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UNIVERSITEIT GENT
FACULTEIT ECONOMIE EN BEDRIJFSKUNDE
ACADEMIEJAAR 2010 - 2011
AN ACCURACY STUDY ON EARNED
VALUE MANAGEMENT EXTENSIONS
USING MONTE CARLO SIMULATION
Masterproef voorgedragen tot het bekomen van de graad van
Master in de Toegepaste Economische Wetenschappen: Handelsingenieur
Evelyn De Blieck en Ellen De Groote
onder leiding van
Prof. dr. Mario Vanhoucke
UNIVERSITEIT GENT
FACULTEIT ECONOMIE EN BEDRIJFSKUNDE
ACADEMIEJAAR 2010 - 2011
AN ACCURACY STUDY ON EARNED
VALUE MANAGEMENT EXTENSIONS
USING MONTE CARLO SIMULATION
Masterproef voorgedragen tot het bekomen van de graad van
Master in de Toegepaste Economische Wetenschappen: Handelsingenieur
Evelyn De Blieck en Ellen De Groote
onder leiding van
Prof. dr. Mario Vanhoucke
Permission
‘The authors give the authorization to make this thesis available for consultation and
to copy parts of it for personal use. Any other use is subject to the limitations of
copyright, in particular with regard to the obligation to explicitly mention the source
when quoting results from this thesis.’
Evelyn De Blieck Ellen De Groote
Abstract
Tijdens de uitvoering van een project heeft de projectleider twee ultieme doelen: kost
en duurtijd van het project controleren en binnen aanvaardbare grenzen houden. Om
deze doelstellingen te halen, kan hij gebruik maken van Earned Value Management
(EVM). EVM systemen voorzien de projectleider van cruciale informatie betreffende
de vooruitgang van het project, zowel op vlak van tijd als op vlak van kost. Bovendien
voorziet EVM de projectleider van vroegtijdige signalen die hem waarschuwen indien
de succesvolle uitvoering van het project bedreigd zou worden. In deze situatie kan
de projectleider corrigerende acties ondernemen om het project opnieuw op het juiste
pad te helpen. De letterlijke vertaling van Earned Value zou verworven waarde zijn.
Tijdens de uitvoering van het project wordt steeds meer waarde verworven. Deze
verworven waarde wordt berekend op basis van het percentueel aandeel van het ge-
plande werk dat al uitgevoerd werd. EVM is bijzonder omdat het, in tegenstelling tot
andere technieken, zowel de geplande als de reele kosten vergelijkt met de verworven
waarde. EVM wordt tijdens de projectuitvoering ook gebruikt bij het voorspellen van
de uiteindelijke kost en de finale duurtijd.
In deze thesis wordt onderzoek gedaan naar de waarde van enkele uitbreidingen en
vernieuwingen op het traditionele EVM, voorgesteld door Dr. Mihaly Gorog in haar
verhandeling ‘A comprehensive model for planning and controlling contractor cash
flow’ [17]. In deze verhandeling voert Gorog een pleidooi voor de incorporatie van
cashflows in EVM. Hiervoor stelt ze een model op dat tot op heden nog niet getest is
op zijn waarde. Het is dan ook het doel van deze thesis om de voorgestelde methode
aan een grondige analyse te onderwerpen en kritisch te oordelen over de waarde die
de methode levert voor een projectleider.
Nadat in het eerste deel van de thesis een beknopt overzicht wordt gegeven van
de traditionele EVM methode, wordt het model van Gorog geıntroduceerd vanuit het
standpunt van de projectaannemer.
Het model brengt heel wat nieuwe definities en formules met zich mee. Een eerste
doelstelling was dan ook grondig inzicht te verkrijgen in het Contractor Cash Flow
(CCF) model. Om dit te bereiken werden alle vooropgestelde maatstaven en indica-
toren beknopt uitgelegd en verduidelijkt met een alomvattend voorbeeld. Hierdoor
krijgt ook de lezer de kans om zich in te werken in de nieuwe materie. Bovendien
werd de CFF methode grondig vergeleken met de traditionele EVM methode, wat
enkele interessante inzichten omtrent de gelijkenissen en verschillen hielp verwerven.
Op die manier werd het mogelijk om duidelijkheid te scheppen over op welke punten
het nieuwe model toegevoegde waarde kan leveren.
Voor het verder onderzoek van deze waardevolle componenten werd in het derde
deel van de thesis een simulatiestudie opgezet, die het mogelijk maakte een breed
gamma realistische scenario’s te creren waar een projectmanager mee geconfronteerd
zou kunnen worden. Dit liet toe het effect van verscheidene parameters op het CCF
model grondig te onderzoeken. De voor deze studie gebruikte methode wordt grondig
uiteengezet en al zijn componenten worden besproken. Een van de elementen uit het
model die naar onze mening toegevoegde waarde kon leveren is de voorspeller voor
marge. Aan de hand van deze simulatie werd het mogelijk om de nauwkeurigheid van
deze voorspeller te testen in verschillende gecontroleerde situaties. In een eerste fase
werden zowel de invloed van netwerkstructuur, variabiliteit in duurtijd van de pro-
jectactiviteiten en stadium van voltooiing getest. Vervolgens werd de impact van het
margesysteem geanalyseerd. In een derde fase werd onderzocht of het mogelijk is om
de nauwkeurigheid van de voorgestelde methode voor het voorspellen van marge met
reeds bestaande methodes te vergelijken. Deze vraag is cruciaal voor dit onderzoek
omdat het toelaat te bepalen of er inderdaad sprake is van een grotere nauwkeurigheid
en dus extra waarde. Er werd nagegaan hoe een projectleider marge zou voorspellen
voor de introductie van het CCF model, en ook op deze methode werden de simulaties
uitgevoerd. Hierdoor werd het mogelijk oude en nieuwe werkwijze voor het voorspel-
len van marge grondig met elkaar te vergelijken.
Tot slot wordt een overzicht gegeven van de belangrijkste conclusies van dit on-
derzoek. Hieruit kon de waarde van het nieuwe model voor de aannemer afgeleid
worden en konden aanbevelingen gedaan worden met betrekking tot het gebruik van
deze nieuwe methode.
Preface
As students Business Engineering, we were first introduced to Earned Value Man-
agement during the course ‘Project Management’, instructed by prof. Dr. Mario
Vanhoucke. His enthusiasm and apparent belief in the usefulness of this system ex-
cited our interest in the subject. When he mentioned that an article was recently
published, presenting an intriguing yet unproven innovation to traditional Earned
Value Management, we accepted the challenge to thoroughly investigate this new
technique. This novelty was proposed by Dr. Mihaly Gorog in her paper ‘A compre-
hensive model for planning and controlling contractor cash flow’ [17].
The document that lies before you is the result of hard work, lots of fun and the
valuable contributions of a few people we therefore would like to thank.
First and foremost, we would like to express our gratitude to our promoter, prof.
Dr. Mario Vanhoucke, for his optimism, open door and the many insights he provided
for this master thesis. We appreciate the opportunity he offered us to be part of and
lecture at the Earned Value Analysis conference in November 2010. Not only did this
provide us with the ambition to obtain and present our first results, above all, it was
an amazing opportunity to get in touch with experts in the field of Earned Value
Management and to be able to exchange ideas. Thank you, Mario!
We would also like to thank our parents for their unconditional faith in the success
of our work, the encouraging phone calls and the many energizing snacks. Thank you,
folks!
A very big thank you also goes to Friedl and Vincent, who carefully read and
reread our thesis and offered many suggestions and corrections to the text. Thank
you, Friedl and Vincent!
i
Table of Contents
Preface i
Table of Contents ii
List of Abbreviations v
List of Figures ix
List of Tables xi
I Introduction 1
1 General introduction 2
2 Introduction to Earned Value Management 6
2.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 EVM Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Performance Measurements . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Earned Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Predicting the future . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 Estimated cost At Completion (EAC) . . . . . . . . . . . . . . 11
2.4.2 Estimated duration At Completion (EAC(t)) . . . . . . . . . . 12
2.5 To Complete Performance Index . . . . . . . . . . . . . . . . . . . . . 15
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
II EVM from a contractor point of view 16
3 A review of the comprehensive model for planning and controlling
contractor cash flow 17
3.1 Measurements in the comprehensive model for planning and controlling
contractor cash flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
ii
3.2 Indicators in the comprehensive model for planning and controlling
contractor cash flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Forecaster in the comprehensive model for planning and controlling
contractor cash flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.1 Components of the EMC formula . . . . . . . . . . . . . . . . . 23
3.3.2 Critical analysis of the EMC formula . . . . . . . . . . . . . . . 24
4 Example project 26
4.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Real scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Aggregate project level . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5 Further insights and critical analysis 37
5.1 Relationship with traditional EVM . . . . . . . . . . . . . . . . . . . . 37
5.1.1 Revenue-based metrics . . . . . . . . . . . . . . . . . . . . . . . 39
5.1.2 Cost-based metrics . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.1.3 Final comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2 Usefulness of Contractor Cash Flow (CCF) Indicators . . . . . . . . . 41
5.3 Practical use of PBPI . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.3.2 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3.3 Baseline optimization . . . . . . . . . . . . . . . . . . . . . . . 44
5.3.4 Baseline Leveling . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.3.5 Milestones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
III Simulation study 52
6 Methodology 53
6.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.2 Triangular distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7 Impact of external factors on the forecast accuracy of EMC 58
7.1 Topological Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
7.2 Variability in activity duration . . . . . . . . . . . . . . . . . . . . . . 62
7.3 Project completion stage . . . . . . . . . . . . . . . . . . . . . . . . . . 65
8 Impact of margin attribution methods on the forecast accuracy of
EMC 67
8.1 Fixed Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8.2 Regressive Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
8.3 Progressive Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.4 Random Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
iii
8.5 Analysis of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
8.5.1 MPI stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
8.5.2 Search for the ideal MPI . . . . . . . . . . . . . . . . . . . . . . 76
9 A comparative study 78
9.1 Impact of external factors on the forecast accuracy of IAC-EAC . . . . 79
9.2 Impact of margin attribution systems on the forecast accuracy of IAC-
EAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
9.3 Comparison of accuracy of EMC and IAC-EAC . . . . . . . . . . . . 81
10 Impact of milestones on ABPI 84
IV Final reflections 87
11 Conclusions 88
11.1 Usefulness of Contractor Cash Flow indicators . . . . . . . . . . . . . 89
11.2 Forecast accuracy of Expected Margin at Completion . . . . . . . . . . 90
11.2.1 Impact of external project parameters . . . . . . . . . . . . . . 90
11.2.2 Impact of margin attribution system . . . . . . . . . . . . . . . 91
11.2.3 Comparison with traditional Earned Value Management . . . . 91
12 Recommendations 93
References xii
iv
List of Abbreviations
A
ABC Activity Based Costing
ABPI Actual Balance Performance Index
ABV Actual Balance Variance
AC Actual Cost
ACWP Actual Cost of Work Performed
AD Actual Duration
AEWP Actual Expenditure of Work Performed
AM Actual Margin
AMC Actual Margin at Completion
APCS Actual Percentage Cash Shortage
API Account Performance Index
AV Account Variance
AVWP Account Value of Work Performed
AVWS Account Value of Work Scheduled
B
BAC Budget At Completion
BCRW Budgeted Cost of Remaining Work
BCWP Budgeted Cost of Work Perfomed
BCWS Budgeted Cost of Work Scheduled
BO Budgetary Objective
v
C
CC/BM Critical Chain scheduling and Buffer Management
CCF Contractor Cash Flow
CPI Cost Performance Index
CV Cost Variance
C/SCSC Cost/Schedule Control System Criteria
E
EAC Expected At Completion (cost)
EAC(t) Expected At Completion (time)
ED Earned Duration
EEWS Expected Expenditure of Work Scheduled
EMC Expected Margin at Completion
ES Earned Schedule
EV Earned Value
EVM Earned Value Management
EVMS Earned Value Management System
EVPMS Earned Value Project Management System
F
FPI Financial Performance Index
FV Financial Variance
I
IAC Invoice At Completion
IPI Invoice Performance Index
IV Invoice Variance
IVWP Invoice Value of Work Performed
IVWS Invoice Value of Work Scheduled
vi
J
JIT Just-In-Time
L
LFT Latest Finish Time
M
MAPE Mean Absolute Percentage Error
MAE Mean Absolute Error
MO Margin Objective
MPE Mean Percentage Error
MPI Margin Performance Index
MSLK Minimum Slack
MV Margin Variance
O
OV Objective Value
P
PBP Performance Based Payment
PBPI Planned Balance Performance Index
PBV Planned Balance Variance
PC Percentage Completed
PCRD Percentage Cash Range Deviation
PCS Percentage Cash Shortage
PD Planned Duration
PF Performance Factor
PIPI Planned Invoice Performance Index
vii
PIV Planned Invoice Variance
PM Planned Margin
PMC Planned Margin at Completion
PPI Plan Performance Index
PV Planned Value
PVar Plan Variance
PVR Planned Value Rate
PVWP Planned Value of Work Performed
PVWS Planned Value of Work Scheduled
R
RCPSP Resource-Constrained Project Scheduling Problem
S
SAC Schedule At Completion
SCI Schedule Cost Index
SM Scheduled Margin
SP Serial Parallel Indicator
SPI Schedule Performance Index
SPI(t) Schedule Performance Index (time)
SV Schedule Variance
SV(t) Schedule Variance (time)
T
TCPI To Complete Performance Index
TCMPI To Complete Margin Performance Index
TV Time Variance
W
WIP Work In Progress
viii
List of Figures
2.1 EVM: key parameters, performance measures, and forecasting indicators 7
2.2 EVM key parameters for a project under four scenarios . . . . . . . . 9
2.3 The ES metric for a late and early project . . . . . . . . . . . . . . . . 10
2.4 The SPI and SV versus SPI(t) and SV(t) performance measures . . . 11
4.1 Example project: Activity-on-the-node representation . . . . . . . . . 26
4.2 Example project: Gantt Chart . . . . . . . . . . . . . . . . . . . . . . 29
4.3 Contractor Cash Flow Metrics . . . . . . . . . . . . . . . . . . . . . . 34
4.4 Contractor Cash Flow Indicators . . . . . . . . . . . . . . . . . . . . . 35
4.5 Contractor Cash Flow Forecast Indicators . . . . . . . . . . . . . . . . 36
5.1 Overview of EVM and contractor cash flow metrics and indicators . . 38
5.2 Methodological approach of the scheduling problem . . . . . . . . . . . 45
5.3 PBPI improvement per SP for baseline optimization problem . . . . . 46
5.4 Variability in Activity Duration: Evolution of MPI . . . . . . . . . . . 47
5.5 PBPI improvement per SP for baseline leveling problem . . . . . . . . 49
6.1 Methodological approach of the simulation study . . . . . . . . . . . . 54
6.2 Triangular Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7.1 Mean Absolute Percentage Error for parallel and serial networks . . . 59
7.2 Activity-on-the-node representation of completely serial network . . . 60
7.3 Activity-on-the-node representation of completely parallel network . . 60
7.4 Impact of topological structure on MPI for the example project . . . . 61
7.5 Impact of variability in activity duration on MAPE . . . . . . . . . . . 63
7.6 Impact of variability in activity duration on MPI for the example project 64
7.7 Impact of Project Completion Stage on MAPE . . . . . . . . . . . . . 65
7.8 MPI, CPI and Margin Error . . . . . . . . . . . . . . . . . . . . . . . 66
8.1 MAPE(%) for different fixed margins per SP-factor . . . . . . . . . . 68
8.2 Evolution of MAPE, MAE, and AMC for different fixed margins . . . 69
8.3 MAPE(%) for different fixed margins and time performance . . . . . . 70
8.4 MAPE(%) for different margin systems . . . . . . . . . . . . . . . . . 71
8.5 MPI stability for fixed margins . . . . . . . . . . . . . . . . . . . . . . 74
ix
8.6 MPI stability for regressive margins . . . . . . . . . . . . . . . . . . . 74
8.7 MPI stability for progressive margins . . . . . . . . . . . . . . . . . . . 75
8.8 MPI stability for random margins . . . . . . . . . . . . . . . . . . . . . 75
8.9 Evolution of TCMPI and MPI for 4 margin attribution systems . . . . 77
9.1 MAPE(%) for IAC-EAC for different Performance Factors . . . . . . . 80
9.2 MAPE(%) for EMC and IAC-EAC (PF=CPI) . . . . . . . . . . . . . 83
10.1 APCS per SP for invoicing at milestones . . . . . . . . . . . . . . . . 85
10.2 APCS per SP for invoicing at milestones with buffer . . . . . . . . . . 86
x
List of Tables
2.1 EAC(t) Forecasting Methods . . . . . . . . . . . . . . . . . . . . . . . 14
4.1 EVM and contractor cash flow measurements . . . . . . . . . . . . . . 31
4.2 EVM and contractor cash flow indicators . . . . . . . . . . . . . . . . 32
4.3 Contractor cash flow predictors . . . . . . . . . . . . . . . . . . . . . . 33
5.1 Comparison of scenario with and without milestones for the example
project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
xi
Part I
Introduction
1
Chapter 1
General introduction
Earned Value Management (EVM) systems have been developed to provide project
managers with crucial information on the performance and progress of their projects
through the unique interaction of three project management elements - the holy trin-
ity - scope, cost and time. In addition, it provides project managers with an early
warning sign for poor performance. Corrective actions can be taken in time to bring
their projects back on track. Where traditional performance measures compare only
actual and budgeted costs, in EVM however, actual and budgeted costs are compared
to the earned value. Since its introduction in 1967 by agencies of the US Federal Gov-
ernment, EVM has seen a rapid growth in government and later on also in private
industry projects. The development and maturation of earned value project manage-
ment systems has led to a broad field of study.
Recently an article was published, presenting an intriguing yet unproven inno-
vation to traditional earned value management. This novelty was proposed by Dr.
Mihaly Gorog in her paper ‘A comprehensive model for planning and controlling con-
tractor cash flow’ [17]. In this paper, two major objections againts the currently
available techniques to plan and control the project implementation process are ex-
pressed :
1. Control models such as Earned Value Management adopt a mainly client-view
and thus do not provide the possibility for contractors to plan and control the
contract cash flow.
