L26_Project Scheduling - CPM

7/25/2019 L26_Project Scheduling - CPM

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CPM and PERT


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CPM and PERT

CPM (Critical Path Method) and PERT(Program Evaluation and Review Technique)

are network based methods designed to assist

in the planning, scheduling, and control opro!ects" # pro!ect is a collection o

interrelated activities with each activit$

consuming time and resources" The ob!ectiveo CPM and PERT is to provide anal$tic

means or scheduling the activities"


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The two techniques, CPM and PERT which

were developed independentl$, dier in

that CPM assumes deterministic activit$

durations, whereas PERT assumes

probabilistic durations"

%irst we discuss CPM and then provide the

details o PERT"


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Network Representation

Each activit$ o the pro!ect is represented

b$ an arc pointing in the direction o

progress in the pro!ect" The nodes o the

network establish the precedence

relationships among the dierent activities

o the pro!ect"


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Two rules are available or constructing the

network&

Rule 1:Each activit$ is represented b$ one,

and onl$ one arc"

Rule 2:Each activit$ must be identiied b$two distinct end nodes"

2 A

#ctivit$ # has two end nodes&

' start node, * end node

1


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Use of dummy activity:

To establish correct precedence relationships,

dumm$ activities are used" # dumm$ activit$,

which is normall$ depicted b$ a dashed arc,consumes no time or resources" %or e+ample,

i two activities that can start concurrentl$

and have the same duration can berepresented using a dumm$ activit$ as&


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1

2

3

1

2

3

r also as

A

B

A

BDummy

Dummy


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Rule 3: To maintain the correct precedence

relationships, the ollowing questions must be

answered as each activit$ is added to thenetwork&

(a) -hat activities must immediatel$ precedethe current activit$.

(b) -hat activities must ollow the current

activit$.

(c) -hat activities must occur concurrentl$

with the current activit$.


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The answers to these questions ma$ require

the use o dumm$ activities to ensurecorrect precedence among the activities"


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Problem 1 problem set 66A pa!e 26"

'"Construct the pro!ect network consisting oactivities # to / with the ollowing

precedence relationships&

(a) #, 0 and C, the irst activities o the

pro!ect, can be e+ecuted concurrentl$"

(b) # and 0 precede 1"

(c) 0 precedes E, % and 2"


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(d) % and C precede 3"

(e) E and 2 precede 4 and 5"

() C, 1, % and 5 precede 6"

(g) 6 precede /"

(h) 4, 3 and / are the terminal activities othe pro!ect"


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1

2

3

#

$

6

% & "A

'

(

)

*

+

, -

.

/

0

*i!ure for problem 1 problem set 66A


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" Construct the pro!ect network consisting o

activities # to 4 with the ollowing precedence

relationships&

(a)# and 0, the irst activities o the pro!ect start

immediatel$"

(b) # and 0 precede C"

(c) 0 precedes 1 and E"

(d) # and 0 precede %"

(e) % and 1 precede 3 and 2"

() C and 3 precede 4"

(g) E, 2 and 4 are

terminal activities


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1

2

A

3

B

4C

5 6

D

E

F G

H

I

Dummy


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Critical Path ComputationsCritical Path Computations

The objective in CP i! the con!t"uction o#

time !che$u%e #o" the &"oject' To (chieve thi!)

*e c(""y out com&ut(tion! th(t &"o$uce the

#o%%o*in+ in#o"m(tion,

-Tot(% $u"(tion nee$e$ to com&%ete the

&"oject-C%(!!i#ic(tion o# the (ctivitie! o# the &"oject

(! c"itic(% (n$ non.c"itic(%


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An (ctivity i! !(i$ to be c"itic(% i# the"e i! no

/ %ee*(y/ in $ete"minin+ it! !t("t (n$ #ini!h

time!' A non.c"itic(% (ctivity (%%o*! !ome!che$u%in+ !%(c0) !o th(t the !t("t time o# the

(ctivity c(n be $e%(ye$ o" ($v(nce$ *ithin

%imit! *ithout (##ectin+ the tot(% com&%etiontime o# the &"oject'

To c(""y out the nece!!("y com&ut(tion!) *e

$e#ine (n event (! ( &oint in time (t *hich!ome (ctivitie! ("e te"min(te$ (n$ othe"!

