the data below
Activity
Predecessor
Duration
A: Construction of production lines
-
8
B:Purchasing
-
11
C: Production of semi finished product-1
A
10
D: Production of semi finished product-2
B
7
E: testing of semi finished product-2
D
13
C,E
15
F: Assembly
 PERT: Project Evaluation and Review Technique. Like CPM,
but ist is a probabilistic model.
 In PERT, activities fall in to 3 categories:
 O : Optimistic
 P : Pessimistic
 M : Medium
 Average Completion Time = (O + 4M + P) /6
 Standart Deviation = (P-O)/6
 Variance = ( (P−O)/6 ))2
 Let’s look at a project with 8 events and 11 activities.

QUESTIONS:




Draw the network of the project.
Compute expected time and variance of each activity.
Find critical path.
Compute the standart deviation of dispersion proving expected time of
project.
 What is the probability of completion of the project in 19 days or less than
19 days?

Draw the network of the ship construction project.

Compute expected time and variance of each activity.

Find critical path.

Compute the standart deviation of dispersion proving expected time of project.

What is the probability of project completion in 36 weeks?
Activity
A
B
C
D
E
F
G
H
I
J
K
Name
Permissions
Budget Preperation
Draft
Constructing
Outer Installation
Electrical Works
Inner Installation
Outer Painting
Inner Painting
Other
Submittal
TR
İzinler
Bütçe Hazırlık
Draft
Kaba İnşaat
Dış Tesisat
Elektrik İşleri
İç Tesisat
Dış Boya
İç Boya
Diğer İşler
Teslim
Processedor
A,B
C
D
D
E
G
F,H
H
I,J
O
2
2
2
5
3
3
5
2
4
2
2
M
3
2
3
7
4
5
6
3
5
3
3
P
4
2
7
9
11
10
10
4
6
4
4