2. The ability to estimate the likely margin is of vital importance if a contractor
wants to be able to elaborate a competitive bid price and is not possible with
traditional Earned Value Management in case of a fixed contract price.
The aim of our thesis is to thoroughly investigate this new technique and try to vali-
date or dismiss the aforementioned objections.
2
The incorporation of cash flows in project management has been studied in several
domains. It has been handled as a scheduling problem with the objective of net present
value optimization for which many heuristic procedures have been created (e.g. [29],
[30], [3], [31], etc.). In recent years, more attention is also paid to cash flow modeling
and forecasting, especially in the construction industry (e.g. [20], [23], [5], etc.). To
the best of our knowledge, the by Gorog proposed model is the first one that integrates
the concepts of cash flow modeling and forecasting in earned value management.
Scope
As mentioned, the goal of this master thesis was to thoroughly investigate a new
EVM technique that incorporates cash flows in the traditional earned value calcu-
lations, and more specifically the accuracy of this technique. In our opinion, the
importance of accuracy in project management models and by extension the purpose
of this document is mainly twofold. On the one hand, it is of vital importance for
the project manager to be able to track the progress of his project ad hoc. Therefore,
the right data needs to be available and observed at the right time. On the other
hand, in order to know the future effect of current performance on project duration,
budget (cost) or margin, accurate forecast measures are indispensable. Note that, on
this latter topic, the scope is restricted to margin forecast measures as both cost and
duration forecasting have already been investigated extensively by for instance Chris-
tensen (e.g. [6], [8], etc.) and Vanhoucke (e.g. [33], [35], [36], [34], etc.) respectively.
A first step towards attaining this dual objective was to bring clarity in the new
Contractor Cash Flow (CCF) model with its many definitions and formulas. By
means of a comprehensive example project with elaborate tables and calculations, we
seek to provide an environment for the reader to familiarize with the basic concepts
of the CCF model. As the basis of this document is a novel, non-proven concept, we
use the application of the CCF model on this example project as a foundation to take
a first critical look into the added value of this new technique to traditional EVM.
The scope will further be limited to those aspects of the new technique that, in our
modest opinion, add the most value from a project management point of view.
In order to test the accuracy of the margin forecasting measure, we have chosen not
to restrict ourselves to the use of a few real project examples from practice. Instead,
a Monte Carlo simulation study is set up and a dataset containing a wide variety of
diverse project network instances is used. This approach is opted in order to be able
to maximally generalize the results from our simulation study.
Brief summary
Chapter 2 starts by giving a short overview of the history of Earned Value Manage-
ment and subsequently summarizes its basic components. The EVM philosophy is
based on the management of three key data : Actual Cost (AC), Planned Value (PV),
3
and Earned Value (EV). In order to easily track the changes in their mutual relations,
some performance indexes are reviewed. These indicators for cost and schedule per-
formance are then compared to a few more recently introduced indicators that deal
with some of the criticized limitations of traditional EVM. Next, as EVM can also be
used to forecast cost and duration at project completion, several different formulas
for predicting cost and duration are reviewed.
Chapter 3 opens the second part of this master thesis which deals with EVM from
the point of view of a project contractor. As mentioned before, more attention is paid
in recent years to cash flow modeling and the incorporation of cash flow performance
as a means of measuring a project contractor’s financial performance. As this work
is mainly built on the article of Gorog, ‘A comprehensive model for planning and
controlling contractor cash flow’ [17], chapter 3 provides a thorough overview of the
various measurements and indicators she proposes. Aside from definitions and basic
equations, we also add further explanation and extended formulas.
Chapter 4 presents a comprehensive example project that we have developed in
order to better demonstrate the use and meaning of the aforementioned measure-
ments, indicators, and forecaster in the contractor cash flow model. As Gorog does
not specify the conditions under which her newly introduced model is best used, some
assumptions are put forward and their relevance and appropriateness for this work is
discussed.
Chapter 5 then provides further insights in the previously presented CCF model.
It extensively evaluates the complex relationship between the CCF metrics and tra-
ditional EVM, which is visualized in a comprehensive framework. From a project
management point of view, not all proposed metrics entail the same utility. Some
indicators clearly serve the contractor while others do not seem to be of great value.
If no added value results from applying a certain measurement or indicator, the con-
tractor will not make use of it. Therefore, chapter 5 also discusses the convenience
and usefulness of the CCF model. The insights from this analysis are then put to the
test and the possibility for improving the cash position of the contractor is investi-
gated in section 5.3.
The third part of this work presents a large Monte Carlo simulation study that
is applied to analyze several different aspects of the new model thoroughly. Chapter
6 describes the methodology used for this simulation. First, some general informa-
tion is provided about Monte Carlo simulations. Second, the applied distribution is
discussed.
Chapter 7 discloses the results of the first simulation run where the impact of
various external project parameters on the forecast accuracy of the Estimated Margin
at Completion (EMC), introduced in part II, is tested on a wide range of networks.
In order to be able to generalize conclusions, it is important to evaluate the influence
of the type of project network, the uncertainty of the project environment and the
4
effect of the moment in the project life on which the forecast is based. These topics
are treated in section 7.1, 7.2 and 7.3 respectively.
In the remainder of part III, some of the previously made assumptions are aban-
doned and their impact on the forecast accuracy of EMC, as well as on other aspects
of the CCF model, is studied. Until this point, the analysis assumed margins to be a
fixed percentage of costs for all activities. This has not to be the case however. The
price value for different activities can be calculated based on varying percentages of
their cost. Chapter 8 examines the influence of the various ways a contractor can
attribute margin to the activities of a project. Aside from attribution systems with
distinct fixed margins, chapter 8 subsequently introduces regressive, progressive, and
random margin attribution systems.
In chapter 9, the question is raised whether it is possible to compare the accuracy
of EMC with other methods for estimating the margin at completion of a project. For
this analysis, several forecasting measures based on traditional earned value indicators
are proposed. They are put through the same tests as performed in chapter 7 and
their accuracy is compared.
Chapter 10 deals with the impact of introducing milestones on a contractor’s cash
position. In previous analysis, it was assumed that after completion of each activity,
invoices corresponding to the price value of the completed activity, could be sent out
to the client. In practice, however, most of the time a contractor will require some
kind of advance from his client at the beginning of a project. In addition, it might
cause too much of administrative fuss if every time an activity is completed, an invoice
needs to be sent out. For these and other reasons, instead of invoicing after activity
completion, it might be more realistic to work with milestones. This analysis builds
on the results of section 5.3.5.
Chapter 11 opens the last part of this master thesis and contains the main con-
clusions from part II and III. In the final chapter, chapter 12, some personal recom-
mendations are made for practitioners.
5
Chapter 2
Introduction to Earned Value
Management
2.1 History
Earned Value Management (EVM) is a method that enables measuring the perfor-
mance of a project in terms of cost and time during its execution. EVM was intro-
duced in 1967 by agencies of the US Federal Government. It was an integral part
of the Cost/Schedule Control System Criteria (C/SCSC) that were brought together
by the Air Force in the early 1960s and were used in large acquisition programs.
The C/SCSC criteria are 35 statements concerning the minimum requirements that
constitute acceptable project management systems. In the private sector, however,
the method was not adopted very well at first. In order to encourage wider use of
EVM in the private sector, the US Federal Government discarded C/SCSC by the
end of 1996 and turned towards a more flexible Earned Value Management System
(EVMS), also called Earned Value Project Management System (EVPMS) [1]. Due
to a better understanding of EVM, a rapid growth of these systems could be observed
in government and private industry projects in recent years. The development and
maturation of EVPMS has led to a very broad field of study with an extensive vo-
cabulary and excessive use of acronyms [13]. Morley ([27], p.8) states that ‘in order
to facilitate the widespread adoption of earned value as a management technique, the
technique should be presented using terms that are familiar to and in use by most
project managers’.
Adopting EVM techniques supports project managers in focusing their money and
energy on projects that mostly need it. Through a unique interaction of three project
management elements, scope, cost, and time, EVM provides project managers with
crucial information on the performance and progress of their projects. Corrective
actions can be taken in time to bring their projects back on track.
6
Figure 2.1: EVM: key parameters, performance measures, and forecasting indicators.[35]
In the following sections, an overview is given of the basic EVM components, as
described by several authors such as Henderson [18], Anbari [1], and Vanhoucke [35].
These components are visualized in figure 2.1.
2.2 EVM Components
The EVM philosophy is based on the management of three key data: Actual Cost
(AC), Planned Value (PV), and Earned Value (EV). The Actual Cost, also called
Actual Cost of Work Performed (ACWP), is the real cost of the work done at a certain
point in time. The Planned Value, also called Budgeted Cost of Work Scheduled
(BCWS), is the scheduled cost for the work done at that point in time, thus if the
project would be executed according to schedule. The planned value for the whole
project, calculated as the sum of the PVs of all project activities, is called the Budget
At Completion (BAC =∑
PV ). This is the budget needed to complete the project,
if every activity is executed according to plan. Due to unforeseen events, however,
this might not always be the case. Activities may take more time to complete than
estimated at the beginning of the project because of employees being sick, machine
breakdowns, strikes, etc. Activities may also start late due to delays in raw material
supply or because of preceding activities ending late. For these and many other
reasons, AC may deviate from PV. This is where Earned Value, also called Budgeted
Cost of Work Performed (BCWP), is introduced. During the execution of a project,
value is acquired or earned. This value is expressed as a portion of the BAC. To
calculate EV, we need to know what percentage of work has already been completed.
7
This portion is called the Percentage Completed (PC). EV can then be calculated as
follows:
EV = PC ∗BAC (2.1)
This can be illustrated with a small example. Suppose the budget of an activity is
1000. At a certain point in time, 20% of the activity is completed and 300 has al-
ready been spent. EV thus equals 200 (20% ∗ 1000) and is independent of the actual
expenditure of 300.
In traditional methods to measure the performance of a project, actual costs are
compared with budgeted costs. In EVM however, actual and budgeted costs are
compared to the earned value. It is in this regard that some interesting measurements
for schedule and cost performance have been defined.
2.2.1 Performance Measurements
Cost Performance : Cost Variance (CV) and Cost Performance Index
(CPI)
CV = EV −AC (2.2)
CPI =EV
AC(2.3)
CV and CPI are measurements to evaluate the cost performance of a project.
If, at a certain point in time, EV is greater than AC, indicating that more value
was earned than the real costs that have been incurred, the project is running
under budget. CV will be positive and CPI will be greater than 1. If however,
EV is smaller than AC, the project is running over budget. CV will be negative
and CPI will be smaller than 1.
Schedule Performance : Schedule Variance (SV) and Schedule Perfor-
mance Index (SPI)
SV = EV − PV (2.4)
SPI =EV
PV(2.5)
SV and SPI are measurements to evaluate the time progress of a project. If, at
a certain point in time, EV is greater than PV, indicating that more value was
earned than budgeted at that moment, the project is running ahead of schedule.
SV will be positive and SPI will be greater than 1. If however, EV is smaller
than PV, the project is running late. SV will be negative and SPI will be smaller
than 1.
8
Figure 2.2: The Earned Value Management key parameters for a project under fourscenarios. [35]Scenario 1: late project, over budget; Scenario 2: late project, under budget;Scenario 3: early project, over budget; Scenario 4: early project, under budget.
Combining both measurements for schedule and cost performance results in 4
possible project scenarios. These scenarios are shown in figure 2.2.
2.2.2 Limitations
In literature, several authors have mentioned the shortcomings of the basic EVM
technique ([18], [13], [25], etc.). First of all, SV expresses schedule performance in
monetary terms instead of in actual time units. Furthermore, if a project starts
earlier than planned, PV will be 0. Consequently, SPI cannot give a measurement for
schedule performance. Moreover, at the end of the project, Percentage Completed is
100% and consequently EV will equal PV. As a result, SV will always be 0 at the
end of the project and SPI will always converge to 1 at the end of the project. When
observing values of 0 and 1 for SV and SPI respectively, one can wonder whether the
project is completed or whether the project is performing perfectly according to plan.
As a consequence of the behavior of EV and PV towards the end of the project, SV
and SPI will no longer be reliable as of a certain point in time.
9
Figure 2.3: The ES metric for a late (left) and early (right) project. [35]
2.3 Earned Schedule
In response to the problems mentioned in section 2.2.2, Lipke ([25], p.5) introduced
the Earned Schedule (ES) indicators. The ES indicators are time-based indicators
instead of cost-based indicators. Since time delays are measured in terms of time,
the Earned Schedule indicators are easier to understand when considering schedule
performance. Moreover, the Earned Schedule indicators are reliable during the whole
time horizon of the project as the adapted formula for schedule performance does not
converge to 1. ES is calculated as follows.
Find t such that EV ≥ PVt and EV < PVt+1
ES = t +EV − PVt
PVt+1 − PVt, where t is time (2.6)
As explained by Lipke [25], it becomes clear from studying equation 2.6 that ‘the
cumulative value of ES is found by using EV to identify in which time increment (t) of
PV the cost value occurs. The value of ES is then equal to the cumulative time to the
beginning of that increment (e.g., months) plus a fraction of it. The fractional amount
is equal to the portion of EV extending into the incomplete time increment divided
by the total PV planned for that same time period.’ Earned Schedule thus defines in
terms of time units, the part of the project value that is earned. The calculation of
ES is also demonstrated in figure 2.3.
Due to the fact that the value of ES is expressed in time units, its value can be
interpreted in relation to the Actual Time (AT), which indicates the time that has
passed from the beginning of the project until the present moment of calculation. The
comparison of AT with ES results in two new schedule performance measures.
SV (t) = ES −AT (2.7)
SPI(t) =ES
AT(2.8)
10
Figure 2.4: The SPI and SV versus SPI(t) and SV(t) performance measures. [35]
When SPI(t) < 1, the value that has been earned (EV) at the considered mo-
ment (AT), is equal to the value that should have been earned at time (ES), where
ES < AT . This thus indicates that the project is running behind schedule. When
SPI(t) > 1, the value that has been earned (EV) at the considered moment (AT), is
equal to the value that should be earned at time (ES), where ES > AT . This thus
indicates that the project is running ahead of schedule.
Figure 2.4 demonstrates the difference in schedule performance using earned value
method and earned schedule method.
2.4 Predicting the future
EVM can also be used to forecast cost and duration at project completion. For both
cost and duration forecasting, several different formulas have been proposed. In this
section an overview of the most important forecasters is given. This overview is not
exhaustive since a complete discussion of forecasters is outside the scope of this master
thesis.
2.4.1 Estimated cost At Completion (EAC)
The general formula for EAC is based on the sum of the Actual Cost incurred at the
considered time and the Budgeted Cost of Remaining Work (BCRW).
EAC = AC + BCRW (2.9)
In order to estimate the cost at project completion more accurately, assumptions
should be made about the performance of future work. If for example, a project
is running above budget, the project manager should decide whether the remaining
work will still be performed within budget or whether the remaining work is likely
to follow the trend of performing above budget. This assumption is expressed by a
Performance Factor (PF), which can then be used to adjust the Budgeted Cost of
Remaining Work. If it can be assumed that the rest of the project will be executed
according to plan, the Performance Factor (PF) is 1. If there are reasons to believe
11
that the rest of the project will be executed at the same level of cost performance
as the work that has already been executed, the Performance Factor is equal to the
Cost Performance Index (CPI). This means that the estimate of future performance
is corrected with the current value of CPI. If it is desirable not only to take the cur-
rent cost performance into account, but also the current schedule performance, the
Performance Factor can be expressed as SCI = CPI ∗SPI. The Schedule Cost Index
(SCI) thus serves as the correcting factor for future performance.
This results in 3 possible formulas for Budgeted Cost of Remaining Work.
BCRW =
BAC − EV, if PF = 1
BAC − EV
CPI, if PF = CPI
BAC − EV
CPI ∗ SPI, if PF = CPI ∗ SPI
(2.10)
2.4.2 Estimated duration At Completion (EAC(t))
In order to forecast the final project duration, the schedule performance measures
need to be translated from monetary units to time units. In literature, three methods
have been proposed and are evaluated and compared extensively with each other by
Vanhoucke [35]. In what follows, the highlights of this research are summarised.
The general formula for predicting a project’s total duration is given by the Es-
timated duration At Completion (EAC(t)) and is based on the sum of the Actual
Duration (AD) of the project thusfar and the Planned Duration of Work Remaining
(PDWR). Note that the Actual Duration is the same as the Actual Time used in
Earned Schedule calculations.
EAC(t) = AD + PDWR (2.11)
Planned Value method of Anbari
The PV method proposed by Anbari [1], is based on the traditional EVM met-
rics as described in section 2.2 and proposes some additional metrics.
Planned Value Rate (PVR)
PV R =BAC
PD(2.12)
The Planned Duration (PD) is defined as the scheduled duration of the en-
tire project, which can be derived from the baseline schedule. It is also known
as the Schedule At Completion (SAC). PVR thus indicates what amount of
12
value would be expected to be earned on average per scheduled time unit of the
project.
Time Variance (TV)
TV =SV
PV R(2.13)
In this method, PVR is used to translate Schedule Variance (SV) into time
units, denoted by Time Variance. The PV method does not directly give an
estimate for the Planned Duration of Work Remaining (PDWR). Instead, the
EAC(t) is based on the TV. Depending on whether PDWR performs according
to plan, follows the current SPI trend or the current SCI trend, three different
formulas are proposed as can be seen in table 2.1.
Earned Duration method of Jacob and Kane
A second method is proposed by Jacob and Kane [22]. This method defines
Earned Duration (ED) by making use of the Schedule Performance Index (SPI)
and the Actual Duration (AD).
ED = AD ∗ SPI (2.14)
In this method, SV and SPI are also translated in time units. For the calcula-
tion of EAC(t), the unearned remaining duration corrected by the Performance
Factor (PF) (see section 2.4.1) is added to the Actual Duration. The resulting
different formulas proposed by this method are shown in table 2.1.
Earned Schedule method of Lipke
As discussed in section 2.2.2, Lipke criticizes the use of SV and SPI as schedule
performance measures because of their unreliability near the end of a project.
He introduced two new schedule performance measures, SV(t) and SPI(t), that
are directly expressed in time units. Lipke calculates EAC(t) as the sum of
AD and the unearned remaining duration corrected by the Performance Factor
(PF). Table 2.1 also shows the resulting formulas for this method.
