EA
ARNED VALUE PROB
E BABILIS
STIC FO
ORECAS
STING
USIN MO
NG ONTE CAARLO SSIMULA
ATION
Ric
cardo Viana Vargas, M
a MSc, IPMA
A-B, PMP
Professor – G
Getulio Vargas Foundation (F FGV) – Brazil
Professor – Fun
P ndação Institut de Administ
to tração (FIA – U
USP) - Brazil
Partner – Macrosolutiions – Brazil
r
ricardo.var
rgas@macrosolu
utions.com.br
© Ricardo V
Viana Vargas. All R
Rights Reserved
Pub
blications
AACE - Ass
sociation for Ad
dvancement of Cost Enginee
f ering 48th Annnual Meeting
Washington - DC – U USA – 2004
Revista B
Brasileira de Gerenciamento de Projetos
Curitiba – PR - Brazil, 2004
C
1/15

ABSTRAC
CT
The aim of this article is to prese a propos of interc
f ent sal connection bbetween moodels and
probabilistic simulations of proje as poss
ect sible ways to determiine EAC (F Final cost)
through Ea arned Value Analysis. The article p
T proves that t use of the 3 main m
the models of
projection (constant iindex, CPI and SCI) as the bas of a triangular pro
sis obabilistic
distribution that, through Monte C
n Carlo simula
ation will per
rmit associa and dete
ate ermine the
probability according t the accom
to mplishment of budgets and costs o the projec
of ct.
EARNED V
VALUE AN
NALYSIS
Earned Value focuses on the rela
s ation betwe actual c
een costs and the work do in the
one
project wit
thin a cert
tain time lim The fo
mit. ocus is on the performance obbtained in
comparison to what w spent to obtain it (FL
n was LEMING & KKOPPELMA 1999a).
AN,
Earned Value can be d defined as th evaluatio between what was o
he on obtained acc
cording to
what was truly spent a to what was planne to be spe in which it is sugge
t and ed ent, ested that
the value t be earne initially by an activity is the valu budgeted for this ac
to ed y y ue d ctivity. As
each activiity or task o a project is accomp
of t plished, that value initia budgete for the
t ally ed
activity, now builds the Earned Va
w e alue of the project.
In order to formalize th concepts mentioned before, ba
he s d ased on the norm ANS
e SI/EIA 748
of the Am merican National Standards Institu ute, a spec
cific termino
ology was m
made up,
based on d data of the forecasted c
cost, real co and earned value.
ost
THE 3 ELE
EMENTS O THE EA
OF ARNED VAL ANALY
LUE YSIS
A project th will be c
hat controlled th
hrough the Earned Valu Analysis needs to be planned
ue e
through the management basic pr
e rinciples, ap
pplicable to a kind of project.
any
Exhibit 1 e
evidences t
these mana agement pr
rocesses. F
Firstly, the w
work to be done is
e
defined. In a second moment, the sche
n d , edules and budgets a are developped. The
measureme and eva
ent aluation of t results of Earned V
the Value are thhen, determ
mined and
compared to the plann values.
ned
2/15

SCH
HEDULE DEVELOPMEN
NT PERFORMAN
NCE
SCOPE DEFINITION
N
AN COST B UDGETING
ND MEASUREME
M ENT
Data
de
20 Status
S
20
Linha de
Base
10 (BCWS)
40 10
Custo
20
Re
eal
(ACWPP)
4
20 4
6
Valor
6
Agregado
(BCWP)
8
12
10
10
1
10
Exhibit 1 – Planning and monitoring s
E g system using Earne Value Analysis (ABBA, 1998).
ed
Likewise, t
the PMI (20000) shows, in its process of pla anning (Exhiibit 2), a deetailing of
processes of planning according to the same steps mentioned by A
t e ABBA (1998) in which
),
the scope definition of the projec (Scope D
ct Definition – 5 is pre-requisite for schedule
5.3)
developme (Schedule Developm
ent ment – 6.4), for resourc allocation (Resource Planning
ce n e
– 7.1) and for cost budgeting (Co Budgetin – 7.3). Based on the conclusion of these
ost ng e n
processes, the project plan is dev
, t veloped (Pro
oject Plan De
evelopment – 4.1).
