Project Management with PERT & CPM Lecture 1
Transcript of Project Management with PERT & CPM Lecture 1
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
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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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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 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.
CE4101 17o Optimistic Most likely Pessimistic
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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19
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%