13
PD
WR
Anb
ari
[1]
Jaco
b(a
)[2
1]
Lip
ke[2
5]
Acc
ord
ing
top
lan
EAC
(t) P
V1
EAC
(t) E
D1
EAC
(t) E
S1
=PD−TV
=PD
+AD∗
(1−
SPI)
=AD
+(P
D−ES
)
Fol
low
ing
curr
ent
SP
I-tr
end
EAC
(t) P
V2
EAC
(t) E
D2
EAC
(t) E
S2
=PD
SPI
=PD
SPI
=AD
+PD−ES
SPI(t)
Fol
low
ing
curr
ent
SC
I-tr
end
EAC
(t) P
V3
EAC
(t) E
D3
EAC
(t) E
S3
=PD
SCI
=AD
+PD−ED
CPI∗S
PI
(b)
=AD
+PD−ES
CPI∗S
PI(t)
(c)
Tab
le2.1
:E
AC
(t)
Fore
cast
ing
Met
hod
s
(a)
Insi
tuat
ion
sw
her
eth
ep
roje
ctdu
rati
on
exce
eds
the
PD
,an
dth
ew
ork
isn
ot
yet
com
ple
ted
(i.e
.w
hen
AD
>P
Dan
dS
PI<
1),
the
PD
wil
lb
esu
bst
itu
ted
by
the
AD
.
(b)
Th
isfo
reca
stin
gfo
rmu
lad
oes
not
app
ear
inJaco
b[2
1]
an
dh
as
bee
nad
ded
by
Van
dev
oord
ean
dV
an
hou
cke
[33].
(c)
Th
isfo
reca
stin
gfo
rmu
lad
oes
not
app
ear
inL
ipke
[25]
an
dh
as
bee
nad
ded
by
Van
dev
oord
ean
dV
an
hou
cke
[33].
14
2.5 To Complete Performance Index
Lipke [26] researched the To Complete Performance Index (TCPI) which describes
the performance efficiency required to achieve a certain budgetary objective. This ob-
jective can be and is usually at the beginning of a project, the Budget At Completion
(BAC). In this case, TCPI is defined as follows:
TCPI =BAC − EV
BAC −AC(2.15)
The outcome of this equation is the minimal cost performance needed for the
remainder of the project to keep the resulting budget below BAC. If the required
cost performance is considerably higher than the actual cost performance, calculated
by CPI, it can be assumed that the budgetary objective is not realistic and that
the project will be completed with higher costs than anticipated. In this case the
project manager can reassess his budgetary objective (BO). The resulting calculation
for TCPI is then:
TCPI =BAC − EV
BO −AC(2.16)
TCPI expresses the required cost performance to keep the total project budget
below the project manager’s objective.
2.6 Conclusion
Although the many formulas may seem overwhelming at first, Earned Value Manage-
ment in se is a quite easy and straightforward technique. The overview that is given
in this chapter mainly contains the elements that will be needed further along this
master thesis, but should not be viewed as an exhaustive summary of all there is in
the field of EVM. For this purpose, the interested reader can be referred to the earned
value bibliography [7].
15
Part II
EVM from a contractor point
of view
16
Chapter 3
A review of the
comprehensive model for
planning and controlling
contractor cash flow
In what follows, an overview of the various measurements and indicators proposed
by Gorog in her paper ‘A comprehensive model for planning and controlling contrac-
tor cash flow’ [17] is given. Aside from the definitions and basic equations, further
explanation and extended formulas are provided. In chapter 4, an example project
is presented that will help to demonstrate the use and interpretation of the various
elements of the Contractor Cash Flow (CCF) model, by means of elaborate tables
and figures.
3.1 Measurements in the comprehensive model for
planning and controlling contractor cash flow
Price Value of Work Scheduled (PVWS)
Gorog [17] defines PVWS as ‘the value, in terms of price, earned by the contractor
when SPI = 1’ and calls it the ‘scheduled financial performance of the contractor’.
During the following chapters, a fixed percentage margin per activity is assumed. This
percentage is equal for all activities. Consequently, PVWS can easily be calculated
as follows:
PVWS = PV ∗ (1 + margin(%)) (3.1)
17
From the contractor’s point of view, PVWS represents the amount he wishes to
receive from his client for executing the project. In this master thesis, a fixed-price
contract is assumed, meaning that even in case of unforeseen difficulties, the client
will pay a price that was stipulated upfront. When cost is assumed to be directly
proportional to time, this is a clear incentive for the contractor to finish the project
on time or early if possible. From the client’s point of view, PVWS of an activity is
the cost of having this activity executed. Consequently, for him, PVWS is no more
than the Planned Value of that activity.
Price Value of Work Performed (PVWP)
In correspondence to PVWS, PVWP shows ‘the earned financial performance of the
actual achievement on a project activity’ [17] and can be calculated as follows:
PVWP = SPI ∗ PVWS (3.2)
Note that PVWP will always converge to PVWS at the end of the project. This is
caused by the conversion of EV to PV over the same time span which allows for SPI
to approach 1. From a contractor’s point of view, PVWP is a better measurement
of earned performance as it takes into account the financial earnings. From a client’s
point of view, PVWP is actually the EV of a project. As a result of working with a
fixed-price contract, the formula for PVWP can further be simplified as follows:
PVWP = SPI ∗ PV ∗ (1 + margin(%)) (3.3)
= EV ∗ (1 + margin(%)) (3.4)
Invoiced Value of Work Scheduled (IVWS)
IVWS is defined as ‘the measurement that expresses the value in terms of price that
could be invoiced by the contractor if the actual achievement (PVWP) was as much as
the scheduled achievement (PVWS)’[17]. It is clear that IVWS is greatly influenced
by both contract price (PVWS) and payment conditions, e.g., the moment a contrac-
tor can charge his client for an activity. In the example in chapter 4, a mechanism
that allows a contractor to invoice the stipulated price of an activity immediately
after completion of that entire activity, will be applied. Notice that this does not im-
plicate a cash flow movement, but only creates an additional value entry in ‘accounts
receivable’.
Invoiced Value of Work Performed (IVWP)
IVWP ‘encompasses that part of the earned financial performance (PVWP) which
may be invoiced’ [17]. IVWP relates to PVWP in the same way IVWS does to
PVWS. After the project is finished, these four values should be equal to one another.
However, this might not occur at the same time as payment mechanisms play an
18
important role in this scenario. If no advance payments exist, IVWP will always be
smaller than PVWP, as well as IVWS will always be smaller than PVWS.
Account Value of Work Scheduled (AVWS)
Gorog [17] defines AVWS as the measurement that ‘shows that part (which could be
100%) of IVWS which could be transferred to the contractor’s bank account if the
contractor’s actual achievement (PVWP) was as much as the scheduled achievement
(PVWS)’ [17]. This measurement depends greatly on the stipulated conditions for
payment delay in the contract, as well as the client’s payment routine, his trustworthi-
ness, etc. In the example in chapter 4, a fixed payment delay of two weeks is applied.
Assuming that the client will optimize his own cash flows and therefore delay his
payment to the maximal extent, the contractor’s account is only credited at the end
of the delay period. For reasons of simplicity it can also be assumed that the client
conscientiously pays the entire invoiced amount in one piece. In contrast to IVWS,
this measurement does in fact translate into an actual cash flow.
Account Value of Work Performed (AVWP)
In accordance to AVWS, AVWP is defined as the measurement that ‘represents that
part of the invoiced value (IVWP) which is transferred to the contractor’s bank ac-
count’ [17]. The necessary data to record the course of AVWP can therefore easily
be found on the contractor’s bank account receipts. It is clear that both AVWS
and AVWP should eventually, after completion of all project activities, be equal to
IVWS and IVWP, and by extension to the respective price values. Under normal cir-
cumstances AVWP and AVWS will always lag behind the respective invoiced values
(IVWS and IVWP), assuming that administrative delays may occur and assuming
that the contractor has granted some kind of payment delay of which the client will
take full advantage.
Expected Expenditure of Work Scheduled (EEWS)
EEWS is ‘the measurement that expresses the amount of money which would be
paid out by the contractor to finance the cost of implementing project activities if
the contractor’s actual achievement (PVWP) was equal to the scheduled achievement
(PVWS)’ [17]. For this measurement, the contractor can be considered as a client
that has obligations to pay its resource suppliers. For instance, in case of labor forces,
the ‘payment mechanism’ can be seen as the frequency with which a worker gets
paid, and the corresponding amount can be considered as the worker’s wage. In the
example in chapter 4, a fixed cost per time unit of an activity is assumed. The cost
per time unit is considered to be equal to the sum of all resource costs for that time
unit. The total cost of an activity (i) can therefore be calculated as the mathematical
19
product of the cost per time unit and the duration (dur) of that activity.
Costi = (cost/time unit)i ∗ duri i = 1, ..., n (3.5)
It becomes clear at once that under these circumstances, the lateness of an activity
has a direct impact on the contractor’s margin. In the example in chapter 4, another
assumption is made in regard to EEWS. ‘Consumed’ costs are paid on a monthly
basis regardless the completion of the activity that has generated them. Note that at
the end of a project, EEWS should be equal to the planned Budget At Completion
(BAC).
Actual Expenditure of Work Performed (AEWP)
AEWP corresponds to ‘the amount of money that is actually paid out by the con-
tractor in order to finance the cost of implementing the project activities’ [17]. At
the end of a project, EEWS should be equal to the planned Budget at Completion
(BAC) as well as AEWP should be equal to the sum of all incurred costs (∑
AC).
However, it is clear that due to payment mechanisms these equations will not be valid
throughout most of the project duration.
3.2 Indicators in the comprehensive model for plan-
ning and controlling contractor cash flow
Financial Variance (FV) and Financial Performance Index (FPI)
FV = PVWP − PVWS (3.6)
FPI =PVWP
PVWS(3.7)
Both indicators show the evolution of the price value of the performed work in com-
parison with the planned work. They are both indicators for the financial perfor-
mance of the contractor, in numerical terms and relative terms respectively. When
FPI < 1 at a certain time in the project, this indicates a lag in financial performance
caused by PVWP < PVWS. When FPI > 1 at a certain time in the project, this
indicates that the current financial performance is better than planned caused by
PVWP > PVWS.
20
Planned Invoice Variance (PIV) and Planned Invoice Perfor-
mance Index (PIPI)
PIV = IV WP − IV WS (3.8)
PIPI =IV WP
IVWS(3.9)
Both indicators show the evolution in terms of price of the actual invoiced amount
in comparison with the planned invoiceable amount, the former in numerical terms,
the latter as a ratio. This variance is strongly correlated with the earned financial
performance variance eventhough payment conditions can make this relatively difficult
to reveal. When PIPI < 1 at a certain time in the project, this indicates a lag in
invoiceable values caused by IV WP < IVWS. When PIPI > 1 at a certain time
in the project, this indicates that the current financial performance is better than
planned caused by IV WP > IVWS.
Invoice Variance (IV) and Invoice Performance Index (IPI)
IV = IV WP − PVWP (3.10)
IPI =IV WP
PVWP(3.11)
Both IV and IPI are indicators for the progress of the invoiced part of the achieved
financial performance in comparison with the entire achieved financial performance.
IV indicates the variance in numerical terms while IPI shows this variance in relative
terms. In the example in chapter 4 it is assumed that invoices can only be sent out to
the client after an activity is completed. This implies that it will be impossible that
IV WP > PVWP and thus that IV will have positive values or IPI > 1. This would
however be possible if premature invoices are allowed.
Account Variance (AV) and Account Performance Index (API)
AV = AVWP − IV WP (3.12)
This indicator shows the amount that is still due to the contractor. The necessary
data to record the course of AV can therefore easily be found on the balance post
‘accounts receivable’. In the example in chapter 4 it is impossible to have a positive
value for AV as advance payments are not taken into account.
API =AVWP
IVWP(3.13)
This indicator makes it possible to monitor the progress of the relative amount that
is still due to the contractor. Corresponding to the fact that AV > 0 does not occur
21
in the example in chapter 4, API > 1 is equally impossible as passive debts are not
allowed. API will always be smaller than 1, indicating that there are still oustanding
debts untill the final phase of the project where the client is assumed to pay the
contract price as stipulated.
Planned Balance Variance (PBV) and Planned Balance Perfor-
mance Index (PBPI)
PBV = AVWS − EEWS (3.14)
This indicator shows the balance of all planned incoming (AVWS) and outgoing
(EEWS) cash flows.
PBPI =AVWS
EEWS(3.15)
PBPI shows the relative evolution of the planned incoming cash flows compared to the
planned outgoing cash flows. Values that exceed 1 indicate a positive cash position,
whereas PBPI = 1 indicates a break-even situation. When PBPI < 1, then the
planned cash flow balance is negative, indicating that there’s a planned cash deficit
or that the project is no longer self-sustainable.
Actual Balance Variance (ABV) and Actual Balance Perfor-
mance Index (ABPI)
ABV = AVWP −AEWP (3.16)
This indicator shows the balance of all actual incoming (AVWP) and outgoing (AEWP)
cash flows.
ABPI =AVWP
AEWP(3.17)
ABPI shows the relative evolution of the actual incoming cash flows compared to the
actual outgoing cash flows. Values that exceed 1 indicate a positive cash position. If
ABPI < 1, then the actual cash flow balance is negative, indicating a cash deficit.
Plan Variance (PVar) and Plan Performance Index (PPI)
PV ar = ABV − PBV (3.18)
PPI =ABV
PBV(3.19)
22
Both indicators show the evolution of a contractor’s actual cash flow balance compared
to his planned cash flow balance. Note that, as ABV and PBV could both have
negative values, only their numerical values are considered. When ABV and PBV
have opposite signs, interpretation becomes more difficult. PV ar > 0 and PPI > 1
both indicate that the actual balance exceeds the planned balance and is a favorable
cash position.
3.3 Forecaster in the comprehensive model for plan-
ning and controlling contractor cash flow
Gorog [17] points out in her paper that in practice, many contractors will compete for
the same project. Therefore, the need exists for a contractor to elaborate a competi-
tive bid price. This might be done by accurately forecasting the likely margin earned
by the contractor. It is in this regard that in this section an additional indicator is
presented that aims at calculating the Expected Margin at Completion (EMC).
EMC = AM + (PMC − PM) ∗MPI (3.20)
3.3.1 Components of the EMC formula
In order to better grasp the formula of EMC, the individual elements are listed below.
Actual Margin (AM)
AM = PVWP −AC (3.21)
Planned Margin (PM)
PM = PVWP − EV (3.22)
Note that the denomination ‘Planned Margin’ can be quite confusing as it in
fact indicates what can better be clarified by the term ‘Earned Margin’. PM is
equal to the difference between the price value of what should be earned based
on the percentage of work completed and the earned value in terms of cost.
Therefore, it is important not to confuse this Planned Margin with what could
be called ‘Scheduled Margin’ (SM). Scheduled Margin can then be defined as
follows: SM = PVWS − PV .
Margin Performance Index (MPI)
MPI =AM
PM(3.23)
23
MPI indicates, as a ratio, the evolution of the contractor’s potential margin at a
certain reporting date. If negative values would occur, MPI should be considered
in absolute terms in order to make sense. AM > PM leads to MPI > 1 which
indicates that the actual margin exceeds the earned margin.
Planned Margin at Completion (PMC)
PMC = IAC −BAC (3.24)
Planned Margin at Completion is equal to the difference between the Invoice
value At Completion (IAC) and the planned Budget At Completion
(BAC). IAC represents the total planned price value of the project (∑
PVWS),
or simply the contract price. BAC is know from traditional earned value calcu-
lations and represents the sum over all planned values (∑
PV ).
3.3.2 Critical analysis of the EMC formula
The proposed formula for EMC seems closely related to the one of the earned value
cost predictor, Estimated cost At Completion (EAC), as discribed in section 2.4.1.
Corresponding to the estimation of cost at completion (equation 2.9), equation 3.20
starts its estimation of the margin at completion at a specific point in the project
duration, from the part of the margin that is already earned at that certain moment.
This part is then augmented with the difference between the scheduled margin at the
time of project completion (PMC) and Planned Margin (PM), to indicate the amount
(in terms of margin) that could still be earned. In order to represent a more realistic
prediction, the second part of the equation is then multiplied by MPI, which should
be an indication for future performance. Comparable, when it is assumed in equation
2.10 that PF = CPI, the resulting equation for EAC indicates that the Actual Cost
is augmented with the cost or value that can still be occurred or earned (Budgeted
Cost of Remaining Work (BCRW)), divided by the Cost Performance Index as an
assumption for future (margin) performance that should provide a more realistic es-
timate.
Although equation 3.20 is very useful for explaining the different components of
EMC, some derivations can be made in order to better indicate how the estimation is
really done. Starting from equation 3.20 and based on equation 3.23, EMC can easily
be rewritten as follows:
EMC = AM + (PMC − PM) ∗ AM
PM
= AM + (PMC ∗AM
PM− PM ∗AM
PM)
= AM + (PMC ∗ AM
PM)−AM
= PMC ∗MPI (3.25)
24
Note that this formula is independent of payment mechanisms or contract type as
it does not contain any measurements that are inherent to pay patterns or pay delay
such as IVWS, IVWP, AVWS, AVWP, etc. Equation 3.25 clearly indicates that apart
from the scheduled margin at project completion, which is a constant, MPI has the
largest impact on this formula.
25
Chapter 4
Example project
In order to better demonstrate the use and meaning of aforementioned measurements,
indicators and forecaster in the model for planning and controlling contractor cash
flows, a comprehensive project is developed and presented. Figure 4.1 contains the
activity-on-the-node representation of the network with for each of the 5 non-dummy
activities its planned duration and resource cost per time unit. Note that the start
and end node are dummy activities to which no duration or resource cost is allocated.
For reasons of simplicity, no resource constraints were taken into account. There-
fore each activity of the project can be scheduled as soon as possible, resulting in a
baseline schedule with a duration of 12 time units and a budget at completion of 161.
Figure 4.1: Example project: Activity-on-the-node representation
26
4.1 Assumptions
Throughout the examples in this text, a variety of assumptions are made that are
mutually consistent and thus form a logical entity.
