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CHAPTER 8: PROJECT MANAGEMENT

The aim is to coordinate and plan a single job consisting lots of tasks between which precedence relationships exist

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Project planning

� Most popular planning tools are utilized in project management

� GANTT chart

� CPM (critical path method)

� PERT (program evaluation and review technique)

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Project planning network

� The project consists of well-defined activities or tasks

� The activities have precedence relationships and must be performed in the proper order

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Network drawing characteristics

A circle represents a node.

An arrow represents an activity.

A dashed arrow represents a dummy activity.

� Arrows, or activities leaving a node, cannot be started until all activities incoming the node have been completed

� The completion of all activities incoming to a node is considered an event

� The length of an arrow has no significance� A dummy activities are used to represent precedence

relationshiphs

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Example 9.1 (project of installing a precision rain gauge/wind sensor station)

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Network drawing of example 9.1

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Critical Path Method

� CPM offers a systematic procedure for

selecting the critical path through the network

� The amount of slack or free time on noncritical paths may be determined

� Knowing the slack on noncritical paths may

permit us to trade off manpower and equipment resources from noncritical activities in order to shorten the critical path

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CPM – forward and backward pass

Notationt = activity duration

TE = earliest event occurence time

TL = latest allowable event occurence time

ES = earliest activity start time

EF =earliest activity finish time

LS = latest allowable activity start time

LF = latest allowable activity finish time

S = total activity slack

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Forward pass

� The forward pass provide the following information:

� The earliest event time (TE)

� The earliest activity start time (ES)

� The earliest activity finish time (EF)

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Forward pass calculations

� The forward pass calculations start with the first activity (or activities)

� TE0 = 0 (initial event occurence time is 0)

� Each activity begins as soon as its predecessor event (node) occurs, that is TE = ES, thus EF = ES + t = TE +t

� The earliest event (node) occurence time is the largest of the earliest finish times of the incoming acivities, TE = max{EF1,EF2,...,EFn}

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Backward pass

� The backward pass provide the following information:

� The latest allowable event time (TL)

� The latest allowable activity start time (LS)

� The latest allowable activity finish time (LF)

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Backward pass calculations

� The backward pass calculations start with the last node

� The latest allowable event time of the terminal (last) node is set to the earliest event time , TE = TL

� The latest allowable finish time for an activity is its successor event’s latest allowable occurence time, LF = TL, thus LS = LF – t = TL – t

� The latest allowable time for an event is the smallest of the latest allowable start times of the leaving activities, TL = min{LS1,LS2,...,LSn}

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Example 9.2

a)Determine the critical pathb)What is the total slack time of the activity D?

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Solution (forward pass)

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Solution (backward pass)

Critical path is defined as the sequence of the activities having no slack

time (ES = LS and EF = LF) and TE = TL for each node

Critical path is as follows:

Activities C and GorNodes 1, 4 and 7

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Solution (slack time)

Total activity slack time = Latest finish – Earliest finish

SD = LF – EF = 35 – 26 = 9 days

Delaying the start of activity D up to 9 days does not change the completion of the project

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Program Evaluation and Review Technique

� PERT utilizes a project network, a critical path and total slack time

� PERT requires three estimated activity times:

� Optimistic time (a minimum time)

� Most likely time (an average time)

� Pessimistic time (a maximum time)

� PERT is used in managing projects involving uncertainty in the durations

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Notation and formulations

to = optimistic time

tm = most likely time

tp = pessimistic time

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4 pmo

e

tttt

++= te = expected time ,

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op

t

ttS

−= St = standard deviation of t,

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6

−=

op

t

ttV Vt = variance of t,

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Example for time distribution

to = 7 days

tm = 9 days

tp = 13 days

33.96

13)9(47

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4=

++=

++=

pmo

e

tttt

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713

6

22

=

−=

−=

op

t

ttV

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Parameters for a selected path

∑=

paththealongactivitiesall

ee tT , Te = expected time of the path

∑=

paththealongactivitiesall

tT VV , VT = total variation of the path

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Standard normal distribution

σ

µ−=

xz

µ = expected value of the distribution

σ = standard deviation

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Example 9.3

� Example 9.2 is copied for precedence relationships between tasks

� Tasks durations are presented in the form of PERT

� Your objective is to find out the probability of accomplishing the project within 47 days

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Task durations

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Critical path

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Parameters of critical path

431033,

=+==∑GC

ee tT

778.18778.2000.16,

=+==∑GC

tT VV

333.4778.18 ==TS

ST = standard deviation along the path

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Probability of Te

≤≤≤≤ 47

923.0333.4

4347=

−=

−=

−=

T

e

S

Txxz

σ

µ

F(z) = F(0.923) = 0.8212 (from table)