TIM
ME
SCOPE E TIME
6.2 - A
Activity
5.2. Scope Pla
anning 6.1 – Activity Definition
Sequencing
COST TIM ME TIME
SCOPEE
7.1
7 – Resource 6.3 - Activity Duration
y 6.4 - Schedule
5.3 – Scope De
efinition
Planning Estima ating Development
COS ST COST
7.2 - Cost E
Estimating 7.3 – C
Cost Budgeting
RISSK INTEGGRATION
11.1 - Risk 4.1 – P
Project Plan
Managemen Planning
nt Deveelopment
Exhibit 2 – Planning proccess (PMI,2000).
ses
BCWS (Bu udget cost of work sc
cheduled) is the value that points out the pa of the
s s art
budget tha should be spent, con
at e nsidering the cost of ba
aseline of th activity, a
he attribution
or resource The BCW is calcu
e. WS ulated as th costs of baseline div
he vided in phhases and
3/15

accumulate until the date of the status, or current date It is the c
ed e e. cost originat in the
ted
budget.
During the execution, the monitor ring of the p
progress of the project is made through the
comparison between the real resu obtained and the o
n t ults ones forecas sted by the project in
the BCWS. In this mo oment, the E Earned Valu of the wo (BCWP) is evaluated, as well
ue ork
as the appropriation of real costs (ACWP).
f
BCWP (Bu udget cost w work performmed) is the value that p
points out th part of th budget
he he
that should be spent, considerin the work done up t the mom
d , ng k to ment and th cost of
he
baseline for the activity attribution or resource. The BCW is also ca
y, n WP alled Earned Value.
d
The way o measurem
of ment of Earn Value, or BCWP, is directly linked to the way the
ned e
project was planned. Without an adequate pplanning, th measurem
he ment of perrformance
has little or no applicab
r bility.
HARROFF (2000) and FLEMING & KOPPELMAN (1999 subdivide the measurement of
9)
Earned Value (BCWP) in different methods:
1. Mile
estone with weighted vvalue: The ccontrol cell is converted in 2 or mo marks
d ore
whe each on of them is defined b a partial d
ere ne by delivery of t work, ge
the enerating,
con
nsequently, a specific c
cost. The su of the co
um osts of accoomplishmen of each
nt
one of these m
e marks is the cost of the item.
2. Fixe formula by CAP: It is the me
ed t ethod that divides CA in 2 part that, if
AP ts
sum mmed up, complete 100% of the w work. In general, the mo used formulas are
ost
25/ /75, 50/50 a 75/25. The formula 25/75 sep
and a parates the work in 2 p
points: the
first point is ac
t ccomplished immediate at the b
d ely beginning of CAP (25% of costs
f %
are already acc counted); th other 74% are accou
he % unted when the work is finished.
n s
The formula 5
e 50/50 point out that 50% of c
ts costs will b accounte at the
be ed
beg ginning of th work and 50% at the end.
he d e
3. Perrcent complete: This m
method attrib
butes to ea element of a certain percent
ach
commplete (betwween 0 an 100%) t each control cycle. This percentage is
nd to
multiplied by t
the forecast
ted cost, aiiming to de
etermine the part of th budget
e he
alre
eady done.
4. Equuivalent unit It is a m
ts: method that calculates the Earned Value base on the
ed
unit produced or made by individu elements of costs, applied in repetitive
ts d ual s
works or whe the elem
ere ments are ddefined in t
terms of direct consum
mption of
resources.
It is commo sense in all Earned Value repor that there is not only one metho able to
on V rts e y od
fulfil all kind of work. Most of the times, com
ds mpanies should allow the use of mo than a
ore
mechanism of Earned Value calcu
m ulation.
4/15

In this artic we decid to choo the use of percent c
cle ded ose complete as a way to d
s determine
Earned Vallue (BCWP), due to its popularity and user-frie
a endliness. The percent complete
T
is being m more used in projects because it is easy to use and it is a stand dard entry
mechanism for earned values in many project manageme software
m d m t ent e.