As mentioned in the introduction of this chapter, no resource constraints are taken
into account. Although this is in fact a simplification, it is common in literature and it
can also be argued that under normal circumstances, a project manager would assess
the requested resources and approves a value for them in the form of an authorized
budget [14].
The previous assumption implies that the proposed project network can be trans-
formed into an as early as possible project schedule, based on the critical path based
forward pass calculations. In literature, however, other scheduling techniques are of-
ten used. Kolisch [24] proposes a study on the use and effectiveness of a wide range of
priority rules for the Resource Constrained Project Scheduling Problem (RCPSP). He
concludes that the Latest Finish Time (LFT) and the Minimum Slack (MSLK) prior-
ity rules result in the most beneficial schedules. In addition, Critical Chain Scheduling
and Buffer Management (CC/BM) [16] is known to depart its analysis from an as late
as possible project schedule in order to grasp some of the same benefits that can be
derived from just-in-time (JIT) methods in manufacturing. These benefits mainly
constitute of the following [19]:
1. Reduced number of Work-In-Progress (WIP).
2. Decreased risk of rework.
3. Optimized Net Present Value by pushing costs until they really need to be
incurred.
Although these arguments might prove to be very viable in certain scheduling
environments, in this example they do not hold much power as a fixed margin is asso-
ciated with each activity. The assumption of a fixed percentage margin (margin(%))
was made for several reasons. First of all, it aides in preserving the analogy with
traditional earned value calculations where value is earned for work as it is accom-
plished. It seems fair to uphold the same methods concerning margin. Second, it has
recently been defended by Anderson [2] that Activity-Based Costing (ABC) is appli-
cable in the context of project management and the encompassing methodology of
Earned Value Management. Because ABC links the performance of an activity with
its resource demand, the revenues from products or services can be directly matched
with the consumed resources [11]. The link with earned value is easily made and the
performance can be measured in terms of margin, thus justifying the use of a fixed
percentage margin per activity.
27
As mentioned in section 3.1, a mechanism that allows a contractor to invoice the
stipulated price of an activity only after completion of that entire activity will be
applied. This entails that, even though it is a common phenomenon in practice, no
advance payments are taken into account. This might limit the use of some of the
indicators as will be demonstrated in section 4.2, yet this mechanism is defended by
Fleming and Koppelman [15]. They state that payments based on the physical com-
pletion of authorized work (Performance Based Payments (PBPs)) are in fact a simple
form of earned value management. With PBPs, nothing is paid to the contractor until
the agreed-to milestones are completely finished. In this part of the document, the
milestones are simply fixed onto the completion of individual activities. Fleming and
Koppelman also argue that PBPs are especially suitable when a fixed-price contract
is assumed. Not only does this additional assumption guarantee consistency in the
entity of assumptions, but it does also improve the possibility to clearly illustrate
Gorog’s concept as described in chapter 3.
In order to keep the example as comprehensible as possible some additional as-
sumptions are made in regard to the payment mechanisms of the client and the
contractor.
1. The client pays the entire amount as invoiced outright.
2. The client is granted a pay delay of 2 time units (weeks) and takes full advantage
of this concept.
3. No administrative delays are taken into account.
4. The contractor pays his resource suppliers on a monthly basis, proportional to
the consumed resources.
5. Change in activity duration results in a proportional change in total cost of that
activity.
4.2 Real scenario
When we assume that due to unforeseen circumstances, the duration of some activi-
ties is altered, a new scenario arises with a new duration of 14 time units and a new
cost at completion of 183.
Figure 4.2 shows a Gantt chart of the original and actual situation. Delays occur
for activity 2, 3 and 5, while activity 4 is able to finish in a shorter time span than
scheduled. The total makespan of the project is altered from 12 to 14 time units, due
to the delay in activity 3, which is on the critical path.
Tables 4.1, 4.2 and 4.3 present values for the measurements, indicators and fore-
casters respectively, as defined in chapter 3. The values are calculated per activity in
28
Activity Time units
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1
2
3
4
5
Planned Duration
Actual Duration
Figure 4.2: Example project: Gantt Chart
order to clearly indicate the effect of earliness or lateness for each activity, and after 7
time units of the example project have passed. Notice that at this point in time activ-
ity 1 has already been completed, as well as activities 2 and 5, despite their lateness.
This can also be concluded from the fact that in table 4.1 their respective Planned
Values and Earned Values are equal to one another. Some interesting observations
can be made.
Table 4.1 contains the aforementioned measurements of the model for planning
and controlling contractor cash flows as well as some of the traditional earned value
metrics. Although activity 3 was able to start at time unit 5 as planned, it is per-
forming behind schedule and the fact that only 30% instead of 37.5% is completed at
time unit 7, leads to a PVWS greater than PVWP. The similar proportional distinc-
tion can be found with PV and EV. As mentioned before, this is to be expected, as
PV and EV indicate more or less the same as PVWS and PVWP respectively, apart
from the incorporation of the scheduled margin and under the assumptions made in
section 4.1. The analogy between these measurements can clearly be observed when
comparing the Schedule Performance Indicator (SPI) and the Financial Performance
Indicator (FPI) for each activity in table 4.2.
Activity 4 on the other hand is performing ahead of schedule, with about 10% more
completed than initially planned, which results in PVWS being smaller than PVWP.
These inequalities between PV and EV as well as PVWS and PVWP, will be leveled
out at time unit 14 and 9 for activity 3 and 4 respectively.
When evaluating AVWS and AVWP of activity 5, it can be seen that if the activ-
ity had been on time, it would have been completed at time unit 5. At this moment,
an invoice equal to the price value could have been sent out to the client and the
amount of PVWS could be transferred to the bank account of the contractor two
weeks later, which would be at time unit 7. However, due to the delay, the invoice
can only be sent out at time unit 7 and as a consequence, the contractor will have
to wait two more weeks to receive the money on his account. This thus results in
29
a difference between AVWS and AVWP, which can also be concluded from looking
at the Account Variance indicator in table 4.2 for activity 5. However, sometimes it
may be necessary to consider both Account Variance and Account Performance Index
simultaneously. In fact, when AV = 0 it can either mean that no amount has been
invoiced yet and therefore no amount is registered on the contractor’s bank account,
or it could also mean that the invoice has indeed been sent out and the money has
already been received by the contractor. When combined with API it becomes clear
at once that when API = 1, one finds himself in the latter situation and when no
value exists for API, the former situation has occurred.
The same need to simultaneously analyze two related indicators can be found
with Planned Invoice Variance (PIV) and Planned Invoice Performance Index (PIPI).
Possible and meaningful combinations of these indicators could be the following:
1. PIV = 0 and PIPI = 1 : The value that was planned to be invoiced at this
time is also invoiced in reality.
2. PIV = −PVWS and PIPI = 0 : This combination indicates that concerning
invoiced value, the project is behind schedule. While IVWS is already equal to
PVWS, nothing has actually been invoiced yet (IV WP = 0).
3. PIV = 0 and PIPI has no value : No amount was scheduled to have been
invoiced yet, nor was any invoice actually sent out.
4. PIV = PVWP and PIPI has no value : The project is ahead of schedule
concerning invoiced value. Although no amount was scheduled to have been
invoiced, IVWS is already equal to PVWP.
Table 4.3 presents the values of the forecaster EMC as well as the values of the
different components which constitute EMC. In section 3.3, the formula for EMC
was rewritten as equation 3.25, indicating that the Margin Performance Index will
probably have the most impact on the forecast accuracy. For activity 1, which started
and finished on schedule, MPI equals 1, meaning that the actual obtained margin is
equal to the planned margin. However, for activity 3, MPI equals 0.5, indicating that
based on current performance, it is projected that only 50% of the planned margin
will be recuperated for this activity due to its lateness.
30
Mea
sure
men
ts
Act
ivit
yP
VE
VA
CP
VW
SP
VW
PIV
WS
IVW
PA
VW
SA
VW
PE
EW
SA
EW
P
132
3232
48
48
48
48
48
48
32
32
224
2436
36
36
36
36
36
36
24
38
315
1215
22,5
18
00
00
00
425
2820
37,5
42
00
00
10
55
3030
4045
45
45
45
45
020
10
Tot
al12
612
614
3189
189
129
129
129
84
86
83
Tab
le4.1
:E
VM
an
dco
ntr
act
or
cash
flow
mea
sure
men
ts
31
Ind
icato
rs
Act
ivit
yS
VC
VF
VP
IVIV
AV
PB
VA
BV
Pva
rM
VS
PI
CP
IF
PI
PIP
IIP
IA
PI
PB
PI
AB
PI
PP
IM
PI
10
00
00
016
16
00
11
11
11
1,5
1,5
11
20
-12
00
00
12
0-1
2-1
21
0,6
71
11
11,5
10
0
3-3
-3-4
,50
-18
00
00
-30,
80,8
0,8
-0
--
--
0,5
43
84,5
0-4
20
-10
-55
81,
121,1
41,1
2-
0-
00
0,5
1,7
5
50
-10
00
0-4
525
-10
-35
-20
10,7
51
11
02,2
50
0,4
0,3
3
Tot
al0
-17
00
-60
-45
43
1-4
2-1
71
0,8
81
10,6
80,6
51,5
1,0
10,0
20,7
3
Tab
le4.2
:E
VM
an
dco
ntr
act
or
cash
flow
ind
icato
rs
32
Forecasters
Activity AM PM IAC BAC MPI EMC
1 16 16 48 32 1 162 0 12 36 24 0 03 3 6 60 40 0,5 104 22 14 52,5 35 1,57 27,55 5 15 45 30 0,33 5
Total 46 63 241,5 161 0,73 58,78
Table 4.3: Contractor cash flow predictors
4.3 Aggregate project level
As mentioned, the tables in section 4.2 provide values for the various measurments
and indicators per activity in order to clearly demonstrate the impact of earliness
or lateness of individual activities. It can be equally interesting to consider these
values on the aggregate project level and to monitor them throughout the entire
makespan of the project. Figures 4.3, 4.4, and 4.5 consecutively show the progress of
the measurements, indicators, and forecaster along the life of the example project.
33
(a)PVW
SandPVW
P(b
)IV
WSandIV
WP
(c)AVW
SandAVW
P(d
)EEW
SandAEW
P
Fig
ure
4.3
:C
ontr
act
or
Cash
Flo
wM
etri
cs
34
(a)FV,PIV
,IV
andAV
(b)FPI,
PIP
I,IP
I,API
(c)ABV
andPBV
(d)ABPIandPBPI
Fig
ure
4.4
:C
ontr
act
or
Cash
Flo
wIn
dic
ato
rs
35
(a) Margin Performance Index
(b) Planned, Actual and Estimated Margin at Completion
Figure 4.5: Contractor Cash Flow Forecast Indicators
36
Chapter 5
Further insights and critical
analysis
5.1 Relationship with traditional EVM
The contractor cash flow (CCF) indicators and measurements, as proposed by Gorog
[17] and thoroughly explained in chapter 3, are closely related with the traditional
EVM metrics reviewed in chapter 2 and 4. The three major components of EVM are
PV, AC, and EV. Based on these three components, schedule and cost performance
indicators are composed as well as predictors to estimate budget and time at com-
pletion. For a detailed description of these elements, the reader is referred to chapter
2. Figure 5.1 gives a comprehensive overview of the CCF measurements and their
relationship with each other and with traditional earned value metrics. Throughout
this chapter, figure 5.1 will serve as a guideline to illustrate some interesting insights.
From a contractor point of view, these basic EVM components can be translated
into other components, which have, in terms of cash flow, a greater meaning for
the contractor according to Gorog [17]. On the one hand, the contractor provides a
product or service, for which he earns a fee. On the other hand, the contractor has
to pay his resource suppliers in order to be able to provide that product or service.
As workers’ salaries, raw materials, etc., need to be paid in time, it is obvious that
sufficient cash should be available. Moreover, it is arguable that the required finan-
cial means to execute a project should be generated by that same project or another
project from the contractor’s portfolio. Gorog proposes some measurements to track
the availability of cash flow.
37
+ Ti
me
shift
of
cont
ract
or’s
pa
y de
lay
+ Ti
me
shift
of
invo
ice
dela
y
+ Ti
me
shift
of
cust
omer
’s
pay
dela
y
!"#
$"#
SV,
SPI(%
)
$"%$#
&"%$#
&"%'#
("%
$#("%
'#+ m
argi
n
PIV,
PIP
I(%)
FV, F
PI(%
)
IV, I
PI(%
)
()#
(!%
$#!!%'#
CV,
CPI
(%)
AV,
API
(%)
$"%'#
AB
V, A
BPI
(%)
PBV,
PB
PI(%
)
+ Ti
me
shift
of
cont
ract
or’s
pa
y de
lay
+ m
argi
n
+ Ti
me
shift
of
invo
ice
dela
y
+ Ti
me
shift
of
cust
omer
’s
pay
dela
y
Fig
ure
5.1:
Ove
rvie
wof
EV
Man
dco
ntr
act
or
cash
flow
met
rics
an
din
dic
ato
rs
38
A direct result of incorporating cash flows in earned value calculations is that
the value that can be earned translates into two different movements, namely cash
inflows and cash outflows. These two movements consequently result into two different
categories of metrics: revenue-based metrics and cost-based metrics. This can be seen
by looking at Planned Value and the metrics related to PV in figure 5.1.
5.1.1 Revenue-based metrics
Revenues are created from the execution of a project. Starting from the Planned
Value, which is the estimated cost for the contractor to carry out a certain task or
project, a margin is added to obtain the Price Value of Work Scheduled. This margin
can be a percentage of the costs or an arbitrary value. Similarly, the Price Value of
Work Performed is obtained by adding the same margin to the Earned Value. PVWP
is thus the value a contractor has already earned, based on the work performed, in
terms of price, whereas EV is the value a contractor has already earned, based on the
work performed, in terms of cost.
As figure 5.1 clearly indicates, the traditional EVM metrics and the CCF metrics
are closely related to one another. Comparing PVWP with PVWS gives rise to two
performance indicators FV and FPI. If the margin is calculated as a percentage of
PV, FPI will always equal SPI. This can be easily understood. Since PVWS and
PVWP will be augmented with the same percentage, their ratio will not change. If
the contractor would sell at cost, the margin would be 0 and PV would be equal to
PVWS whereas EV would be equal to PVWP.
Before the contractor can receive the money, he should send an invoice to his
client. In practice, invoices are not sent continuously, but they are sent at specific
milestones or at specified time intervals. In the example project presented in chapter
4, the contractor can send an invoice to the client after an activity is finished. As a
consequence, the Invoice Value of Work Scheduled will evolve in steps. Every time an
activity is estimated to be completed, the PVWS of that entire activity is added to
the IVWS. In the same way, every time an activity is finished when actually execut-
ing the project, PVWP of that activity is added to IVWP. Since, for every individual
activity, PVWS always equals PVWP at the end of the activity, IVWS and IVWP
are incremented with the same value, but at different time units because of distinc-
tions between the real and the planned scenario. IVWS and IVWP are compared to
each other, which result in two performance indicators PIV and PIPI. In addition,
IVWP is compared with PVWP resulting in IV and IPI. For a detailed explanation
of the indicators, the reader is referred to section 3.2. If however, there would be a
possibility to invoice all costs and the corresponding margin directly after they were
incurred, IVWS would be equal to PVWS and IVWP would be equal to PVWP. As
a consequence, IV and IPI would always be 0 and 1 respectively.
39
After the invoice is sent, the client is usually not required to pay immediately. In
most real-life scenarios, he can choose between a price reduction or a pay delay. In
the example project presented in chapter 4, it was assumed that the client always
pays exactly 2 weeks after the contractor sent the invoice. If a fixed pay delay is
assumed and the contractor receives the money directly when the client performs the
transaction, AVWS at time t will always be equal to IVWS at time (t−y), with y the
fixed pay delay. In contrast with the other measurements, AVWP and AVWS are not
compared to each other. AVWP is compared with IVWP resulting in AV and API.
For a detailed explanation of the indicators, the reader is referred to section 3.2. If
there is no pay delay however, AVWS will always be equal to IVWS and AVWP will
always be equal to IVWP. As a consequence, AV and API will always equal 0 and 1
respectively.
5.1.2 Cost-based metrics
As mentioned, each ‘project value’ has an associated revenue, which is the result of
value being delivered to the customer, and an associated cost, which the contractor
incurred while executing a certain activity. In traditional EVM, the PV is an indi-
cation of the estimated costs of a project or activity. The contractor will not have
to pay these costs directly after they occurred, however. Therefore, in the contractor
cash flow (CCF) model, this cost is presented by the Expected Expenditure of Work
Scheduled (EEWS), which takes on the amount of the cost when it manifests itself.
In the example project presented in chapter 4, it is assumed that the contractor
pays all costs at the end of every month. As a consequence, the Estimated Expenditure
of Work Scheduled will increase with steps. At the end of every month, EEWS
will be increased with the PV of the work scheduled during that month. AC might
deviate from PV however due to unforeseen events. The Actual Expenditure of Work
Performed is incremented at the end of every month with the real costs incurred during
that month. EEWS is compared with AVWS and AEWP with AVWP resulting in
ABV, ABPI, PBV and PBPI. For a detailed explanation of the indicators, the reader
is referred to section 3.2.
5.1.3 Final comparison
To illustrate the relationship with EVM, assume that there is no invoice delay and
no pay delay for customer and contractor. Moreover, the margin is still assumed to
be a fixed percentage of PV. In that case
PV ∗ (1 + margin(%)) = PVWS = IV WS = AVWS
40
and
EV ∗ (1 + margin(%)) = PVWP = IV WP = AVWP.
Moreover
PV = EEWS
and
AC = AEWP.
As a consequence,
SPI = FPI = PIPI
and
FV = PIV.
IV and IPI will be 0 and 1 respectively, as will be AV and API. PBV will be equal
to the scheduled margin and PBPI will be equal to (1+scheduled margin(%)). In this
case, where no invoice delay nor pay delay is taken into account, (1+scheduled margin(%))
is a constant. In the same way, ABV will be equal to the actual margin and ABPI
will be equal to (1 + actual margin(%)).
