lecture 5 pert-cpm (2)

7/18/2019 Lecture 5 Pert-cpm (2)

http://slidepdf.com/reader/full/lecture-5-pert-cpm-2 1/56

PERT AND CPM

• PERT (program evaluation and review technique)and CPM (critical path method) are two o themo!t widel" u!ed technique! or planning and

coordinating large !cale pro#ect!$• %" u!ing PERT or CPM manager! are a&le to

o&tain' A graphical di!pla" o the pro#ect activitie!

An e!timate o how long the pro#ect will tae

An indication o which activitie! are mo!t critical

An indication o how long an activit" can &e dela"ed

without lengthening the pro#ect



Network Models PERT & CPM

• PERT *nitial u!e wa! or the Polari! Mi!!ile Pro#ect+ ,ate -./0!

• CPM wa! developed to plan and coordinate

maintenance pro#ect! in chemical indu!tr"$• Although two technique! were developed

independentl"1 the" have a great deal in common$

• *nitial dierence! &etween them have di!appeared$

• 2!ed to planning and controlling man" program! 3 pro#ect! con!i!ting o variou! activitie! (all activitie! &e completed)



The ramewor o PERT and CPM

• 4or proceeding with PERT5CPM ollowing

common !i6 point! have to &e ollowed'

Deine the pro#ect with !igniicant activitie! or ta!!

Develop relation!hip among the activitie!

Draw networ connecting all activitie!

A!!ign time and5or co!t e!timate! to each activit"

Compute the critical path

2!e networ to help plan1 !chedule1 monitor and

control the pro#ect



Terminolog"

• Activity' A !peciic or !et o ta!! required &" the pro#ect

• Event' 7utcome o one or more activitie!

• Network ' Com&ination o all activitie! and event!• Path: Series of connected activities or between

any two events

• Critical path: on!est " Any delay wo#ld delay

the pro$ect

• Slack%float: Allowable slippa!e for a path



Precedence Diagramming Method

(PDM) Activitie! on Node! (A7N) 4ini!h+to+!tart (mo!t oten u!ed) A+%8 %+C8 etc 4ini!h+to+ini!h %+E 9tart+to+!tart %+D 9tart+to+ini!h 4+C

9tartA % C

4ED

4ini!h

No repetitive activities or conditionalloops! No Dummies!

Often used for Three Point Estimates (was

called PERT) and Critical Path Methods



Arrow Diagramming Method

(ADM) Activitie! on Arrow! (A7A)

-

:

; <

/

=

Start

Finish

dummy

Finish to start only (need additional nodes forleads and lags)

No repetitive activities or conditional loops

May use “dummies”

%

&

$

'

#

F



A !imple pro#ect networ diagram

-

;

<

:

/ =

,ocate

acilitie!

*nterview

7rder urniture

Remodel

4urniture !etup

>ire 3 train

Movein



Activit" relation!hip

a

b

c

a &

c



a

&

c

d

a

&

c

#''y Activity



a

&

c

d



( )

*

+

,A-

,.-

,C-

,-

Activity /''ediate

Predecessors

A +

% +

C A

D A1 %



( ) *

0 +

#''y Activity

A

%

D

C



)

+ 0(

*

,A- ,.-

,C- ,-

,E-

Activity ist for a Two"Machine Maintenance Pro$ect

Activity escription E1pected Ti'e

,in days-

A 7verhaul machine * ?

% Ad#u!t machine * <

C 7verhaul machine ** =

D Ad#u!t machine ** <

E Te!t !"!tem ;



) 0

2( + 3

* 4

Ro#tin!

,C-Prod#ct

esi!n

,A-

MarketResearch

Plan,.-

Prototype

,-

Marketin!.roch#re

,E-

CostEsti'ates

,5-Testin!

,6-

MarketS#rvey

,7-

Pricin!and

5orecast,/-

5inalReport

,8-

C9MPET/9N

Activity list for the a#!herty Porta"ac Pro$ect

Activity escription /''ediate

PredecessorsA R3D product de!ign +% Plan maret re!earch +C Routing (manuacturing engineering) AD %uild protot"pe model AE Prepare mareting &rochure A4 Co!t e!timate! (indu!trial engineering) C@ Preliminar" product te!ting D> Maret !urve" %1 E

* Pricing and oreca!t report > 4inal report 41 @1 *



PERT DiagramActivit" Preceding Activit"

A ++% ++

C ++

D A

E A4 C

@ C

> E1 %1 4

* E1 %1 4 D1 >

B @1 *1



)

+ 4(

*

E

0

.

C

@

B ?

>

*

A

D

4



9ale! Management Training Program

• A Plan topic

• % 7&tain !peaer!• C ,i!t meeting location!

• D 9elect location

• E 9peaer travel plan!

• 4 4inal chec with !peaer!

• @ Prepare and mail &rochure

• > Tae re!ervation!

• * ,a!t minute detail!



Networ Diagram

A%

C

D

@

E

>

4

-

;

<

:

/

=

?