On the other hand, it b brings a hug obstacle in its use, w
ge which is the strong subjjectivity in
its evaluatio It is influ
on. uenced direc by the e
ctly evaluator’s perception. Since the d
data entry
relies on th individual perception the perce complete method c be threa
he n, ent e can atened by
clients’ pre
essure or b managem
by ment staff, and as a c consequenc it could harm the
ce
results obt tained. In oorder to minnimize thos problems some co
se s, ompanies have been
using internal evaluatio procedu
on ures of perc
cent comple ete. The use of Earned Value in
e d
projects lea to more precise est
ads e timates.
The actual costs (ACW are me
WP) easured and evaluated by the project team that is in
d
charge of a accounts payable and receivable or by the f
finance department of the same
company. T team is supposed to report th real cost of the proje until the dead line
The s he ect
(status) in a specified accounts plan, defin
d ned by the controller’s departme of the
s ent
enterprise.
ACWP (Act tual cost of work perfor
rmed) prese ents the actu costs resulting from the work
ual m
already don by a reso
ne ource or act
tivity, until th status da or actua date of th project,
he ate, al he
due to finaancial data. When thos 3 parame
se eters are de
efined, the analysis of results is
obtained bbased on th correlatio among th values fo
he on he ound for ea one of t
ach them in a
certain stat date.
tus
WS
BC
ACWP
Cumulative Cost
BCWS
P
P
W
BCWP
W
AC
BC
Status
Time
Date
Exhibit 3 – Graphic example of BCWS, BCWP and ACWP within a time length.
e P n
5/15

PROJECT EVALUAT
T TION AND DEVELOP
D PMENT OF PROJEC
F CTIONS
WITH THE EARNED VALUE AN
E NALYSIS
The correla
ation among the values of BCWS, BCWP and ACWP allo
g s d ows the verif
fication of
the results of the pro
oject and co
ontinue the evaluations and future projection of final
s e ns
costs
In order to relate betw
ween BCWP and the parameters B
P BCWS and ACWP ther are the
re
following in
ndexes:
A) SPI (Sch
hedule Perfoormance Inddex) – Division between the Earne Value (BC
n ed CWP) and
the planne value in t baseline (BCWS). The SPI sh
ed the e hows the coonversion ra of the
ate
forecasted value in Ear
rned Value.
BCWP
SPI=
BCWS (equ
uation 01)
When the SPI equals 1 it means that the p
s planned value was inte egrally earned to the
project. Wh the SPI is less tha 1 it mean that the project is b
hen an ns being done iin a lower
conversion rate than th forecaste one. In o
he ed other words, the forecas
, sted financia amount
al
to be earned in the pe eriod define couldn’t be obtained and the project is la When
ed d, ate.
the SPI is s
superior to 1 it means that the pro
1, oject is earning results f
faster than e
expected,
in other wo
ords, it is advanced.
B) CPI (Co Performa
ost ance Index) – Division b
between the Earned Va
e alue (BCWP and the
P)
actual cost (ACWP). The CPI in ndicates whhich the conversion is between the actual
values used by the pro
d oject and the earned va
e alues in the s
same period
d.
BC
CWP
CPI=
AC
CWP (equ
uation 02)
When the CPI equals 1, it mean that the value spen by the p
s ns nt project was integrally
earned to t project (project with the budget). When the CPI is lless than 1, it means
the hin ,
that the project is sp
pending mo than forecasted until that mo
ore oment. If th CPI is
he
superior to 1, it mean that the project cos less than forecasted until that moment.
o ns sts n d
When CPI equals 1, it means that the project is accordin to the for
t t ng recasted bu
udget until
the reference date. According to p
project forec
casting, the following te
erminology is used:
s
A) EAC (Esstimated at Completion – finance value that represents the final co of the
n) e ost
project when concluded. It includ the actual costs (A
des ACWP) and the rest of estimate
f
values (ETC
C)
EAC= AC
CWP+ ETC
C (equ
uation 03)
B) ETC (Esstimated to C
Complete) – financial va
alue necess
sary to comp
plete the pr
roject. It is
calculated according to mathematical models to be presented.
s
6/15

C) VAC (Vaariation at C
Completion) – difference between th budgeted cost (BAC and the
e he d C)
projected final cost (EA
AC).