5.2 Usefulness of Contractor Cash Flow (CCF) In-
dicators
Some of the indicators proposed by Gorog [17] clearly serve the contractor, others
do not seem to be of great value. For instance, in case the margin is defined as a
fixed percentage of cost, Financial Variance and Financial Performance Index give
the exact same information as Schedule Variance and Schedule Performance Index.
The formula of FPI is based on the same metrics as SPI, yet both the nominator and
the denominator are multiplied with an identical factor (1 + margin(%)). There is
no added value for the contractor so he will not have an incentive to make use of them.
PIV and PIPI provide information about the difference between IVWP and IVWS.
IVWP and IVWS will not equal one another if the real project scenario deviates from
the planned project scenario. Eventhough Planned Invoice Variance can be a good
first warning sign of a certain amount of cash inflows being ahead or behind invoice
schedule, the performance of IVWP compared to IVWS is fully dependent on the time
performance, expressed by SPI, and the invoice conditions. As a consequence, the
interpretation of PIPI is very difficult since the contractor should take only the com-
pleted activities into account, as wel as their individual time performances. Moreover,
the information provided by the indicator is actually nothing more than an indication
of time performance which can be measured more easily by SPI.
41
IV and IPI evaluate the deviation of PVWP and IVWP. This deviation fully de-
pends on the invoice conditions and not on the performance of a project. The same
goes for AV and API. These indicators evaluate the deviation of IVWP and AVWP
which is only dependent on the payment conditions for the customer. Although the
gap between IVWP and AVWP, denoted by Account Variance, is obviously very
important from a bookkeeping perspective, monitoring the progress of accounts re-
ceivable is not interesting from a project management point of view. It would be inter-
esting however to look at the difference between IVWP(t) and AVWP(t+ pay delay)
since this would be an indication of customers not meeting the payment conditions.
But again, this belongs more to the accounting department than to the field of track-
ing project performance. The added value of AV and API to traditional EVM is
therefore questionable.
It was mentioned in section 5.1 that the first result of incorporating cash flows in
earned value calculations is that (planned) value is translated into two movements,
namely a revenue inflow and a cost outflow. Taking into account the moment in the
project duration at which these flows are scheduled to occur, results in AVWS and
EEWS. Their relationship is expressed by Planned Balance Variance and Planned
Balance Performance Index, which indicate the planned cash-position of the contrac-
tor. These indicators are more likely to be of great value to the contractor as they
provide information about the self-financing capacity of a project. Futhermore, PBPI
can help the contractor to schedule project activities in a way that avoids a negative
cash-position ex ante. The use of PBPI is further elaborated in section 5.3. ABV and
ABPI are an indication of the real cash-position of the contractor as they compare
EVWP and AEWP. Planned and real cash position will deviate due to differences in
planned and real time and cost performance, expressed by CPI and SPI.
In practice, whether or not a contractor hauls in a project at the expense of his
competitors, depends to a great extent on the time in which he deems it possible to
execute the project, as well as on the price he states for his services. As mentioned,
Gorog points out in her paper [17] that in this regard, it is important for a contractor
to be able to propose a competitive bid price when in the running for a project.
Therefore, not only does he need to have good insights on the risks involved when
executing the project, but above all he should be able to make an accurate estimate
of what his final margin will be under various circumstances. The proposed indicator,
Estimated Margin at Completion (EMC), could thus be of great use. That is, under
the condition that EMC is able to accurately forecast the margin a contractor can
expect at the end of the project. Therefore, a simulation study will be set up in part
III, in order to test this accuracy under various circumstances.
42
5.3 Practical use of PBPI
5.3.1 Introduction
During the project execution, the contractor is confronted with cash inflows and cash
outflows. A project is defined as self-financing if the total cash inflow is greater than
or equal to the total cash outflow. It is only logical that at the end of a project, the
planned cumulative cash inflows exceed the planned cumulative cash outflows, other-
wise the contractor would not have undertaken the project in the first place. However,
taking into account that resource suppliers need to be remunerated on a regular basis,
and client payments only come in on predefined milestones, the fact that a project is
self-financing as a whole is not enough to make sure that the contractor can meet all
the payment conditions applicable to his project. If the project is not self-financing
at a certain moment during its life, the contractor should take this into account. He
should make sure that enough cash inflows from other projects are available or that
cash providers are able to provide the amount needed in order to be able to pay his
debts. Therefore, he should make a scheme of the planned cash position throughout
the project taking all payment conditions into account. This can be done through the
Planned Balance Variance (PBV). If at a certain point in time PBV is greater than
0, cash outflow is smaller than cash inflow and the contractor will be able to pay his
creditors in time. If PBV is smaller than 0 however, the contractor should look for
other cash inflows in order to be able to pay his creditors.
The contractor knows the price value of all activities and the planned times at
which he will receive this amount from the client, based on the contract and his
project schedule. He also knows the moments he should pay his suppliers, employees,
etc. When the same assumptions regarding payment conditions, cost structure and
margin (50%) are applied as described for the example project in chapter 4, the Net
Present Value (NPV) of the project will be maximized if all activities are scheduled
as soon as possible. However, if this type of scheduling at times puts the contractor
in a difficult cash position, it might be worthwhile for him to give up part of his Net
Present Value and to improve his cash position by postponing non-critical activities.
Note that critical activities are excluded from this analysis as the project makespan
is assumed to stay fixed to the originally scheduled makespan.
The Planned Balance Performance Index (PBPI) measures the planned cash per-
formance of the contractor. PBPI provides the same information as PBV but is
expressed as a ratio. The contractor should avoid values of PBPI below 1 since this
indicates that he will be confronted with a cash shortage somewhere during the life
of the project.
43
5.3.2 Dataset
In this section, the possibility for improving the cash position of the contractor by
postponing non-critical activities is investigated. For this analysis, a set of 900 project
networks is used [12]. This dataset was generated under a highly controlled design to
guarantee maximum diversity. The topological structure of a network can be defined
by the combination of 4 topological indicators, namely the Serial or Parallel (SP)
indicator, the Activity Distribution, the Length of Arcs, and Topological Float. As
only SP is likely to influence the results, the other topological indicators will take on
random values and will not be discussed any further.
As described by Vanhoucke ([34], p.57), ‘SP can take on values between 0 and 1
and measures the closeness of a given network to a serial or parallel structure. More
precisely, when SP = 0, all activities can be executed in parallel, and when SP = 1,
the project network is built up entirely out of serial activities. Between these two
extreme values, networks can be generated close to a serial or parallel network. Hence,
the SP indicator determines the maximal number of levels of the network, defined as
the longest chain (in terms of number of serial activities) in the network’.
The SP indicator can be formulated as follows:
SP =
1, if n = 1m− 1
n− 1, if n > 1
(5.1)
With n the number of non-dummy activities in an Activity-on-the-Node network and
m the maximal progressive level.
For an extensive study of the other topological indicators, the reader is referred
to Vanhoucke [34].
These 900 project instances represent a wide variety of diverse projects on which
this analysis will be based. No resource constraints are taken into account and each
network is transformed into an as early as possible project schedule, based on the
critical path based forward pass calculations. Costs per time unit are generated
randomly for each activity. In this analysis a linear relationship between costs and
the duration of each activity is assumed as shown in equation 3.5.
5.3.3 Baseline optimization
For each project network, the baseline metrics AVWS and EEWS are calculated as
well as the resulting indicators PBV and PBPI. This makes it possible to investigate
the scheduled cash performance, for each of the 900 project network instances by
tracking values of PBPI below 1. For this analysis, the Percentage Cash Shortage
(PCS), defined as the sum of all scheduled PBPI deficits, is calculated for each project.
PCS =
T∑t=1
(1− PBPI(t)) if PBPI(t) < 1 (5.2)
44
The objective is to minimize PCS for every project by rescheduling non-critical
activities. The project schedule resulting in the smallest PCS possible is found by
applying a local search algorithm on the network. The procedure can be described
as follows. The earliest and latest start times for each activity are found by applying
the critical path based forward and backward pass calculations. The slack, defined
as the difference between both, is an indication of the degree of freedom an activity
has for being scheduled. The initial value of the objective value (OV), PCS, is then
calculated based on the earliest start schedule. Next, an algorithm was created that
allows certain combinations of activities to use up a part, which could be 100% of their
slack in order to obtain different schedules. For each of these different schedules, the
objective value is recalculated and the ones that result in an improved OV are being
saved. When no more improvements on the OV can be found, the total improvement
is calculated through comparison of the initial and best OV.
PBPImax Improvement =PCSinitial − PCSbest
PCSinitial(5.3)
This procedure is repeated for all of the 900 project network instances and is
schematically depicted in figure 5.2.
OVinitial = OVbest
!"#$%&'()"*+%
,#'-."/+%0+#'+%0*1"$2-"%
3(*#-%0"#'*1%4-5('.+16%
7"8%0*1"$2-"%
RanGen (Demeulemeester
et al.[12])
Repeat If OVnew< OVbest then OVbest = OVnew
OVnew
Figure 5.2: Methodological approach of the scheduling problem
45
The mean PBPI improvement is calculated per 100 networks belonging to the
same SP factor. The results of this analysis are shown in figure 5.3. The largest
average improvements are found for parallel networks. This is easy to understand as
parallel networks on average have more slack, which result in more possibilities to
reschedule and to tune cash inflows and cash outflows. The improvements for serial
networks are considerably lower.
!"
#!"
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%!"
&!"
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+,-!.'"
+,-!.("
+,-!.)"
+,-!.*"
+,-!./"
PBPI improvement(%)
Figure 5.3: PBPI improvement per SP for baseline optimization problem
As mentioned above, postponing activities results in postponing client payments
and thus diminishes net present value, especially as the paid amounts are calculated
based on the incurred costs plus margin. The contractor should take both the im-
provements of his cash position and the deterioration of NPV into account. As can be
seen for an example project in figure 5.4b, NPV does not necessarily move downwards
in a straight line. After decreasing for a while, it is possible that for improved values
of PBPI, NPV slightly recovers. The contractor should balance both NPV and his
Cash Shortage when making his scheduling decisions. Note that this trade-off also
depends on the number of possibilities the contractor has to bridge cash deficits (in
a costless manner).
46
(a) Progress of PCS with procedure (EV200 [12])
(b) Progress of NPV with procedure (EV200 [12])
Figure 5.4: Variability in Activity Duration: Evolution of MPI
47
5.3.4 Baseline Leveling
Applying the same procedure used for minimizing PCS, it is possible to level PBPI
around a favorable range. In this case, the objective is to minimize extreme values
of PBPI both under 1 and above 1. Lets assume that the lower level x and the
upper level y bound the favorable range and it is still undesirable to have values of
PBPI below 1. The Percentage Cash Shortage is calculated in the same way as in
equation 5.2. For values of PBPI greater than 1, the deviation from the favorable
range is examined. The Percentage Cash Range Deviation (PCRD) is then calculated
as follows:
For PBPI ≥ 1 :
PCRD =
T∑t=1
(Z ∗ (x− PBPI(t)) + (1− Z) ∗ (PBPI(t)− y))(5.4)
and Z =
1, if PBPI(t) ≤ x
0, if PBPI(t) ≥ y
The objective is now to minimize a linear combination of PCS and PCRD by
rescheduling non-critical activities. The objective function for every project can be
written as follows.
Min ω1
∑PCS + ω2
∑PCRD (5.5)
The penalty cost ω1 is greater than ω2 as cash shortages are more harmful than
cash excesses. The initial value of the objective funtion is calculated based on the
earliest start schedule. Next, each network is run through the algorithm described
in section 5.3.3. When no more improvements on the OV can be found, the total
improvement is calculated through comparison of the initial and best OV.
PBPIlevel Improvement =OVinitial −OVbest
OVinitial(5.6)
This procedure is repeated for all of the 900 project network instances. The values
of the lower level x and the upper level y of the favorable range were arbitrarily
fixed at 1.2 and 1.3 respectively. The mean PBPIlevel improvement is calculated
per 100 networks belonging to the same SP factor. The results of this analysis are
shown in figure 5.5. As expected, the biggest average improvements are found for
parallel networks which can be explained in the same way as the PBPImax problem.
Moreover, the average improvement per SP-factor is lower as in the case of baseline
optimization since the requirements for PBPI are more precise.
48
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&!"
'!"
(!"
)!"
*!"
+,-!.#"
+,-!.$"
+,-!.%"
+,-!.&"
+,-!.'"
+,-!.("
+,-!.)"
+,-!.*"
+,-!./"
PBPI improvement(%)
Figure 5.5: PBPI improvement per SP for baseline leveling problem
5.3.5 Milestones
Until now, the contractor is assumed to send an invoice to his client every time an
activity is completed. For most of the activities, the contractor already pays a consid-
erable amount of the total cost before he receives the price value of that activity from
the client. This is unfavorable for his cash position and causes PBPI to approach
values of 1 or below 1. In practice, a contractor might require some kind of advance
from his client at the beginning of the project. In addition, it might cause too much of
administrative fuss if every time an activity is completed, an invoice needs to be sent
out. Therefore, instead of invoicing after activity completion, the contractor could
decide to work with milestones. Milestones are certain points in time on which the
client has to pay a certain percentage of the agreed-upon contract price. In combina-
tion with advance payments, milestones also give the possibility to charge part of the
contract price before the project is started. As mentioned, this is common practice
in real life projects and ensures the contractor that he will not directly run out of
money after starting the first activities of the project. In addition, the advance also
serves as a guarantee for the contractor, which is advisable for highly tailored or cus-
tomized projects. As a consequence, PBPI will be greater than 1 in the beginning of
the project, which has a positive impact on PCS, as defined in the previous sections.
In case of milestones, it is very important to decide carefully on the time and size
of the milestones in order to obtain an optimal cash position throughout the project
execution. First of all, the contractor should make a scheme of the planned cash out-
flow. Thereafter, he should decide on the margin as a percentage of cost and calculate
the fixed contract price. This contract price should be spread among the milestones
in such a way that the cumulative cash inflow is greater than the cumulative cash
outflow at all times.
49
It is assumed that the contractor applies a mechanism with four milestone pay-
ments, advance included, spread over the execution of the project, and one at the end
of the project. In total, five payments will be received, all consisting of 20% of the
Invoice At Completion (IAC). The advance is invoiced before the project is started
and the money is assumed to be on the contractor’s bank account at the starting time
of the project. The project manager begins the execution of the initial activities and
pays all related costs. PBV gradually decreases proportionally to the work carried
out until it reaches a value of 0. At this point, the contractor should receive his
second milestone in order to force PBPI above 1. Again, PBV gradually decreases
proportionally to the work carried out, and when a value of 0 is reached, the third
milestone should be received. The same is applied for the fourth milestone. The last
milestone is received when the project is completed. This gives the contractor the
needed incentive to complete the project as soon as possible. In case of milestones
and a positive margin, the contractor’s planned cash position will always be positive.
The use of milestones can be illustrated on the example project introduced in
chapter 4. As can be seen in table 5.1, in case no milestones nor any kind of advance
payments are used, PBPI regularly has values below 1, thus resulting in a negative
cash position for the contractor. With the introduction of milestones and an advance
payment, however, this can be avoided. For the example project, only 3 milestones
of 20% of the total contract price of 241.5 are needed, advance included, in order
to guarantee PBPI to be above 1 at all times. The final payment at the end of the
project will thus consist of twice the value of a regular milestone. In the example
project, client payments of 48.3 occur at time 0, 4 and 8 respectively and of 96.6
after project completion. Keeping into account that the client takes full advantage of
the granted pay delay, invoices need to be sent out 2 weeks in advance as mentioned
under ‘Assumptions’ in section 4.1.
Note that the actual cash position can deviate from the planned one however, due
to unforeseen events resulting in delay. It is still possible that the Actual Balance
Performance Index (ABPI) sinks under 1, resulting in an actual cash shortage for the
contractor. The contractor should take this risk into account and cover himself by
applying appropriate buffers. The effects of applying milestones and buffers on the
real cash position are illustrated in the simulation study in part III.
50
Ori
gin
al
Sce
nari
oS
cen
ari
ow
ith
Mil
esto
nes
Tim
eP
VP
VW
SE
EW
SIV
WS
AV
WS
PB
VP
BP
IIV
WS
AV
WS
PB
VP
BP
I
120
300
00
0-
48.3
48.3
48.3
-2
4060
036
00
-96.6
48.3
48.3
-3
6394
.50
36
00
-96.6
48.3
48.3
-4
8612
986
84
36
-50
0.4
296.6
96.6
10.6
1.1
25
106
159
86
129
36
-50
0.4
296.6
96.6
10.6
1.1
26
116
174
86
129
84
-20.9
8144.9
96.6
10.6
1.1
27
126
189
86
129
129
43
1.5
144.9
96.6
10.6
1.1
28
136
204
136
129
129
-70.9
5144.9
144.9
8.9
1.0
79
146
219
136
181.5
129
-70.9
5144.9
144.9
8.9
1.0
710
151
226,
5136
181.5
129
-70.9
5144.9
144.9
8.9
1.0
711
156
234
136
181.5
181,5
45,5
1.3
3144.9
144.9
8.9
1.0
712
161
241,
5161
241.5
181.5
20,5
1.1
3144.9
241.5
80.5
1.5
Tab
le5.
1:C
omp
aris
on
of
scen
ari
ow
ith
an
dw
ith
ou
tm
iles
ton
esfo
rth
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am
ple
pro
ject
51
Part III
Simulation study
52
Chapter 6
Methodology
In order to test the forecast accuracy of EMC a simulation study with a full factorial
design is set up. Figure 6.1 gives an overview of the methodological approach followed
in this simulation study. Every step within the figure will be explained in detail in
this chapter.
A full factorial experiment lends itself very well for the objective of testing the
accuracy of EMC as it allows the effect of each individual factor as well as the in-
teractions between factors to be investigated. The main factors under consideration
are the topological structure of a project network and the probability of an activity
finishing early, on time or late (i.e. activity duration variability).
For this simulation, a set of 900 project networks is used [12]. This dataset was
generated under a highly controlled design to guarantee maximum diversity. For a
detailed description of this dataset, the reader is referred to section 5.3.
For every intermediate value of SP (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9), 100
project networks are generated with random values for Activity Distribution, Length
of Arcs and Topological Float since they are unlikely to influence the results. These
900 project instances represent a wide variety of diverse projects on which this anal-
ysis will be based. As no resource constraints are taken into account, each network is
transformed into an as early as possible project schedule, based on the critical path
based forward pass calculations. This allowes calculating the baseline metrics PV,
PVWS, IVWS, AVWS and EEWS for each activity.