*



Activitie! o a pro#ectActivit" Predece!!or Activit"

a +

& +

c +

d ae &1c

&1c

g &1ch c

* g1h

# d1e



•

Networ) Diagram

-

;

:

<

=

/

?

a

&

c

d

e

g

h

i

#

M N t Di



Mae a Networ Diagram

Activity Ti'e

,days-

Precedin!

Activity

A = ++

% ; ++

C ; ++

D < ++

E A

4 / %1 E@ . C1 41 D

> < ++

* ; P1 >

< %1 E

B -0 @

, - D

M -0 *1 1 B

N < ,1

7 / M1 N

P : A

/ @

* ;



-

<

:

;

= ?

/

.

-0

--

A1=

>1 <

%1 ;

C1 ;

D1 <

B1 -

1 /

@1 .

N1 <

B1

-0

1 <

*1 ;

71 /

Dum-

P1 :M1 -0

E1

41 /

A =



• A ++ =

• % ++ ?

• C ++

• D A /• E A =

• 4 A

• @ C /

• > C =• * %1 @1 4 =

• %1 @1 4 :

• B E1 1 , <

• , *1 > /• M *1 > :

• N ,1 E1 ;

• 7 B1 D :

• P M1 N1 7 :

i



Networ Diagram

-

;

<

:

?

= .

/

A1 =

%1 ?

C1

D1 /

E1 =41

@1 /

>1 =

*1 =,1 / M1 :

Dum

71 :

P1 :1 : N1;



Pro&lem

* %1 E1 4

-

;

<

:

/

=

A ()

% (-0)

C (<)

D (?)

E (=)

@ (/)

4 (?) > (<)

(Activit" time in da"! in parenthe!i!)



ue!tion!

• *denti" the critical path

• >ow long will it tae to complete thi! pro#ect

• Can activit" E &e dela"ed without dela"ing

the entire pro#ect

• Can activit" D &e dela"ed without dela"ing

the entire pro#ec1 or how man" da"!F

• Ghat i! the !chedule or activit" 4 (*$e$1 !tartand completion time!)



Critical Path Anal"!i!

• Provide! activit" inormation• Earlie!t (E9) 3 late!t (,9) !tart

• Earlie!t (E4) 3 late!t (,4) ini!h

• 9lac (9)' Allowa&le dela"

• *dentiie! critical path• Longest path in networ

• Shortest time pro#ect can &e completed

• An" dela" on activitie! dela"! pro#ect• Activitie! have 0 !lac



Critical Path Anal"!i!

E6ample



Networ 9olution

AA

EE..

CC 55

66

(

4 ) *

(

+*



Earlie!t 9tart 3 4ini!h 9tep!

• %egin at !tarting event 3 wor orward

• E9 H 0 or !tarting activitie!

• E9 i! earlie!t !tart

• E4 H E9 I Activit" time

• E4 i! earlie!t ini!h

• E9 H Ma6imum E4 o all predece!!or! ornon+!tarting activitie!

A i i A



Activity ES EF LS LF Slack

A 0 1

BC

D

EF

Activit" A

Earlie!t 9tart 9olution

5or startin! activities; ES < =>5or startin! activities; ES < =>

AA

EE..

CC 55

66

(

4 ) *

(

+*



Earlie!t 9tart 9olution

AA

EE..

CC 55

66

(

4 ) *

(

+*



,ate!t 9tart 3 4ini!h 9tep!

• %egin at ending event 3 wor &acward

• ,4 H Ma6imum E4 or ending activitie!

• ,4 i! late!t ini!h8 E4 i! earlie!t ini!h• ,9 H ,4 + Activit" time

• ,9 i! late!t !tart

• ,4 H Minimum ,9 o all !ucce!!or! or non+ending activitie!




A 0 1

B 1 7C 1 4

D 7 9

E 9 12

F 4 8

G 12 13 13

AA EE

.

.

CC 55

66

(

4 ) *

(

+*




A 0 1 0 1

B 1 7 1 7C 1 4 4 7

D 7 9 7 9

E 9 12 9 12F 4 8 7 12

G 12 13 12 13

,ate!t 4ini!h 9olution

AA

EE..

CC 55

66

(

4 ) *

+*



Compute 9lac



Critical Path

AA

EE..

CC 55

66

(

4 ) *

(

+*



@antt Chart + E9

0 5 10 15 20 25 30 35 40

A

B

C

D

E

F

G



E6erci!e!

E6$ -

Draw a PERT Networ1 *denti" Critical Path

and Calculate Critical Time$



Activities Precedin! Activities #ration ,ays-

A """" )

. """" *

C """" (

A;.;C +

E )

5 *

6 +

7 E;R )

/ E;R )

8 7;/ (

9 / (

? E;5;6 *

6;@ )M 6;@ (

N ;M *

P N;?;9;8 +

@ A; .; C +

R A; .; C *



CR/T/CA PAT7 CACAT/9NS

The critical path calculation! include two pha!e!$ The ir!t

pha!e i! called the forward pass1 where calculation! &egin

rom the J!tartK node and move to the JendK node$

The !econd pha!e1 called the backward pass1 &egin!

calculation! rom the JendK node and move! to the J!tartK

node1 repre!ent! the late!t occurrence time o the

corre!ponding event$ The orward pa!! i! con!idered now$



Duration E!timate!