VAC= BA EAC
AC− (equ
uation 04)
EAC
EAC Projection Us
sing
CPI
C
VAC
Cumulative Cost
BAC
WS BAC
BC
ACWP
BCWS
P
P
W
BCWP
W
AC
BC
Status
Time
Date
E
Exhibit 4 – Earned Value forecasting of final deadlines a final costs (GE
and EROSA & CAPODIF
FERRO, 1999).
INDEXES USED FOR PROJECT
R TION OF P
PROJECT F
FINAL COS
STS
The generic formula fo the remain
c or ning estimat cost is function of a performanc factor
ted ce
BA BCWP
AC− P
ETC=
Índice (equ
uation 05)
where BAC is the final budge of the final project and index is the
et
performance index of th project.
he
The perform mance index is determined by the combination of the Cos Performance Index
x n st
(CPI) with t Scheduled Perform
the mance Index (SPI), acco
ording to wh is described next,
hat
in its usual cases.
ETC throug the const
gh tant deviatio index (op
on ptimistic)
It assumes that the res of the wo to be do by the p
s st ork one project will be done acc
b cording to
the origina plan and that an o
al d occurred deeviation will not repreesent a ten
ndency of
degeneratio or recove of the fo
on ery orecasted bu
udget.
This estima is comm
ate monly called the Optim
d mistic Estima
ation, becau
use, the inddexes CPI
and SPI are usually les than 1, th
e ss herefore per
rmanence in the plan tu
n urns out to b a good
be
result.
7/15

Índice = 1
BA − BCWP
AC P
ETC= = BAC− B
BCWP
Índice
EAC = AC
CWP+ ETC= ACWP+ BAC− BC
C CWP (equ
uation 06)
ETC throug costs performance in
gh ndex (realist or more p
tic probable)
It assumes that the r
s rest of the work to be done by t
e the project will follow t
the same
finance per
rformance o
obtained un this mom
ntil ment, throug the costs performan index
gh nce
(CPI).
A negative or positive tendency oobtained up to the mom ment in term of CPI, w project
ms will
the same tendency for the final co
r osts of the p
project. Sinc there is a natural ten
ce, ndency to
work with C indexes inferior to 1, this estim
CPI s 1 mate is comm monly called Realistic E
d Estimation
or more pro
obable.
Índice= C
CPI
BA − BCWP BAC− B
AC P BCWP
ETC= =
CP
PI
Índice
BAC− BC
CWP
EAC= AC CWP+ ETC= ACWP+
C
CPI (equ
uation 07)
ETC throug future scheduled cos index SCI (pessimistiic)
gh st
It assumes that the re of the w
s est work (future to be don by the p
e) ne project will f
follow the
finance pro
ojection determined by the cost performance index (CCPI), as we as the
ell
scheduled projection determined by the schheduled per
rformance in
ndex, generating the
scheduled cost index S
SCI.
This proceddure aims to catch a n
natural huma tendency of recover
an y ring the time wasted,
e
and this try means to spend more resources to do the same work planned be
y s efore. The
SCI index is strongly applicable in EAC pro ojection in case of late projects, and with
forecasted costs oversspent. The product SPPIxCPI make up the st
es trictest index in order
x
to determin the EAC.
ne
Since there is a natur tendency to work w CPI and SPI index inferior to 1, this
e ral y with xes
estimate is usually calle Pessimis Estimation.
ed stic
Índice= S = SPIxC
SCI CPI
BA − BCWP BAC− B
AC P BCWP
ETC= =
SPIxCPI
Índice
BAC− BC
CWP
EAC= AC CWP+ ETC= ACWP+
C
SPIxCPI (equ
uation 08)
8/15

When the 3 ways of Estimated at completion is deter rmined, a p probabilistic model is
applied in the dada, in order to allow verifica
t n a ation, in a de
esired reliab
bility degree which is
e,
the projected final cost for the pro
t oject.