Costs per time unit are generated randomly for each activity. In this analysis
a linear relationship between costs and the duration of each activity is assumed as
shown in equation 3.5. To define the actual duration of each activity, a Monte Carlo
simulation (see section 6.1) with triangular distributions (see section 6.2) is set up.
Activities running behind or ahead of schedule are staged by using triangular distribu-
tions tailed to the right or left respectively. These fictitious project execution results
53
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71$0*#+('8%#1$%9('"*#8+"'8%
RanGen (Demeulemeester
et al.[12])
Triangular Distribution
PV, PVWS, IVWS, AVWS, EEWS
EV, AC, PVWP, IVWP, AVWP, AEWP
SV, SPI; CV, CPI FV, FPI; PIV, PIP IV, IPI; AV, API PBV, PBPI; ABV, ABPI PVar, PPI EAC, EAC(t), EMC Repeat
Figure 6.1: Methodological approach of the simulation study
are used to calculate the Earned Value and Contractor Cash Flow measurements and
indicators.
6.1 Monte Carlo Simulation
The term ‘Monte Carlo’ was first used in the 1940s by physicists working on nuclear
weapon projects in the Los Alamos National Laboratory, behind the famous Monte
Carlo casino in Monaco, a gambling venue based on random-number generation.
As described by Ricardo Viana Vargas ([37], p.7), ‘Monte Carlo simulation is a
method in which the distribution of possible results is produced from successive recal-
culations of the data of the project, allowing the construction of multiple scenarios.
In each one of the calculations, new random data is used to represent a repetitive
and interactive process. The combination of all these results creates a probabilistic
distribution of the results.’
To describe interactions in a system, mathematical models are used extensively.
They depend on a number of input parameters which are transformed in output pa-
rameters based on mathematical expressions in the model. These input parameters
are often dependent on external factors however. Deterministic models do not take
the risk and variability in input factors into account. They base their calculations on
the most likely values of the input parameters. Consequently, deterministic models
are not a good representation of reality and reliability is poor.
54
To increase the reliability of experiments, different scenarios can be considered.
Instead of only calculating the output for the most likely values of the input param-
eters, the calculations can be repeated for the worst possible values and the best
possible values of the input variables. Even better is to consider the whole range of
possible values associated with each risky input variable. A method to achieve this,
is the Monte Carlo simulation [28].
Monte Carlo simulations are used in various scientific applications, characterized
by significant uncertainties, such as NASA projects, economic applications and project
management. Also in planning problems, extensive use is made of this method. Time
and cost, the two major concerns of a project manager, can be estimated based on
network representations and critical path calculations. The real duration and cost of
each activity in the network will vary however due to unforseen events. In order to
take this uncertainty in input variables needed to calculate the final time and cost of
a project, into account, authors among which Vanhoucke [35] [36] and Van Slyke [32]
made use of Monte Carlo simulations.
These applications clearly illustrate the conditions under which the method is
mostly used. First of all, due to uncertainty, the results of a single simulation would
not be an accurate reflection of reality. Secondly, the variability of the input vari-
ables should be known. The values of the input variables can then be simulated
based on a given nominal value, a range, and a distribution within that range. As
a result, a statistical distribution must be identified for each of the input variables.
Random samples from these distributions are representative for the values of the in-
put variables. Based on these input variables, output variables are calculated using a
mathematical model.
This is done for each simulation run. The respective values serve as the input for
the mathematical model with a particular output variable as result. Finally, statistical
analysis of the output variables is performed to characterize the output variation [28].
6.2 Triangular distribution
To define the actual duration of each activity, a Monte Carlo simulation with tri-
angular distributions is set up. In probability theory and statistics, the triangular
distribution is a continuous probability distribution with lower limit a, upper limit
b and mode c. Activities running behind or ahead of schedule are staged by using
triangular distributions tailed to the right or left respectively.
f(x|a, b, c) =
2(x−a)
(b−a)(c−a) , if a ≤ x ≤ c
2(b−x)(b−a)(b−c) , if c ≤ x ≤ b
0 otherwise
(6.1)
55
(a) Probability Density Function (b) Cummulative Distribution Function
Figure 6.2: Triangular Distribution [38]
The upper and lower limit are indicators for the probability of being late or early
and the value on the y-axis corresponding to the mode c shows the probability of
being on time. The probability density function and the cummulative distribution
function of this triangular distribution are shown in the figures 6.2a and 6.2b.
In this simulation study, upper and lower limits on activity durations are calcu-
lated based on the Planned Duration. This Planned Duration is multiplied by a factor
‘early’ between 0.1 and 1 for the lower limit a and by a factor ‘late’ between 1 and 1.9
for the upper limit b. These factors ‘early’ and ‘late’ are fixed for all activities of the
same network. This does not mean however that a and b will have the same values
for all activities. Whether this is the case or not depends on the planned duration for
these activities.
These fictitious project execution results are used to reflect the variation in activity
duration. Based on these results, the traditional Earned Value and Contractor Cash
Flow measurements and indicaters are calculated.
6.3 Assumptions
For this analysis, some additional assumptions are made on top of those introduced in
chapter 4 in order to simplify the model. First of all, it is assumed that the duration
of activities is distributed according to a triangular distribution. As mentioned by
Kwong Wing Chau [4], one of the major reasons why this assumption is made is that
it simplifies the calculations carried out during the simulation. It should be noticed
however that this assumption results in an upward bias in the probability of exceeding
the mode c. This should be taken into account when analyzing the simulation results.
The second assumption is that once a project is started, no corrective actions are
taken in case the project is running ahead or behind schedule. Although corrective
56
actions are common in real-life projects, they are difficult to include in the model
because the effects of those actions are not well-understood. The work in system
dynamics modeling of projects can give some indications of what those effects would
be. This issue falls out of the scope of this thesis. The reader is referred to [39] for
an extensive discussion about realism in network simulation.
Furthermore, resources are assumed to be available at all times. As a conse-
quence, all activities can be started earlier or later than scheduled, depending on the
performance of the previous activities.
57
Chapter 7
Impact of external factors on
the forecast accuracy of EMC
In order to evaluate the forecasting measures and to determine the forecast accuracy,
the Mean Percentage Error (MPE) and the Mean Absolute Percentage Error (MAPE)
are calculated for each network. They both calculate the difference between the
Expected Margin at Completion (EMC) and the Actual Margin at Completion (AMC)
as a percentage of AMC.
MPE =1
T
T∑t=1
EMC(t)−AMC
AMC∗ 100 (7.1)
MAPE =1
T
T∑t=1
|EMC(t)−AMC|AMC
∗ 100 (7.2)
With T the actual project duration and t the time under consideration.
By setting up different simulations where each time a few of the parameters are
fixed to a certain value, the impact of one single parameter on the forecast accuracy
of EMC can be investigated. In what follows, the effect of topological structure,
variation in activity duration and project completion stage is further explored.
7.1 Topological Structure
The objective of the first part of the simulation was to explore the effect of the topo-
logical structure on the forecast accuracy of EMC. As mentioned in chapter 6, the
dataset consists of a population where for every value of the Serial or Parallel Indica-
tor (SP), 100 project networks are generated with random values for the remaining
topological indicators Activity Distribution, Length of Arcs and Topological Float as
Vanhoucke [34] points out that they are unlikely to influence the results. For each
58
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MAPE (%)
Figure 7.1: Mean Absolute Percentage Error for parallel and serial networks (a = 1,b = 1.5)
group of 100 project networks with identical SP, new scenarios are generated based on
a simulation with fixed combinations of a and b. When comparing the Mean Absolute
Percentage Error for networks with different SP and fixed lower and upper limits on
activity duration, the impact of topological structure on the forecast accuracy of EMC
can be evaluated. For project networks with an increasing SP-factor, an increasing
trend in MAPE, and thus a decreasing trend in forecast accuracy is observed. This
is illustrated in figure 7.1. This indicates that, the more a network consists of serial
activities, the greater the difference between the Estimated Margin at Completion
and the ultimate margin at the end of the project.
This observation can be explained as follows. The Estimated Margin at Comple-
tion is calculated each time unit by correcting the Planned Margin at Completion
with the Margin Performance Index. The Margin Performance Index is an indica-
tion of how the project is performing at that specific moment. In a completely serial
network, the Margin Performance Index is in fact the ratio of the sum of the Actual
Margins and the sum of the Planned Margins of all activities already completed and
the single activity that is executed at that moment but still has to be completed. In
a parallel network however, the Margin Performance Index is the ratio of the sum
of the Actual Margins and the sum of the Planned Margins of all activities already
completed and several (more than one) activities that are executed at that moment
but still have to be completed. The effect of this subtle difference can be illustrated
with the help of a small example. When forecasting the EMC of a project, consisting
of serial activities, in the very beginning of the project (time unit 1), the forecast will
be based on the Margin Performance Index of the first activity. If this activity how-
ever, is not representative for the rest of the project, the EMC will not be accurate
at all. If the project consisted of several parallel activities however, the MPI at the
59
Figure 7.2: Example project: Activity-on-the-node representation of completely serialnetwork
very beginning of the project would be an average of all activities already started. As
a consequence, the value of MPI will be less extreme as activities performing early or
on time compensate for activities running late. This averaged value of MPI will be
more representative for the performance of future activities.
Consider the illustrative example project of chapter 4. If all activities can only
be scheduled one after the other, a completely serial network arises. The activity-
on-the-node representation of this network can be seen in figure 7.2. If activity 1
in this network is late with 4 time units, the Mean Percentage Error is -156%. The
evolution of MPI is shown in figure 7.4a. As from the start of activity 1, MPI takes
on a very extreme value of -1 and a negative margin at completion is estimated. At
the moment activity 1 is completed, MPI starts recovering slowly until the end of
the project. Because activity 1 took twice as much time as planned, but the other
activities did not follow this trend, activity 1 was not representative for the whole
project. MPI was deluded by the bad performance of activity 1.
It is also possible to transform the network in a completely parallel network. The
activity-on-the-node representation of this network is shown in figure 7.3. If activity
1 is late again with 4 time units, the Mean Percentage Error is 25,28%. The evolution
of MPI is shown in figure 7.4b. The values of MPI are more balanced due to the fact
that the performance of all activities is taken into account to estimate the margin at
completion.
Figure 7.3: Example project: Activity-on-the-node representation of completely par-allel network
60
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Figure 7.4: Impact of topological structure on MPI for the example project
61
7.2 Variability in activity duration
In the second part of the simulation, the impact of the variability in activity dura-
tion is examined. In other words, the impact of the variability between planned and
actual activity duration on the forecast accuracy of EMC is tested. This is done by
simulating new scenarios for project networks with varying upper and lower limits
on activity duration for a fixed SP-factor. The variability in activity duration can
then be defined as the range between the upper and lower limit. The Mean Absolute
Percentage Error was calculated for each possible combination of a and b. A few
interesting observations can be made.
When keeping the lower limit fixed at the Planned Duration (a = 1), increasing
estimation errors for increasing upper limits on activity duration (b ∈ 1.1, 1.2, 1.3, . . .)
are observed. Similarly, when keeping the upper limit steady at the Planned Du-
ration (b = 1), an increasing trend in estimation errors for decreasing lower limits
(a ∈ 0.9, 0.8, 0.7, . . .) is observed. In general can be observed that, the greater the
range of possibilities for an activity to end early or late and thus the greater the vari-
ability in activity duration, the greater the Mean Absolute Percentage Error of EMC.
In other words, the forecast accuracy of EMC decreases with an increasing amount of
variability in activity duration. Figures 7.5a and 7.5b illustrate this trend for projects
ending late and early respectively.
The explanation for this observation is quite straightforward. The Estimated Mar-
gin at Completion is calculated each time unit by correcting the Planned Margin at
Completion with the Margin Performance Index. The Margin Performance Index is
an indication of how well the project is performing at a certain moment in time. If the
variability is great, two consecutive activities may have a very different performance.
However, the Margin Performance Index supposes that the current performance is a
reliable indicator for future performance. Therefore, a greater error is made as MPI
will take on values that are far more extreme than the values for a project with the
same Margin at Completion but with less variable activity durations.
Lets illustrate this again with the example introduced in chapter 4. If the real
duration of activity 1 is 6 instead of 4 (+2 time units) and the real duration of activity
3 is 6 instead of 8 (-2 time units), the final duration of the project will not change.
The Mean Percentage Error is -16%. The evolution of MPI is shown in figure 7.6a. If
the real duration of activity 1 is 8 (+4 time units) and the real duration of activity
3 is 4 (-4 time units), the Mean Percentage Error is -32%. The evolution of MPI is
shown in figure 7.6b.
62
!"!!#$"!!#%"!!#&"!!#'"!!#("!!#)"!!#*"!!#+"!!#,"!!#
$!"!!#
-.#/01# 2341#
567!"$#
567!"&#
567!"(#
567!"*#
567!",#
8#MAPE(%)
(a) Project ending late
!"!!#
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456!"$#
456!"&#
456!"(#
456!"*#
456!"7#
8#MAPE(%)
(b) Project ending early
Figure 7.5: Impact of variability in activity duration on MAPE
63
(a) Project with Low Variability in AD
!"#$%
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"%
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./0%
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(b) Project with High Variability in AD
Figure 7.6: Impact of variability in activity duration on MPI for the example project
64
(a) Project ending early (b) Project ending late
Figure 7.7: Impact of Project Completion Stage on MAPE
7.3 Project completion stage
The third objective of the simulation study was to explore the effect of the project
completion stage on the forecast accuracy of EMC. This can easily be done by di-
viding the project horizon into three parts based on the Planned Value (PV ∈[0%−30%], [30%−70%], [70%−100%]), representing different stages of project comple-
tion, while applying fixed combinations of upper and lower limits on activity durations
and fixed SP. After calculating MAPE for each of the described scenarios, the impact
of the completion stage of work can be evaluated. Figures 7.7a and 7.7b clearly indi-
cate that for early projects as well as for late projects, the forecast accuracy increases
for increasing project completion stages.
It is easily understood and quite logical that near the end of a project, the contrac-
tor is less confronted with uncertainty than in the beginning of the project. Looking
back at equation 3.20 it can be seen that, as the completion stage of the project
advances, the Actual Margin will deliver a more potent part of the final value of the
Expected Margin at Completion. This implies that the Planned Margin will also
present a higher value than in earlier stages of the project, thus reducing the part of
the value of EMC that still needs to be estimated. These findings are comparable to
the results of a study performed by Vanhoucke [34] on the forecast accuracy of the
65
Figure 7.8: MPI, CPI and Margin Error
Estimated duration At Completion (EAC(t)) as defined by Anbari [1], Jacob [21] and
Lipke [25] in different completion stages of work.
In chapter 5, the comparison is made between traditional EVM and the CCF
method presented by Gorog [17] that takes into account contractor cash flows. It can
be pointed out that the formula for Margin Performance Index (MPI) (equation 3.23)
is also quite comparable to the formula of Cost Performance Index (CPI) (equation
2.3). In both the numerator and the denominator of MPI, the components of CPI,
Earned Value and Actual Cost, are deducted from the Price Value of Work Performed
to form the ratio of the Actual Margin and Planned Margin. Christensen has proven
the concept of CPI stability ([10], [9]) which states that the value of CPI does not
change more than 10% once the project is 50% completed. It can be conjectured that
this stability is also applicable to the Margin Performance index and thus contributes
to the improved forecast accuracy of EMC in the second and third stage of the project.
This can be illustrated with figure 7.8.
66
Chapter 8
Impact of margin attribution
methods on the forecast
accuracy of EMC
Until this point, the analysis assumed margins to be a fixed percentage of costs for all
activities. This has not to be the case however. The price value for different activities
can be calculated based on different percentages of their cost. In general, when the
assumption of a fixed margin is abandoned, these percentages can be attributed in
three distinct ways. First of all, the contractor might argue that the activities that
add the most value to the project are located more at the beginning of the project.
In order to obtain a representation that is as accurate as possible, he might choose
to work with a regressive margin. Secondly, if the opposite were to be the case,
the application of progressive margins might be preferable. Finally, a third case
is assumable where no clear order in value-adding activities can be detected, but
where more or less value-adding activities alternate one another. This case is best
represented by applying a random margin per activity. The impact of the various ways
a contractor can attribute margin to the different project activities on the forecast
accuracy of the Expected Margin at Completion (EMC), is evaluated in this chapter.
8.1 Fixed Margin
Before entirely abandoning the assumption of fixed margins (%) for all activities, the
impact of the magnitude of this fixed margin on EMC can be evaluated through a
simulation study where the Mean Absolute Percentage Error is observed. For the
methodology used, the reader is referred to chapter 6. The results of the previous
simulation run, presented in chapter 7, reveiled that variability has a baleful influence
on the forecast accuracy of EMC. In order to rule out too much variability while test-
ing the impact of the magnitude of the budgeted margin, the triangular distribution
67
!"
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%#!"
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!($" !(%" !(&" !('" !(#" )*+,-."
/01!($"
/01!(&"
/01!(#"
/01!(2"
/01!(3"
)405"678"
Figure 8.1: MAPE(%) for different fixed margins per SP-factor
in this simulation run is fixed. The lower limit a is set at 1 and the upper limit b
is set at 1.5, thus simulating projects that run late on average. The results of the
simulation with margins varying from 10% to 50% are presented in figure 8.1.
A first and obvious observation that can be made from looking at this figure is
that the previously drawn conclusion that serial networks result in greater estimation
errors than parallel netwerks, formulated in section 7.1, is still valid. Higher values
for MAPE are observed for projects with a Serial/Parallel-factor (SP) closer to 1.
Secondly, it can clearly be seen that the Mean Absolute Percentage Error (MAPE)
peaks at margins of about 30%, and this for all values of SP.
These observations can be explained as follows. Due to the fact that the trian-
gular distribution is fixed to values of 1 and 1.5 for lower limit a and upper limit b
respectively, the projects simulated in this study will have an average real duration
of 1.3 times the planned duration. As a consequence, real costs will be 1.3 times the
planned costs since costs are defined as a function of duration (cfr. equation 3.5).
