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Earned Value Probabilistic Forecasting Using Monte Carlo Simulation
 

Earned Value Probabilistic Forecasting Using Monte Carlo Simulation

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The aim of this article is to present a proposal of interconnection between models and probabilistic simulations of project as possible ways to determine EAC (Final cost) through Earned Value ...

The aim of this article is to present a proposal of interconnection between models and probabilistic simulations of project as possible ways to determine EAC (Final cost) through Earned Value Analysis. The article proves that the use of the 3 main models of projection (constant index, CPI and SCI) as the basis of a triangular probabilistic distribution that, through Monte Carlo simulation will permit associate and determine the probability according to the accomplishment of budgets and costs of the project.

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    Earned Value Probabilistic Forecasting Using Monte Carlo Simulation Earned Value Probabilistic Forecasting Using Monte Carlo Simulation Document Transcript

    • 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