MONTE C
CARLO SIM
MULATION
“Monte Ca arlo” was a n
nickname of a top-secr project re
f ret elated to the drawing a to the
and
project of atomic wea apons deve eloped by th mathematician John von Neum
he n mann. He
discovered that a sim
d mple model of random samples co ould solve ccertain mat
thematical
problems, tthat couldn’t be solved up to the m
moment.
The simulaation refers, however, to a method in which th distributio of possib results
o he on ble
is produce from suc
ed ccessive re ecalculations of the da of the p
s ata project, allo
owing the
constructio of multiple scenarios In each o of the calculations, new rando data is
on s. one om
used to re epresent a repetitive a and interactive process The com
s. mbination of all these
results crea
ates a probaabilistic distr
ribution of th results.
he
The feasibbility of prod
duced distribution relie on the f
es fact that, fo a high n
or number of
repetitions, the modell produced reflects the characteristics of the original dis
, e e stribution,
transformin the distr
ng ribution in a plausible result for a
analysis. Th simulation can be
he
applied in s
schedules, ccosts and otther project indexes.
Mathematic cally the res of the simulation be
sult ecomes a reeasonable aapproximatio for the
on
original dat In an infin number of repetitions, we could define tha
ta. nite r at
+∞
Re sults = . ∫ xF ( x)dx
−∞ (equ
uation 09)
where X is the variable analys and F is its density of p
v sed probabilities
function.
Since the e
exact determ
mination of the integrattion xF(x) is rather com
mplex, the simulations
permits an approximat form of re
te esults with le complex
ess xity.
A B E %
Start Finish
Foreca of Final Co
ast ost
C
D
Exhibit 5 – Const
truction of model o distribution of co
of osts and activities or work packages making up a final distribution from r
s random data of
the project (PRITCCHARD, 2001).
9/15

EXECUTIO OF THE SIMULAT
ON E TION
The execuution of the simulation assumes tthat all data of SPI, C and EA
a CPI AC’s have
already be
een determined for eac activity o work pa
ch or ackage, acccording to w
what was
evidenced in the projec example shown as fo
ct ollows.
1
Exhibit 6 – Proje example using the simulation .
ect t
Nome % Complete Budget BCWS BCWP ACWP CV
Simulação 41% R$ 50.000,00 R$ 41.200,00 R$ 35.100,00 R$ 37.400,00 (R$ 2.300,00)
Desenhar requeerimentos 100% R$ 4.000,00 R$ 4.000,00 R$ 4.000,00 R$ 5.000,00 (R$ 1.000,00)
Preparar dados
s 50% R$ 4.000,00 R$ 3.000,00 R$ 2.000,00 R$ 5.000,00 (R$ 3.000,00)
Obter ferramentas 25% R$ 6.000,00 R$ 6.000,00 R$ 1.500,00 R$ 3.000,00 (R$ 1.500,00)
Desenhar soluçção 100% R$ 12.000,00 R$ 12.000,00 R$ 12.000,00 R$ 10.000,00 R$ 2.000,00
Comprar equipaamentos teste 100% R$ 15.000,00 R$ 15.000,00 R$ 15.000,00 R$ 13.500,00 R$ 1.500,00
Dados de teste completos 0% R$ 0,00 R$ 0,00 R$ 0,00 R$ 0,00 R$ 0,00
Construir ambie de testes
ente 10% R$ 6.000,00 R$ 1.200,00 R$ 600,00 R$ 900,00 (R$ 300,00)
Aguardar chega equipamento
ada 30% R$ 0,00 R$ 0,00 R$ 0,00 R$ 0,00 R$ 0,00
Testar 0% R$ 3.000,00 R$ 0,00 R$ 0,00 R$ 0,00 R$ 0,00
Nome SV CPI SPI E
EAC Constant EAC CPI EAC SCI
Simulação (R$ 6.100,00) 0,94 0,85 R$ 52.300,00 R$ 62.500,00 R 100.100,00
R$
Desenhar requeerimentos R$ 0,00 0,80 1,00 R$ 5.000,00 R$ 5.000,00 R$ 5.000,00
Preparar dados
s (R$ 1.000,00) 0,40 0,67 R$ 7.000,00 R$ 10.000,00 R$ 12.500,00
Obter ferramentas (R$ 4.500,00) 0,50 0,25 R$ 7.500,00 R$ 12.000,00 R$ 39.000,00
Desenhar soluçção R$ 0,00 1,20 1,00 R$ 10.000,00 R$ 10.000,00 R$ 10.000,00
Comprar equipaamentos teste R$ 0,00 1,11 1,00 R$ 13.500,00 R$ 13.500,00 R$ 13.500,00
Dados de teste completos R$ 0,00 - - R$ 0,00 R$ 0,00 R$ 0,00
Construir ambie de testes
ente (R$ 600,00) 0,67 0,50 R$ 6.300,00 R$ 9.000,00 R$ 17.100,00
Aguardar chega equipamento
ada R$ 0,00 - - R$ 0,00 R$ 0,00 R$ 0,00
Testar R$ 0,00 - - R$ 3.000,00 R$ 3.000,00 R$ 3.000,00
Exhibit 7 – Initia basic data of sim
al mulation and determ
mination of the 3 m
models of EAC (opt
timistic, pessimistic and realistic).