For a fixed margin of 30%, almost the entire margin will be consumed by excessive
costs and the resulting Actual Margin (AM) will approximate 0. As a consequence,
MPI will take on values near to 0 and the margin at completion will be predicted
to approach 0. Under these circumstances, this seems to be a realistic estimate and
therefore may appear to be in contradiction with the high values of MAPE. However,
in order to come to a better understanding of the error made, the Mean Absolute
Error (MAE) is introduced.
MAE =1
T
T∑t=1
|EMC(t)−AMC| (8.1)
With T the actual project duration and t the time under consideration.
68
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'##$
#(&$ #(%$ #("$ #('$ #()$
*+,-./0$
*+-$
+*1$
Figure 8.2: Evolution of MAPE, MAE, and AMC for different fixed margins
Figure 8.2 clearly illustrates that for varying values of fixed margins per activity,
the course of MAE is not in accordance with the course of MAPE. When comparing
MAE and MAPE for projects with a fixed margin of 30%, it becomes clear that the
answer to the difference between both measurements lies in the magnitude of Actual
Margin at Completion (AMC), which serves as the denominator for MAPE (cfr. equa-
tion 7.2). When applying a fixed margin that is almost equal to the likely tardiness of
the project, AMC will be very small in absolute terms and as a consequence, the error
as a percentage of |AMC| will be very large. This conclusion can also be made when
looking at the values of MAE and MAPE for projects with other margins in figure 8.2.
For all fixed margins of the simulation run, the Mean Absolute Error (MAE), which is
the mean error made per time unit, is within the same range. This value is compared
with AMC to measure the error in percentages (MAPE). For break-even situations,
AMC will approach 0 and as a consequence, MAPE will be very big. For projects
with a small fixed margin, AMC will be smaller than 0 and for greater percentages,
AMC will be well above 0. In the figure, it is the distance between AMC and the x-
axis that determines the value for MAPE, regardless its position above or underneat it.
This conclusion can be confirmed by changing the lower and upper limit a and b of
the triangular distribution from 1 and 1.5 to 1.2 and 1.7 respectively. This triangular
distribution will cause projects to end 50% late on average. Based on the arguments
mentioned above, the largest errors are now expected to occur when a fixed margin
of 50% is applied. The results of this simulation run are shown in figure 8.3.
To conclude it can be stated that in absolute terms, the estimation error is more
or less the same for varying fixed percentages. When this error is compared with
AMC however, greater errors (%) are made for break-even situations. The further a
project moves away from the break-even situation the better the accuracy of EMC.
69
!"
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$#!"
%!!"
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&#!"
!'$" !'%" !'&" !'(" !'#" !')" *+,-./"
+0$1"20$'#"
+0$'%1"20$'3"
MAPE (%)
Figure 8.3: MAPE(%) for different fixed margins and time performance
8.2 Regressive Margin
In the next part of this chapter, the assumption of a fixed margin (%) for all activities
is abandoned. As mentioned, a contractor might argue that the activities located in
the beginning of the project add more value than the ones at the end. This situa-
tion is best represented through the use of a regressive margin scheme. Instead of
fixed margins per activity, the attributed margin can vary between 10% and 100%
(in discrete steps of 10%). In a regressive margin scheme, the greatest margins are
attributed to the activities that are executed early on in the project and will decrease
for activities towards the end of the project. The first activity will thus have a margin
of 100% whereas the last activity will always have a margin of 10%. Margins of the
other activities depend on their start time within the network.
Intuitively, it could be presumed that the Mean Absolute Percentage Error for
projects with a regressive margin would be equal to the MAPE for projects with a
fixed margin corresponding to the resulting average overall margin obtained through
the application of regressive margins. For instance, projects with margins decreasing
from 100% to 10%, following a uniform distribution, can be supposed to correspond
to projects with a total (fixed) margin of 55%. As a consequence, the error made
in this case is also expected to be in accordance with the error observed for projects
with a fixed margin per activity of 55%. This intuitive prophecy does not match the
results of the analysis however. This is shown in figure 8.4, where MAPE for the fixed
(55%) as well as the regressive margin scheme can be observed for varying values of
SP. In general, the errors made for projects with a regressive margin, corresponding
to an overall margin of 55%, are well above the errors made for projects with a fixed
margin of 55%. These results will be analyzed further in section 8.5.
70
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MAPE (%)
Figure 8.4: MAPE(%) for different margin systems
8.3 Progressive Margin
In contrast to the arguments for applying a regressive margin scheme, a contractor
might be confronted with a project where the activities that add the most value are
located more at the end of the project. Therefore, a progressive margin scheme may
be more fit to accurately represent the project. Margins will still vary between 10%
and 100%, but now the smaller margins are attributed to activities that are scheduled
early on in the project and increase for activities towards the end of the project. The
first activity will thus have a margin of 10% whereas the last activity will always have
a margin of 100%. Margins of the other activities depend on their start time within
the network.
For the same reasons as stated in the previous section it could intuitively be
presumed that the Mean Absolute Percentage Error would be equal to the MAPE for
projects with a fixed margin corresponding to the resulting average overall margin
obtained through the application of progressive margins. For instance, just as was
the case for decreasing margins, projects with margins increasing from 10% to 100%,
following a uniform distribution, can be supposed to correspond to projects with a
total (fixed) margin of 55%. As a consequence, the error made in this case is also
expected to be in accordance with the error observed for projects with a fixed margin
per activity of 55%. Again, this intuitive prophecy does not match the results of the
analysis. This is shown in figure 8.4, where MAPE for the fixed (55%) as well as
the progressive margin system can be observed. As can be seen in the figure, the
errors made for a progressive margin, corresponding to an overall margin of 55%,
are far above the errors made for a fixed margin of 55%. Furthermore, the error is
considerably larger than for projects with a regressive margin system. These results
will be analyzed further in section 8.5.
71
8.4 Random Margin
When no clear ascending or descending order can be detected for value-adding activi-
ties, but more and less value-adding activities alternate each other, a random margin
scheme seems to be a good representation. To guarantee comparable results, varying
margins are attributed between 10% and 100% with a uniform distribution. This
scenario will result in a final overall margin of about 55%.
Again, it could intuitively be expected that the Mean Absolute Percentage Error
would be in accordance with the error observed for projects with a fixed margin of
55%. This intuitive expectation does not entirely match the results of the analysis
however. This is shown in figure 8.4. These results will be analyzed further in section
8.5.
It should be noticed that although random margins are attributed, the randomness
of the project does not increase. Before the project execution starts, the random
margins are known and the baseline metrics can be calculated as usual.
8.5 Analysis of results
The obtained results from this simulation study proved to deviate from what was
intuitively expected. In general, the Mean Absolute Percentage Error for both the
progressive, regressive, and the random margin scheme exceeded the MAPE of com-
parable projects with fixed margin scheme, albeit not to the same extent.
8.5.1 MPI stability
Figures 8.5, 8.6, 8.7, 8.8 show the evolution of AM, PM and MPI for 4 scenarios
of an example project of 30 non-dummy activities with an SP-factor of 0.2 from
the dataset population. These scenarios correspond to each of the different margin
attribution systems. As all scenarios are based on the same project with the same
time and cost performance, EV, AC, and PMC are the same for all of them. For
the calculation of EMC at each time unit, PMC is multiplied by MPI. As PMC
is the same in each scenario, it is certain that the difference in estimation error is
caused by MPI. MPI is the ratio of AM and PM with AM = PVWP − AC and
PM = PVWP − EV (cfr. equation 3.23). As EV and AC are the same for the 4
scenarios, the difference in estimation error fully depends on differences in PVWP.
PVWP is obtained by multiplying EV with (1 + margin(%)). EV is the same for
the 4 scenarios but margin(%) is not. In case of regressive margins, margin(%)
will be high in the beginning of the projects, resulting in a higher marginal increase
of the cummulative PVWP than in the case of progressive margins. At the end of
the project, margin(%) will be small, resulting in a smaller marginal increase in the
cummulative PVWP than in the case of progressive margins. The different behavior
72
of PVWP in the 4 scenarios has a great impact on het evolution of MPI. It can be
concluded from figure 8.5 that in the case of fixed margins, MPI converges quickly to
its stable value. For this stable value, the margin is estimated correctly. Due to the
fast convergence, less errors are made. In the case of random margins (figure 8.8),
MPI is not as stable as in the case of fixed margins. Both values above and under
the stable value occur but the difference between the stable value and the maximum
and minimum value respectively are not too big. In the case of regressive margins
(figure 8.6), the difference between the maximum value and the final stable value
is considerably larger, thus resulting in less MPI stability. For progressive margins
(figure 8.7), MPI is very variable and it takes a long time to reach the stable value of
MPI. The EMC accuracy for the 4 scenarios depends on their respective MPI stability.
The more stable MPI, the more accurate EMC and the smaller the values for MAPE.
73
(a)PVW
P(b
)AM
andPM
(c)MPI
Fig
ure
8.5
:M
PI
stab
ilit
yfo
rfi
xed
marg
ins
(a)PVW
P(b
)AM
andPM
(c)MPI
Fig
ure
8.6
:M
PI
stab
ilit
yfo
rre
gre
ssiv
em
arg
ins
74
(a)PVW
P(b
)AM
andPM
(c)MPI
Fig
ure
8.7
:M
PI
stab
ilit
yfo
rp
rogre
ssiv
em
arg
ins
(a)PVW
P(b
)AM
andPM
(c)MPI
Fig
ure
8.8
:M
PI
stab
ilit
yfo
rra
nd
om
marg
ins
75
8.5.2 Search for the ideal MPI
Another way to demonstrate the difference between the 4 scenarios is by comparing
MPI with what MPI should be in order to estimate the Actual Margin at Completion
(AMC) correctly. In section 2.5, the To Complete Performance Index (TCPI) was
reviewed. Corresponding to TCPI, a new indicator TCMPI can be defined. TCMPI
is the To Complete Margin Performance Index and can be interpreted as the margin
performance required to obtain the margin objective (MO).
TCMPI =MO −AM
PMC − PM(8.2)
It is not the aim to promote TCMPI as an extra tool to assess the attainability of
the objective margin. This is a topic for further research but is outside the scope of this
thesis. It is possible however to use this indicator to evaluate ex post what the margin
performance index should have been in order to accurately predict the margin at
completion. By simply inserting the obtained value for AMC as the margin objective
in equation 8.2, the TCMPI can be calculated for each time unit. The resulting
TCMPI thus will reflect the value that MPI should have been in equation 3.20 in order
not to make an estimation error for EMC. These values can then be compared to the
values of MPI (resulting from equation 3.23) for the 4 margin scenarios. This is done
for the example project subjected to the 4 possible margin attribution systems. The
results can be seen in figure 8.9. The deviation of the evolution of TCMPI and MPI
is an indication of the margin error made when estimating the margin at completion
with equation 3.20. For fixed margins, the deviation of TCMPI and MPI is small.
MPI takes on values near to the required values for a correct margin estimation.
The deviation of TCMPI increases for random, regressive, and progressive margin
attribution systems respectively. As a consequence, in case the project manager
does not work with fixed margins, MPI is not a good indicator and too instable to
accurately estimate a margin at completion.
76
(a)Fixed
margin
(b)Reg
ressivemargin
(c)Progressivemargin
(d)Random
margin
Fig
ure
8.9:
Evo
luti
onof
TC
MP
Ian
dM
PI
for
4m
arg
inatt
rib
uti
on
syst
ems
(EV
250
[12])
77
Chapter 9
A comparative study
Even after thoroughly examining the impact of various external factors and margin
attribution systems on EMC, it is very difficult to assess the accuracy of EMC without
comparing the results with other methods used to estimate the margin at completion
of a project. EMC is only of great value for the contractor if he is able to predict
the margin at completion more accurately with than without the metric EMC. As
mentioned, the main concerns Gorog expressed concerning traditional EVM are that
no cash flows are taken into account and no forecaster exists for predicting the margin
at completion. This said, it can be assumed that when contractors were faced with
the challenge of estimating the likely margin before the introduction of this model,
they would just have used the available data in their traditional EVM systems. The
estimated margin at completion could for instance be obtained by deducting the Es-
timated cost At Completion (EAC) from the fixed contract price (IAC). The main
difference between EMC and IAC-EAC is that in the latter case, it is not necessary to
attribute a margin to every activity. The only data the contractor should possess are
the traditional EVM metrics (PV, EV, and AC), and the value of the fixed contract
price (IAC).
For the Estimated cost At Completion, different formulas are proposed, based on
different assumptions made about the performance of future work, expressed by the
Performance Factor (PF). For a detailed description of EAC, the reader is referred
to chapter 3. In his paper ‘Determining an accurate estimate at completion’, Chris-
tensen [6] reports about the results of three EAC studies and research related to EAC
evaluation. These studies made some generalizations possible. The most important
conclusion for the research conducted in this chapter is that no one formula for EAC
is always best. ‘Assigning a greater weight to the SPI early in the contract is appro-
priate. Because SPI is driven to unity, it looses its predictive value as the contract
progresses. SCI-based formulas were thus shown to be better predictors in the early
stages by Riedel and Chance. In the late stages, the SCI and CPI have nearly the
same values and were shown to be accurate predictors by Bright and Howard, and
78
by Riedel and Chance.’ ([6], p.6). Based on these findings, it is useful to examine
the behavior of IAC-EAC for the three possible scenarios as presented in chapter 3.
In the first scenario, PF=1, indicating that the rest of the project is expected to be
executed according to plan. In the second scenario, PF=CPI, indicating that the rest
of the project is expected to be executed at the same level of cost performance as the
work that has already been executed. If it is desirable not only to take the current
cost performance into account, but also the current schedule performance, PF can be
expressed as SCI = SPI ∗ SCI. This is the case in the third scenario.
In order to maximize the comparability of the accuracy of EMC and the accuracy
of IAC-EAC, it is appropriate to conduct exactly the same simulation study as the
one in chapter 7.
9.1 Impact of external factors on the forecast accu-
racy of IAC-EAC
For the three scenarios mentioned above, the impact of topological structure, vari-
ability in activity duration and project completion stage on the accuracy of IAC-EAC
was investigated. The methodology used is described in chapter 6 and 7. The results
of this simulation study can be seen in figure 9.1.
The first objective was to test the impact of topological structure. Therefore, the
lower and upper limit of the triangular distribution were fixed at 1 and 1.5 respectively.
In accordance with the findings from chapter 7, an increasing trend in MAPE for
projects with an increasing SP-factor can be observed in figure 9.1a. The more a
network consists of serial activities, the greater the estimation error.
To test the impact of variability in activity duration, projects with a fixed lower
limit a but varying upper limits b were simulated. For each possible combination
of a and b, the estimation error was calculated. In accordance with the findings
from chapter 7, increasing errors are observed for increasing upper limits on activity
duration. This can be seen in figure 9.1b. In general, it can be concluded that, the
greater the range of possibilities for an activity to end late and thus the variability in
project duration, the greater MAPE is for IAC-EAC for all three scenarios of PF.
The third objective was to test the impact of project completion stage. There-
fore, the lower and upper limit of the triangular distribution were fixed at 1 and 1.5
respectively and the SP-factor was fixed at 0.5. The results in figure 9.1c clearly
show an increasing forecast accuracy for increasing project completion stages. This
observation is in accordance with the findings from chapter 7.
For all three simulation runs previously mentioned and under the assumption made
in section 4.1, it can be concluded that the accuracy of IAC-EAC is always better for
PF=CPI than for PF=1, which in its turn always outperforms PF=SPI*CPI.
79
0
20
40
60
80
100
120
140
160
SP=0,1
SP=0,2
SP=0,3
SP=0,4
SP=0,5
SP=0,6
SP=0,7
SP=0,8
SP=0,9
PF = 1
PF = CPI
PF = CPI*SPI
MAPE(%)
(a) Impact of topological structure on accuracy of IAC-EAC
0
10
20
30
40
50
60
on +me late
PF = 1
PF = CPI
PF = CPI*SPI
MAPE(%)
(b) Impact of variability in activity duration on accuracy of IAC-EAC
0
10
20
30
40
50
60
0%-‐30% 30%-‐70% 70%-‐100%
PF = 1
PF = CPI
PF = CPI*SPI
MAPE(%)
(c) Impact of project completion stage on accuracy of IAC-EAC
Figure 9.1: MAPE(%) for IAC-EAC for different Performance Factors
80
9.2 Impact of margin attribution systems on the
forecast accuracy of IAC-EAC
Since IAC-EAC does not base its forecast of the margin at completion on the margin
attributed to individual activities, the margin attribution method has no impact on
the accuracy of the estimator IAC-EAC. This is very interesting since this observation
is in contrast with the observations made in chapter 8. For EMC, increasing estima-
tion errors could be observed when switching to random, regressive, and progressive
margins due to increasing MPI instability.
9.3 Comparison of accuracy of EMC and IAC-EAC
It is most interesting to compare the accuracy of EMC with the best alternative for
IAC-EAC. As mentioned in section 9.1, the accuracy of IAC-EAC is always best for a
Performance Factor (PF) equal to CPI. Note that this observation is in contrast with
the results of Christensen who stated that ‘no single formula for EAC is always best’
[6]. This can be explained by the fact that his conclusions are drawn from case-specific
results whereas our academic approach, while making our results easier to generalize,
is supported by and dependent of the assumptions made in section 4.1.
When carefully observing MAPE for all possible scenarios for both EMC and
IAC-EAC (PF=CPI), it can be concluded that the accuracy of EMC and IAC-EAC
(PF=CPI) is exactly the same. This is only possible when the formula for EMC
as proposed by Gorog can be written as IAC-EAC (PF=CPI). This is proven alge-
braically as follows.
EMC = AM + (PMC − PM) ∗ AM
PM
= AM +
(PMC ∗AM
PM− PM ∗AM
PM
)
= AM +
(PMC ∗ AM
PM
)−AM
= PMC ∗ AM
PM...
81
...