• The time e!timate! are calculated &a!ed on

two e6erci!e! in Networ Diagram!

4orward Pa!!' To determine Earlie!t time!

%acward Pa!!' To determine ,ate!t time!



Method! or calculating 4wd and %cwd Pa!!

• Lero Method

A!!ume! !tart point a! Lero

E4 H E9 ID or orward pa!!

,9 H ,4 ID 4or &acward pa!!



E6ample Lero Method



9lac or 4loat

• Total 5loat' The total amount o time that a !chedule activit" ma" &e

dela"ed rom it! earl" !tart without dela"ing the pro#ect ini!h date1 or

violating a !chedule con!traint$

Total Float = LS – ES

• 5ree 5loat' The amount o time that a !chedule activit" can &e dela"ed

without dela"ing the earl" !tart date o an" immediatel" ollowing

!chedule activitie!

Free Float = ESs – EFp - Lag



,ead and ,ag

• ead Ti'e' Part o activit" which mu!t &e done &eore

ollowing activit" can !tart

• a! Ti'e: Part o activit" cannot &egin until the precedingactivit" have ini!hed



E6erci!e!

E6$ ;

Tae a Real Gorld or >"pothetical Pro#ect1

*denti" Activitie!1 E!timate Activit" Time and

Draw a PERT Networ$ *denti" Critical Path

and Calculate



PERT Calculation!

• 9tep -' Deine ta!!

• 9tep ;' Place Ta!! in a logical order1 ind the critical path

The longe!t time path through the ta! networ$ The !erie! o ta!!(or even a !ingle ta!) that dictate! the calculated ini!h date

• 9tep <' @enerate e!timate!

7ptimi!tic1 pe!!imi!tic1 liel" and PERT+ e6pected

9tandard Deviation and variance

• 9tep :' Determine earlie!t and late!t date!

• 9tep /'Determine pro&a&ilit" o meeting e6pected date• 9tep! - and ; are logic and legwor1 not calculation the!e require a

clear goal

http://en.wikipedia.org/wiki/Critical_path

http://en.wikipedia.org/wiki/Critical_path



PERT Calculation!

• E!timated duration! per ta!

Most 9pti'istic ,T9- B best case scenario

Most ikely ,T- nor'alD scenario

Most Pessi'istic ,TP- orst case scenario

• 4ormula derive! a pro&a&ilit"+&a!ed e6pected duration

,T9 1 ( F T 1 + F TP 1 (- % 4 < TE

Read thi! ormula a! the !um o (optimi!tic 6 - I liel" 6 : I pe!!imi!tic 6 -)

divided &" = H e6pected ta! duration

• Complete thi! calculation or all ta!!



PERT Activit" Time!

• < time e!timate!

• 7ptimi!tic time! (a)

• Mo!t+liel" time (m)• Pe!!imi!tic time (b)

• 4ollow &eta di!tri&ution

• E6pected time' t H (a I :m I b)5=• ariance o time!' v H (b + a);5<=



Pro#ect Time!

• E6pected pro#ect time

(T)

• 9um o critical pathactivit" time!1 t

• Pro#ect variance (V )

•9um o critical pathactivit" variance!1 v

=

: bma ET

++=

( )

<=

;

; ab −=σ



E6ample

Activit" a m & ETO variance

A ; : :$<< -

% < =$- --$/ =$: ;

C : -0 ?$=? -

Pro#ect -$/ :

CC..AA

+>** =$: 2>42



9D and ariance

• 9tandard deviation and variance

9tandard deviation (9D) i! the average deviation rom the e!timated

time

• 9DH(TP+T0)5= read a! (pe!!imi!tic+optimi!tic)5=Q

• A! a general rule1 the higher the !tandard deviation the greater the amount

o uncertaint"

ariance () relect! the !pread o a value over a normal di!tri&ution

• H9D; (9tandard deviation !quared)



Goring E6ample

• Con!ider the !ample pro#ect *n!talling computer!

with urniture1 !et up u!ing a li!t

• 9tart &" !etting up a ta&le to organie dataTask / escription #ration

- Mar Electricit" and networ point!

; 9et up wiring

< %u" computer!

: %u" 4urniture

/ *n!tall 4urniture

= *n!tall Computer!



-

Mar

2tilitie!

;

%u"

Computer!

<

%u" 4urniture

:

9et up

Giring

/

*n!tall

4urniture

=

*n!tall

Computer

!



n considering all tass on the previous slide, a tablemight loo lie thisCritical Path Tasks

/ T= TP T TE S

- ; : < < 0$<< 0$-0.

: ; : < < 0$<< 0$-0.

/ < / : : 0$<< 0$-0.

= - ; - -$; 0$-=

7ther Pro#ect Ta!!

; < / : : 0$<< 0$-0.

< ; < ; ;$; 0$-= 0$0;/=

T0 H Time 7ptimi!tic1

TP H Time Pe!!imi!tic

T, H Time ,iel"

TE H Time E6pected (Derived &" PERT)

9D H 9tandard Deviation

H ariance

lecture 5 pert-cpm (2)

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