From a complete data abase, the function of distribution of probability is determined for
the 3 EAC data, building the med
dium EAC a a result o distributio as show at table
as of on, wn
below.
The functio of dens
on sity of prob
bability used in the simulation w be the triangular
will
distribution This distribution is determined based on its minim
n. d n mum value, its more
probable v value and its maximum value. This function is probably the most d
s m s direct and
simplest ammong distrib
butions (GRE 1995), requiring onlly 3 points in its built.
EY, r n
1
In this paper a the case stud data are displa
all dy ayed in Brazilian Portuguese, as the original article.
n s
10/15

EACCPI
Probability
EAC EAC
E
Cost For
recast
1 SCI
Exhibit 8 – F
Function of density of triangular prob
y bability for EAC.
Using the s
simulation so
oftware @Risk, we could determine the final E
EAC from the function
e
RiskTriang (EAC1, EAC cpi, EAC s
C sci), making up the resu evidenc at table below.
g ults ced
Nome EAC Constant EAC CPI EAC SCI EAAC EAC
Simulação R$ 52.300,0
00 R$ 62.500,0 R$ 100.100,0
00 00 =RiskOutput(() R 71.633,33
R$
Desenhar requeerimentos R$ 5.000,0
00 R$ 5.000,0
00 R$ 5.000,0
00 =RiskTriang(E F16; G16)
E16; R$ 5.000,00
Preparar dados
s R$ 7.000,0
00 R$ 10.000,0
00 R$ 12.500,0
00 =RiskTriang(E F17; G17)
E17; R$ 9.833,33
Obter ferramen
ntas R$ 7.500,0
00 R$ 12.000,0
00 R$ 39.000,0
00 =RiskTriang(E F18; G18)
E18; R 19.500,00
R$
Desenhar soluçção R$ 10.000,0
00 R$ 10.000,0
00 R$ 10.000,0
00 =RiskTriang(E F19; G19)
E19; R 10.000,00
R$
Comprar equipaamentos teste R$ 13.500,0
00 R$ 13.500,0
00 R$ 13.500,0
00 =RiskTriang(E F20; G20)
E20; R 13.500,00
R$
Dados de teste completos R$ 0,0
00 R$ 0,0
00 R$ 0,0
00 =RiskTriang(E F21; G21)
E21; R$ 0,00
Construir ambie de testes
ente R$ 6.300,0
00 R$ 9.000,0
00 R$ 17.100,0
00 =RiskTriang(E F22; G22)
E22; R 10.800,00
R$
Aguardar chega equipamento
ada R$ 0,0
00 R$ 0,0
00 R$ 0,0
00 =RiskTriang(E F23; G23)
E23; R$ 0,00
Testar R$ 3.000,0
00 R$ 3.000,0
00 R$ 3.000,0
00 =RiskTriang(E F24; G24)
E24; R$ 3.000,00
Exhibit 9 – Fun
nction of density of triangular probab
f bility determined for the final EAC.