= (BAC ∗m) ∗ PVWP −AC
PVWP − EV
= (BAC ∗m) ∗ EV (1 + m)−AC
EV (1 + m)− EV
= (BAC ∗m) ∗ EV (1 + m)−AC
EV ∗m
=BAC ∗ EV (1 + m)
EV− BAC ∗AC
EV
= BAC ∗ (1 + m)− BAC
CPI
= IAC − BAC
CPI+ AC −AC
= IAC −(AC +
BAC − (AC ∗ CPI)
CPI
)
= IAC −
(AC +
BAC − (AC ∗ EVAC )
CPI
)
= IAC − EAC
With m = margin(%) and PF = CPI
From this comparative study, it can be concluded that the accuracy of EMC
equals the accuracy of IAC-EAC (PF=CPI) under the assumption of fixed margins.
If no fixed margins are applied, the accuracy of IAC-EAC is much better than the
accuracy of EMC. This is a logical consequence of the fact that IAC-EAC does not
experience the baleful influence of MPI instability. IAC-EAC is however dependent
on the stability of CPI, but CPI is not affected by the margin attribution system. As
a consequence, for a fixed SP-factor and fixed lower and upper litmits a and b of the
triangular distribution, but for different margin attribution methods, IAC-EAC will
always be the same. The difference with EMC is shown in figure 9.2. It should be
noticed that in all 4 scenarios, the final margin is 55%.
82
!"
#!"
$!"
%!"
&!"
'!"
(!"
)*+,-"""""""./01*2"
3/2-4."./01*2"
3,10,55*6,"./01*2"
70410,55*6,"./01*2"
89:"
;<:=8<:">7)?:7;@"
MAPE (%)
Figure 9.2: MAPE(%) for EMC and IAC-EAC (PF=CPI)
83
Chapter 10
Impact of milestones on ABPI
In this last chapter of part III, the impact of introducing milestones on a contractor’s
cash position is investigated. Throughout this thesis, it was assumed that a contrac-
tor sends an invoice to the client whenever an activity is completed. In section 5.3.5,
it was stated already that a contractor can also work with milestones. Lets assume
again that the contractor applies four milestones, advance included, spread over the
execution of the project, and one additional payment at the end of the project. In
total, five payments will thus be received, all consisting of 20% of the Invoice At Com-
pletion (IAC). The advance is invoiced before the project is started and the money is
assumed to be on the contractor’s bank account on the starting time of the project.
Whenever PBV reaches a value of 0, a new milestone should be appointed in order
to force PBPI above 1. The last milestone is received when the project is completed.
This way, the contractor’s planned cash position will always be positive. The actual
cash position can deviate from the planned one however, due to unforeseen events
resulting in delay. It was mentioned before that it is still possible that the Actual
Balance Performance Index (ABPI) sinks under 1 resulting in cash shortage for the
contractor. To avoid this, the contractor can introduce buffers by moving up the
milestones.
First of all, ABPI is investigated for projects subject to the assumption of invoicing
at specific milestones without buffer. The contractor can, based on his planned cash
inflows and cash outflows, determine at what points in time, milestones should be
appointed in order to avoid values of PBPI under 1. These milestones correspond
with certain percentages of work completed. When these postulated percentages of
work completed are reached in the real scenario, an invoice is sent to the client. In
line with the calculation of Percentage Cash Shortage (cfr. equation 5.2), the Actual
Percentage Cash Shortage (APCS) is calculated per network as follows:
APCS =
T∑t=1
(1−ABPI(t)) if ABPI(t) < 1 (10.1)
84
Figure 10.1: APCS per SP for invoicing at milestones
For this analysis, the lower (a) and upper (b) bound of the triangular distribution
to calculate the real duration of activities are fixed to 1 and and 1.5 respectively.
This way, activities that run late on average are simulated, which is needed for this
analysis. The range between lower and upper limit is not too wide, however, so that
the impact of variability is not harmful for the analysis. APCS is calculated for all
900 project network instances [12] and averages are taken per SP-factor. The results
can be seen in figure 10.1.
When no buffers are applied, milestones are scheduled on points in time where
AVWS equals EEWS. If the contractor wants to reduce the risk of negative cash
positions in the real scenario, he should schedule these milestones on points in time
where AVWS equals (1+x)∗EEWS with x the magnitude of the buffer (0 ≤ x ≤ 1).
Again, APCS is calculated as in equation 10.1 for the 900 network instances [12] and
for different buffer sizes. Averages are taken per SP-factor. The results are shown in
figure 10.2.
For greater buffers, the performance of ABPI improves. For parallel networks,
there is less buffer needed to avoid cash shortages in the real scenario than for serial
networks. This can be explained as follows. In order to reach a milestone, a certain
percentage of work should be completed. In a serial network, a percentage of work
will only be completed if a range of consecutive activities is completed. If an activity
is late, subsequent activities will also end late and as a consequence, the needed
percentage completed will be reached after the planned duration of these activities
plus the delay. The milestone will be postponed with the whole delay of that activity.
If an activity ends late in a parallel network, other activities that can be performed
simultaneously will make it possible to reach the needed percentage completed before
the planned time of the milestone plus the delay. The milestone will be postponed
but not with the same amount as the delay of that activity.
85
0
2
4
6
8
10
12
SP=0,1
SP=0,2
SP=0,3
SP=0,4
SP=0,5
SP=0,6
SP=0,7
SP=0,8
SP=0,9
buffer=0
buffer=0,1
buffer=0,2
buffer=0,3
APCS
Figure 10.2: APCS per SP for invoicing at milestones with buffer
86
Part IV
Final reflections
87
Chapter 11
Conclusions
Since the introduction of Earned Value Management systems, project managers were
provided with a simple and straightforward way to track the performance of their
project in comparison to the baseline cost and time schedule. Through the unique
interaction of scope, cost, and time, project managers can thus receive early warn-
ing signs of poor performance and take appropriate corrective actions to bring their
project back on track. One of the important features of EVM systems therefore is its
ability to forecast the final project budget and duration.
Although in this regard, many studies have examined the accuracy of EVM cost
and time forecasters, a more margin-based approach to this research has not been
applied until recent. While more attention is paid to cash flow modeling and forecast-
ing in recent years, linking the common practices of this domain to the field of EVM
has, to the best of our knowledge, never been explored before Gorog introduced ‘A
comprehensive model for planning and controlling contractor cash flow’[17].
The research of this master thesis is focused on revealing the added value − or
lack thereof − of this model to the field of project management and to Earned Value
Management in particular. In specific, after reviewing some of the basic EVM con-
cepts, the aim was to bring clarity in the new model by use of an extensive example
project. In our opinion, this comprehensive example succeeded in creating an envi-
ronment to familiarize with the basic concepts of the new model and was of great use
when analyzing the many measurements and redefining the scope of this document
to those measurements that appeared to be of greater value. For these elements, the
practical usefulness was evaluated and tested.
In what follows, the main conclusions of this analysis will be reviewed. Thereafter,
based on these conclusions, some recommendations will be proposed for practicing
project managers in chapter 12.
88
11.1 Usefulness of Contractor Cash Flow indicators
In part II, the Contractor Cash Flow (CCF) indicators as proposed by Gorog have
been presented and illustrated with an example project. They have been carefully
analyzed and compared with the traditional EVM metrics and indicators. Further-
more, their usefulness for the contractor has been thoroughly investigated. It became
clear that two of the proposed indicators can be of great value for the contractor. The
first one is the Planned Balance Performance Index (PBPI), which shows the relative
evolution of the planned incoming cash flows compared to the planned outgoing cash
flows. PBPI is as such an indication of the cash position of the contractor. When the
planned cash flow balance is negative, there is a planned cash flow deficit. In that
case, the project is no longer self-sustainable. The fact that a project is self-financing
as a whole is not enough to make sure that the contractor can meet all the payment
conditions applicable to his project however. If a project is not self-financing at a
certain moment during the life of the project, the contractor should look for addi-
tional financing to assure his survival in the marketplace. Additional cash inflows can
be provided by other projects executed by the contractor or by external cash providers.
All project activities that need to be executed to successfully complete a project,
carry costs with them and generate revenues. The contractor can control, influence,
and improve his planned cash position by scheduling and rescheduling these activities.
He can also make use of the values of PBPI to determine the most advantageous
invoice milestones and pay delay conditions to be fixed in the contract. The aim is
to have a positive planned cash position at all times.
Due to unforeseen events, the actual cash position can be worse than the planned
one. To hedge against this downward risk, it can be recommended to make use of
buffers of which the size will be dependent on the degree of risk the contractor is faced
with. The impact of rescheduling and the introduction of milestones and buffers was
investigated and resulted in considerable improvements of PBPI. The degree of im-
provement was dependent however on the extent to which a project network structure
is close to a serial or parallel network. It can be concluded that the improvements
for parallel networks are greater than those for serial networks. It should be no-
ticed however that the schedule corresponding with the best planned cash-position is
not necessarily the schedule with the best Net Present Value (NPV). The contractor
should make a trade off between PBPI and NPV. If the contractor is in a difficult
cash position, it can be worthwhile to give up part of his NPV to improve his cash
position. In chapter 10, the positive impact of the use of milestones and buffers on the
Actual Balance Performance Index (ABPI) was established by setting up a simulation
study in which the downward risk of performing late was incorporated. It could be
concluded that for greater buffers, the performance of ABPI improved. Furthermore,
for parallel networks, there is less buffer needed to avoid cash shortages in the real
scenario than for serial networks.
89
A second interesting indicator proposed by Gorog is the forecaster to estimate the
margin at completion. In an environment characterized by increasing competition, it
is important for a contractor to be able to propose a competitive bid price when in
the running for a project. Therefore, not only does he need to have good insights on
the risks involved when executing the project, but above all he should be able to make
an accurate estimate of what his final margin will be under various circumstances.
The Estimated Margin at Completion (EMC) is of great value for the contractor in
the decision of a project’s fixed contract price, under the condition that EMC is a
reliable forecaster. To test the accuracy of EMC, a simulation study was set up.
11.2 Forecast accuracy of Expected Margin at Com-
pletion
In part III, several simulation studies have been performed in order to analyze the
most important aspects of the new model for planning and controlling contractor
cash flows. It was mentioned before, that besides PBPI, EMC is one of the indicators
that seemed promising, if and only if the accuracy of this forecasting measure was
to be guaranteed. As the goal of this master thesis was to maintain an academic
perspective, an extensive Monte Carlo simulation was a preferred methodology over
a case-wise approach.
11.2.1 Impact of external project parameters
Chapter 7 thoroughly evaluated the forecast accuracy of EMC under several project
parameters in three simulation runs. The impact of the type of project network, the
uncertainty of the project environment and the effect of the evaluation moment dur-
ing the project life cycle is tested one after the other for two main reasons. The first
purpose was to examine to what extent it would be possible to generalize the results.
The second purpose was to track situations in which the forecasting measure, EMC,
performs the best. In order to be able to compare the results of the simulation runs
for a wide range of various project network instances, the mean absolute percentage
error between estimated margin and actual margin at completion was introduced.
The first simulation run, which aim was to analyze the effect of the project network
or topological structure, has revealed that the closeness to a complete serial or par-
allel network has a great impact on the forecast accuracy. The behavior of the mean
absolute percentage error between estimated margin and actual margin at completion
indicated that projects with a tendency towards a serial network structure, on aver-
age make larger estimation errors than projects with a tendency towards a parallel
structure. The forecast accuracy of EMC, and as a consequence its reliability, thus
decreases when projects move from a parallel to a serial network structure. The sec-
ond simulation run was set up to test the impact of the variability between planned
90
and actual activity duration on the forecast accuracy of EMC. The probability of
an activity ending early or late was simulated by attributing a percentage lower and
upper limit on activity duration respectively. The variability in activity duration can
then be defined as the range between that lower and upper limit. It could be con-
cluded that the forecast accuracy of EMC was greatly influenced by the variability in
activity duration. More precise, increasing amounts of activity variability led to an
increased estimation error and thus to a poorer performance of the forecaster. In the
last simulation run of chapter 7, the impact of the completion stage of the project on
the forecast accuracy of EMC was tested. This analysis revealed that for early as well
as for late projects, significantly smaller estimation errors were made near the end of
the project in comparison to the beginning of the project.
11.2.2 Impact of margin attribution system
Chapter 8 introduced various ways a contractor can attribute margin to the activities
of a project. In different simulations runs, the influence of fixed, regressive, progres-
sive, and random margin attribution systems was examined. The first simulation run,
which purpose was to test the impact of various values of fixed margin per activity on
the forecast accuracy of EMC, generated some interesting insights. When the over-
all financial result of a project is close to a break-even situation, the mean absolute
percentage error between expected margin and actual margin at completion becomes
very high, thus indicating that EMC is not a reliable forecaster when the average per-
centage expected duration overrun is close to the margin(%) that is attributed. The
remaining simulation runs revealed that for the regressive, random, and above all the
progressive margin attribution system, the forecast accuracy of EMC is worse than in
the case of a fixed margin attribution system. This is due to instability of the Mar-
gin Performance Index (MPI), one of the essential elements of which the Estimated
Margin at Completion consists.
11.2.3 Comparison with traditional Earned Value Management
To assess the real value of EMC, it was recommended to compare its accuracy with
the accuracy of previously used methods to estimate the margin at completion. Before
the introduction of Gorog’s model, it could be assumed that a contractor would just
have used the traditional EVM metrics to estimate the margin at completion. This
could for instance be done by deducting the Estimated cost At Completion (EAC)
from the fixed contract price (IAC). In literature, several formulas for EAC were
proposed, taking into account different possibilities for the performance of future work.
Under the assumptions made in this master thesis, the formula for EAC based on a
performance factor equal to CPI resulted in the best forecast accuracy. Comparing
this accuracy with the accuracy of EMC revealed that EMC is not more reliable than
traditional EVM to forecast the margin at completion. For projects with a fixed
margin, the accuracy for both methods was exactly the same. An extensive algebraic
91
deduction, starting from the EMC formula as proposed by Gorog, confirmed our
findings and proved the equality of EMC and IAC-EAC, under certain conditions.
When random, regressive, or progressive margins were applied, the traditional EVM
method for estimating the margin at completion was more accurate than EMC. In the
simulations performed in this master thesis, EMC was in the best case as accurate as
the method using the traditional EVM metrics. It should be noticed however, that
under different assumptions, it is possible that the formula of EAC leading to the best
accuracy, would be one with a different performance factor than CPI. If the contractor
has sufficient knowledge about which performance factor to use best, he will be able
to estimate the margin at completion in an accurate way by using traditional EVM.
If the performance factor does not equal CPI, the accuracy of EMC will even in the
best case, be less than the accuracy of the traditional EVM method.
92
Chapter 12
Recommendations
Gorog expressed two major concerns in the currently available techniques to plan and
control the project implementation process, which can be summarized as follows:
1. Control models such as Earned Value Management adopt a mainly client-view
and thus do not provide the possibility for contractors to plan and control the
contract cash flow.
2. The ability to estimate the likely margin is of vital importance if a contractor
wants to be able to elaborate a competitive bid price and is not possible with
traditional Earned Value Management in case of a fixed contract price.
What we have come to realize when evaluating the Contractor Cash Flow (CCF)
model, is that it does serve the purpose of canceling out part of the first objection.
Especially in the case of activities that, notwithstanding their duration or cost, do not
all add the same value to the project in general, Planned Value based on the incurred
costs, does not succeed in accurately representing this value. The Price Value (of
Work Scheduled) then is a more precise measurement.
Although we do recognize the importance of being able to accurately plan cash
flows and control whether or not the invoiced value is received on the contractors
bank account entirely and as planned, it still seems to belong more to the field of
interest of an accountant than to that of a project manager. In addition, controlling
all of this would imply a huge increase in measurements and indicators to monitor on
top of the EVM metrics. We fear that this would only complicate things and thus
eliminate part of the value of EVM systems, namely their simplicity.
One of the more promising elements was the Planned Balance Performance Index
(PBPI). We have proven its usefulness and even its necessity when trying to sched-
ule the project with the objective to avoid negative cash balance situations while
remaining within the predefined duration limitations set by the baseline schedule. In
addition, we have suggested another interesting application of this indicator, where it
can be used to determine the optimal number, location (and value) of milestone pay-
ments in the project schedule, with the same objective of eliminating negative cash
93
positions. Therefore, we do recommend the use of PBPI and its many applications as
a planning tool. It provides valuable information for the contractor and the software
needed for these scheduling applications is not very challenging to create, nor to use.
It should be fairly straightforward to provide the contractor with a software extension
that, based on the planned value used in his EVM package and only few additional
data (pay delay, margin), can provide the contractor with the optimal schedule and
milestones plan. We would not however recommend it as a way to perform more
extensive controlling when the project is actually being implemented. This would
imply that even more measurements and indicators would need to be monitored in
order to track changes in the Plan Performance Index, which ultimately compares
the Planned Balance Performance Index and the Actual Balance Performance Index.
This indicator is far from being a candid warning signal.
The second objection towards Earned Value Management, namely the impossibil-
ity to estimate the likely margin in case of a fixed contract price, was evaluated by
means of an extensive simulation study. Under the same set of assumptions as the
one Gorog had stipulated for her model, we have been able to prove that only under
two conditions the proposed formula for Expected Margin at Completion performs
well. The first being that the Cost Performance Index is the best indicator for future
performance and can thus be used as the basis for estimating the likely total cost at
project completion, the second being the assumption that the same fixed margin(%)
can be attributed to each activity.
In case the first assumption is not satisfied and CPI is not a reliable indicator
for future cost performance, then EMC loses its predictive ability. When the second
assumption is not satisfied and margins cannot be expressed with the same fixed
percentage per activity, we were able to prove the decrease in predictive ability of
EMC as well.
However, even in the ‘best case scenario’ where both assumptions are satisfied,
we still would not recommend the use of the proposed formula for Expected Margin
at Completion, as we have also proven its equality to a much simpler formula for
which only the currently available EVM measurements are needed. Through these
discoveries, our belief in the Earned Value Management System ‘as is’ has grown
substantially. We are glad to be able to dismiss the second objection raised against
EVM and to conclude that no elaborate or oversophisticated formulas are needed to
postulate a competitive bid price.
Furthermore, we believe that these conclusions can be of great value for anyone
who is occupied with trying to model, control and predict cash flows. It is there-
fore that we argue in favor of introducing Earned Value Management in this part of
project management discipline as well. In that respect, we very much agree with and
support the effort made by Gorog to incorporate Earned Value Management into this
discipline.
94
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