!t("te$' In te"m! o# the net*o"0) (n event

co""e!&on$! to ( no$e'


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Given (n event j) *e $e#ine

j e("%ie!t occu""ence time o# theevent j'

Cj j (te!t occu""ence time o# the

event j'Dij $u"(tion o# the (ctivity i)j

The $e#inition! o# the e("%ie!t (n$ %(te!t

occu""ence time! o# the event j ("e !&eci#ie$"e%(tive to !t("t (n$ com&%etion time o# the

&"oject'

Ej


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It i! to be note$ th(t the e("%ie!t occu""ence

time o# the event j i! the e("%ie!t time (t*hich (%% the (ctivitie! em(n(tin+ #"om the

no$e j c(n !t("t'

imi%("%y) the %(te!t occu""ence time o# theevent j i! the %(te!t time by *hich (%%

(ctivitie! th(t en$ (t the no$e j mu!t be

com&%ete$'


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The c"itic(% &(th c(%cu%(tion! invo%ve t*o

&(!!e!,

the #o"*("$ &(!! $ete"mine! the e("%ie!t

occu""ence time! o# the event! (n$

the b(c0*("$ &(!! c(%cu%(te! thei" %(te!toccu""ence time! '


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Fo"*("$ P(!! E("%ie!t ccu""ence Time!,

The com&ut(tion! !t("t (t no$e 1 the !t("tno$e (n$ ($v(nce "ecu"!ive%y to en$ no$e n'

Initi(% !te&, 7e !et E1 8 Thi! me(n! the

&"oject !t("t! (t time 8'

Gene"(% te& j, I# &) j) 9) j) :) v) j ("e the

(ctivitie! en$in+ (t no$e j) *e $e#ine

Ej (; < E&= D&j)E9= D9j):) Ev=Dvj>

The #o"*("$ &(!! en$! *hen Enh(! been

com&ute$ *hich i! the $u"(tion o# the &"oject'


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B(c0*("$ P(!! (te!t ccu""ence Time!,

The com&ut(tion! no* !t("t (t no$e n the

en$ no$e (n$ ($v(nce "ecu"!ive%y to !t("tno$e 1'

Initi(% !te&, 7e !et Cn En

Gene"(% te& i, I# i) &) i) 9) :) i) v ("e the

(ctivitie! !t("tin+ (t no$e i) *e $e#ine

Ci in < C&. Di&)C9. Di9):) Cv. Div>

The b(c0*("$ &(!! en$! *hen C1h(! been

com&ute$ *hich i! !t("t time o# the &"oject'


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Critical activity defnedCritical activity defned

B(!e$ on the &"ece$in+ c(%cu%(tion!) (n

(ctivity i) j i! c(%%e$ c"itic(% i#,

-Ei Ci

-Ej Cj

-Ej? Ei Cj? Ci Dij

Thu! (n (ctivity i) j i! criticali# the e("%ie!toccu""ence time (n$ (te!t occu""ence time

o# it! en$ no$e! ("e the !(me (n$ thei"

$i##e"ence i! the $u"(tion o# the (ctivity'


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A c"itic(% &(th o# the &"oject i! ( &(th

com&"i!in+ o# c"itic(% (ctivitie! o# the &"oject'

It i! to be "emembe"e$ th(t

- ( &"oject c(n h(ve mo"e th(n one c"itic(%

&(th)- Any c"itic(% &(th *i%% !t("t (t no$e 1 (n$ *i%%

en$ (t no$e n (n$ th(t

- The !um o# the $u"(tion! o# the (ctivitie!

%yin+ on ( c"itic(% &(th i! the $u"(tion o# the

&"oject'


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Dete"mine the c"itic(% &(th o# the &"oject

net*o"0 +iven be%o*'

1

3

2

2

2

3

5

@

6

3 2

3

2

5

4

6

@8

2

3

6

6

13

1

1

13

6

6

3

4

8


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1

2

A

3

B

4C

56

D

E

F

GH

I

Dummy

Dete"mine the c"itic(% &(th o# the

&"oject net*o"0 +iven be%o*'

2

3

5

4

2 @

18

6 38

8

8

33

3

3

@

@

13

14

1@

1@4

Documents

L26_Project Scheduling - CPM