When we build the fu unction of density of pr
d robability, th parameters of simu
he ulation are
determined as well as the numb of iteratio and rep
d, s ber ons petitions of simulation a other
and
information In this artic 50,000 iterations we made.
n. cle i ere
The numbe of iteratio is important to det
er ons termine the quality of the results, therefore,
the more it terations are made, the more the function of final density gets clos to the
f ser
original fun
nctions. Howwever, this k
kind of proce requires a long exe
ess s ecution time even for
e,
fast compu uters that are able to ma the simulation in hig speed.
ake gh
Summary In nformation
Workbook Name eva.xls
Number of Simulations 1
Number of Iterations 50.000
Number of Inputs 9
Number of Outputs 1
Sampling TType Latin Hypercube
Simulation Start Time 20/1/2004 13:26
4
Simulation Stop Time 20/1/2004 13:27
4
Simulation Duration 00:00:55
Random Se eed 11029742 243
Exhibit 10 – S
Simulation data.
11/15

ANALISYS OF THE R
S RESULTS
After doing the simula
g ation, the prroduct gene erated is a d
distribution of probabiliity of final
EAC of the project, called “Simula
e ation”, evidenced in the following exxhibits.
Distribution for Sim
mulação / EAC
C/N2
6
Mean=7163
33,34
5
Values in 10^ -5
4
3
2
1
0
50 62,5 75 87
7,5 100
0
Values in Th
housands
5% 90%
% 5%
61,1023 85,079
9
Distri
ibution for Sim
mulação / EAC/
/N2
1,000
1
Mean=7163
33,34
0,800
0
0,600
0
0,400
0
0,200
0
0,000
0
50 62,5 75 87
7,5 100
Values in Thousands
5% 90%
% 5%
61
1,1023 85,079
9
Exhibit 11 – D
Distribution for the final EAC of the Pr
roject “Simulation” with an interval of confidence of 90% and cumulative distribution for
” f
the finall EAC of the Projec “Simulation”.
ct
%tile Valu
ue %tile Valu
ue
5% R$661.102,32 55% R$771.753,30
10% R$662.673,17 60% R$772.871,88
15% R$663.868,52 65% R$774.055,95
20% R$664.892,36 70% R$775.366,22
25% R$665.850,78 75% R$776.773,88
30% R$666.776,27 80% R$778.350,77
35% R$667.728,09 85% R$880.126,48
40% R$668.686,84 90% R$882.236,36
45% R$669.675,42 95% R$885.078,99
50% R$770.702,85
Exh
hibit 12 – Percenta distribution of final EAC of Projec “Simulation”.
age ct
According to prior dat we can assume for sure (abou 90% of ce
ta, ut ertainty), for example
r
that the pro
ojected finall cost will be between $
e $61,102 and $85,078.
d
12/15

These inte
ervals could be altered in order to determin more or less precision. For
d d ne r
example, a
assuming a certainty o 99% reg
of garding the values, we obtain th interval
e he
between $557,858 and $90,792, aaccording to what is sho
o own in the fo
ollowing exh
hibit.
Distribu
ution for Sim
mulação / EA
AC/N2
6
Mean=7163
33,34
5
Values in 10^ -5
4
3
2
1
0
50 62
2,5 75 87,5 100
Values in Th
housands
,5% 99%
9 ,5%
%
57,8581 90,7921
Exhibit 13 – Distribu
E ution for the final E
EAC of the Project “Simulation” with an interval of confiidence of 99%.
CONCLUS
SIONS
The use of Simulation Monte Car with the data of fina EAC of th project, c
f rlo al he can, in an
associated way, contr ribute to a probabilistic vision and not a dete
c d erminist visiion of the
final costs eelaborated for the proje without the addition effort in its construct
f ect, nal tion.
