CE 4101

Project Planning and Construction Management

Credit 3.0

Md KhalekuzzamanBSc(Civil Eng.), MASc(Env.Eng.), P.Eng. (Canada), FIEB

Assistant Professor

Department of Civil Engineering

PERT –Program Evaluation And Review Technique

CPM –Critical Path Method

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References:

1. Introduction to Operations Research

By Frederick S Hillier and Gerald J. Lieberman (Chapter 10)

2. Project Management for Engineering & Construction By

G.D. Oberlender (2nd Ed.)

3. Operations Research: An Introduction Eighth EditionBy

Hamdy A. Taha

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Definition:

• Activity

• Network

• Duration

• Early Start (ES)

• Early Finish (EF): ES+D

• Late Finish (LF):

• Late Start (LS): LF- D

• Total Float (TF): LE- EF = LS – ES

• Free Float (FF) : FFi = ESj – EFi

• Critical Path: TF & FF = 0

• Dummy Activity

Page 145 of G.D. Oberlender (2nd Ed)

“PM for Engineering & Construction”

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Definition:

• Activity on Node (AON): is a project network, where each activity is

represented by a node.

• Activity on Arc (AOA): is a project network, where each activity is

represented by an arc.

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Example – The Reliable Construction CO. Project

(10.1 from Hillier & Lieberman):

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Example – The Reliable

Construction CO. Project

(10.1 from Hillier & Lieberman):

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Problem:

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Problem:

Start End

1

4

5

6

3

2

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Problem:

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Problem:

Start

EndA

C

D G

E

B

F

H

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The Critical Path:(Table 10.2

From Hillier & Lieberman):

Critical path:

START → A→B → C → E → F → J → L → N → FINISH

(Estimated) project duration = 44 weeks.

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G E

H

ES=2

EF=29

ES=16

EF=22

ES=29

64

D

E

C

LS=20

LF=26

LS=16

LF=20

LF=16

ILS=18

LF=25

7

7

4

9

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Example – The Reliable

Construction CO. Project

(10.7 from Hillier & Lieberman):

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Example 6.5-2

Pg-270/Taha

Determine the critical path for the project network. All the

durations are in days.

activity (4,6) satisfies the first two conditions for a

critical activity (∆4=□4=13 & ∆6=□6=25) but not the

third(□6-□4≠D46). Hence, the activity is noncritical.

PERT Network:

• PERT differs from CPM in that it bases the duration of an activity on three

estimates:

1. Most likely estimate (tm or m)

= estimate of the most likely value of the duration

2. Optimistic estimate (t0 or a or 0)

= estimate of the duration under the most favorable conditions.

3. Pessimistic estimate (tp or p or b)

= estimate of the duration under the most unfavorable

conditions.

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Figure: Time Distribution Curve

PERT Calculation Procedure:

• PERT Procedure:

1. Draw the project network.

2. Expected duration of each activity, µ or 𝑡𝑒 =𝑡𝑜+4𝑡𝑚+𝑡𝑝

6

3. Standard normal deviation, 𝑧 =𝑇𝑠−𝑇𝑒

𝜎𝑐where, 𝜎𝑐

2 =𝑡𝑝−𝑡𝑜

6

2

σc = Variance

Ts = Specified or scheduled time to complete the project

Te = Duration of the project.

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Calculation of µp(te)

and σ2 for Critical

Path

µp(te) = 2+4+10+4+5+8+5+6=44

σ2 =1/9+1+4+4/9+1+1+1+4/9 =9

Activity on

Critical Path

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PERT Calculation Procedure (cont.):

Approximating the probability of Meeting the deadline (Ts=47 as mentioned at

the beginning of the Problem)

𝑧 =𝑇𝑠−𝑇𝑒

𝜎𝑐=

47−44

√9= 3

3= 1

P ( T ≤ d) = P ( Standard normal ≤ z)

≈0.8413

≈ 84%

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