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OPERATIONS RESEARCH
CHAPTER VIII
CPM-PERTInstructor : Lect.Volkan ÇETİNKAYA
PROJECT
“A project is a series of activities directed to accomplishment of a desired
objective.”
Plan your work first…...then work your plan!
INTRODUCTION
PERT: (Project Evaluation and Review
Technique
CPM: (Critical Path Method)
CPM-PERT APPLICATION FIELDS
Building, Airport, Roadway and similar
construction projects.
Loading of new computer systems.
Design of new products.
Ship Constructing
QUESTIONS TO BE REPLIED VIA CPM-PERT 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?
INTRODUCTION 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.
DIFFERENCE BTW. PERT and CPM
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.
CPM-PERT FARKI
DIFFERENCE BTW. PERT and CPM
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.
GANNT CHART
Advantages
- Gantt charts are quite commonly
used. They provide an easy
graphical representation of when
activities (might) take place.
Limitations
- Do not clearly indicate details regarding the progress of activities
- Do not give a clear indication of interrelation ship between the separate activities
USE OF NODES AND ARROWS
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.
COMMON STEPS for CPM&PERT 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.
EXAMPLE-1 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
F: Assembly C,E 15
EXAMPLE-2
FINDING CRITICAL PATH
□j = Earliest occurence time of event ‘j’
∆j = Latest occurence time of event ‘j’
Dij = Duration of activity
FINDING CRITICAL PATH 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.
FINDING CRITICAL PATH An activity(i,j) will be critical if it satisfies these 3 conditions.
□i = ∆i
□j = ∆j
∆j - ∆i = □j - □i = Dij
EXAMPLE-3
CONSTRUCTION of TIME SCHEDULE Time Schedule for Example 3
EXAMPLE-4 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
F: Assembly C,E 15
PERT 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
PERT Average Completion Time = (O + 4M + P) /6
Standart Deviation = (P-O)/6
Variance = (
EXAMPLE-5 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?
EXAMPLE-6 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 Name TR Processedor O M PA Permissions İzinler - 2 3 4B Budget Preperation Bütçe Hazırlık - 2 2 2C Draft Draft A,B 2 3 7D Constructing Kaba İnşaat C 5 7 9E Outer Installation Dış Tesisat D 3 4 11F Electrical Works Elektrik İşleri D 3 5 10G Inner Installation İç Tesisat E 5 6 10H Outer Painting Dış Boya G 2 3 4I Inner Painting İç Boya F,H 4 5 6J Other Diğer İşler H 2 3 4K Submittal Teslim I,J 2 3 4