As mention in the st
ned tudy of CHR STENSE (1993), t
RI EN there isn’t a agreemen in order
an nt
to define w
which foreca model p
ast presents the best preciision and ap
e pplicability. However,
many stud dies have b been made in order to compar many m
e re models for t the costs
estimated in a certain project or group of pro
i g ojects, after its conclusiion, aiming t identify
to
which mod dels are mor precise and in which phases of the project they are a
re a h f t applicable,
as well as t associate a certain ty of project to a certa index.
to e ype ain
The need o estimates and costs projection is mentio
of s s ns oned and ch
haracterized by DOD
d
(1997) in In
nstruction 50
000.2R in 19 in 2 crit
997 terion.
Sta with an estimate ar for the f
art rea final cost,
reflecting the best and w
worst scenar
rios.(DOD,
1997).
Deetermine the estimate f the final cost that
e for
reflects the best pro ofessional judgment
concerning coosts. If the contract is at least
s
15% complete and the e
e estimate is less than
the calculate
e ed using the acc cumulated
performance index, give a explanation (DOD,
an
1997).
13/15

However, n none of thes studies p
se provides a p probabilistic treatment fo the proje
or ects, since
the most aadequate final EAC for the project is no longer an isolated value and turns out
t r d
to be a valu area wit certain pr
ues th robabilities, as suggeste in this art
ed ticle.
As a suggeestion for ne works, th next step will be to evaluate the results pro
ew he p e oduced in
the simulattion with th real resu of conc
he ults cluded projects in ord to deter
der rmine the
precision o data obtained, aiming to produc cases ass
of g ce sociated to the simulatiion model
applied to EMVS.
E
ABREVIAT
TIONS
ACWP – Ac ctual cost o work perfo
of ormed
BAC – Buddget at completion
BCWP – Budget cost of work per rformed
BCWS – Budget cost of work sch heduled
C/SCSC – Cost/Sched dule System Control C
ms Criteria
CAPs – Co Account Plans
ost
CPI – Cost Performanc Index
ce
CV – Cost variation
DOD – Unit States o America D
ted of Department of Defense
EAC – Estim
mated at coompletion
EMVS – Eaarned Value Manageme Systems
ent s
ETC – Estim
mated to coomplete
EVMS – Eaarned value Analysis
PMBOK - A guide to th Project M
he Managemen Body of K
nt Knowledge
PMI – Proje Management Institu
ect ute
SCI – Sche
eduled Cost Index (SPIxxCPI)
SPI – Sche
eduled Perfoormance Inddex
SV – Schedduled variatiion
VAC – Variation at com
mpletion
REFEREN
NCES
ABBA, W. F. (1998). D
Defense Acq
quisition Refo and Pro
orm oject Manag
gement. Lon Beach:
ng
29th Annua Project Management Institute Se
al eminars & Sy
ymposium.
CHRISTEN NSEN, D. S. (1993). Det
termining an Accurate Estimate at Completion Vienna:
n t n.
National Co
ontract Man
nagement Joournal.
DOD (1997 Earned Value Man
7). nagement Im
mplementat
tion Guide. Washington: United
States of A
America Dep
partment of Defense
FLEMING, Q. W. & KOOPPELMAN J. M. (199 Earned value Projec Managem
N, 99). ct ment, 2nd
Ed. Newton Square: P
n Project Mana
agement Ins
stitute.
GEROSA S. & CAPOD
S DIFERRO C. (1999). Eaarned value Manageme (EMV) Te
ent echniques
form Engin
neering and Prototype Production A
P Activities. P
Philadelphia: 30th Annu Project
ual
Manageme Institute Seminars & Symposium
ent m.
14/15

GREY, S. (1995). Pra
actical Risk Assessmen for Proje Managem
nt ect ment. West Sussex:
t
John Wiley & Sons.
y
HARROFF, N. N. (2000 Discrete Versus Lev of Effort. Milford: NNH Enterprise
, 0). vel e.
PMI (2000) A guide t the Project Managem
). to ment Body of Knowled
dge. Newton Square:
n
Project Ma
anagement Institute.
PRITCHAR C. L. (20
RD, 001). Risk M
Management Concepts and Guidan
t: nce. 2ª Ed. Arlington:
ESI Interna
ational.
SCHUYLER J. R. (1994). Decisio Analysis in Projects: Monte Car Simulatio Upper
R, on : rlo on.
Darby: Projject Manage
ement Institute.
15/15