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Traditional Earned Value Management (EVM) index-based methods for Cost Estimate at Completion (CEAC) of an ongoing project have been known for their limitations inherent with both the assumption that past EVM data is the best available information and early-stage unreliability. In an attempt to overcome such limitations, a new CEAC methodology is proposed based on a modified index-based formula predicting expected cost for the remaining work with the Gompertz growth model via nonlinear regression curve fitting. Moreover, the proposed equation accounts for the schedule progress as a factor of cost performance. To this end, it integrates into its equation an Earned Schedule-based factor indicating expected duration at completion. The proposed model shows itself to be more accurate and precise in all early, middle, and late stage estimates than those of four compared traditional index-based formulae. The developed methodology is a practical tool for Project Managers to better incorporate the progress status into the task of computing CEAC and is a contribution to extending EVM research to better capture the inherent relation between cost and schedule factors. © 2013 Elsevier Ltd. APM and IPMA. All rights reserved.

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An earned schedule-based regression model to improve cost

estimate at completion

Timur Narbaev, Alberto De Marco

INTERNATIONAL JOURNAL OF PROJECT MANAGEMENT -

Elsevier - PrePrint

Abstract

Traditional Earned Value Management (EVM) index-based methods for Cost Estimate at

Completion (CEAC) of an ongoing project have been known for their limitations inherent with

both the assumption that past EVM data is the best available information and early-stage

unreliability.

In an attempt to overcome such limitations, a new CEAC methodology is proposed based on

a modified index-based formula predicting expected cost for the remaining work with the

Gompertz growth model via nonlinear regression curve fitting. Moreover, the proposed equation

accounts for the schedule progress as a factor of cost performance. To this end, it interpolates

into its equation an Earned Schedule-based factor indicating expected duration at completion.

The proposed model shows itself to be more accurate and precise in all early, middle, and late

stage estimates than those of four compared traditional index-based formulae.

The developed methodology is a practical tool for Project Managers to better incorporate the

progress status into the task of computing CEAC and is a contribution to extending EVM

research to better capture the inherent relation between cost and schedule factors.

Keywords: Cost estimate at completion; Earned schedule; Earned value management;

Regression analysis.

1. Introduction

Forecasting project cost at completion is of great importance to project management success.

It is a forward looking tool to assist Project Managers with the task of making timely and

appropriate decisions about cost outcome of their in-progress projects (Fleming and

Koppelman, 2006).

For over four decades, Earned Value Management (EVM) has been used to forecast cost at

completion. This objective methodology integrates project cost, schedule and scope metrics into

a single measurement system. It is widely applied for measuring and analyzing project actual

status against its baseline, and for providing estimates of project cost and duration at completion

(De Marco and Narbaev, 2013). In particular, EVM is used to compute Cost Estimate at

Completion (CEAC), a top-down estimate of the project total cost based on the project's status.

Within the EVM framework, several methods exist to compute CEAC, classified as either

index-based (IB) or regression-based techniques (Christensen et al., 1995 ; Lipke, 2004 ).

In general, IB methods have an inherent limitation due to their only reliance on past

information: they assume that remaining budget is adjusted by a performance index (Fleming

and Koppelman, 2006; Kim and Reinschimdt, 2011). The second concern associated with the

traditional approach is that it provides unreliable cost forecasts early into a project life because

of few available EVM data (Fleming and Koppelman, 2006; Zwikael et al., 2000 ). In this

regard, some studies (Anbari, 2003; Cioffi, 2006; Kim et al., 2003; Lipke, 2004 ) simplified

practical implementation and/or extended applications of IB forecasting methods whereas other

researches (e.g., Kim and Reinschmidt, 2011; Lipke et al., 2009; Marshall et al., 2008 )

employed statistics into EVM forecasting system to benefit from deeper analysis to support

decision making. Caron et al. (2013) , Naeniet al. (2011) , and Pajares and Lopez-Paredes (2011)

integrated risk management techniques to consider also uncertainty as a potential source of

structural change in cost and schedule performance in the project dynamic environment.

With the purpose of overcoming the two mentioned weaknesses of IB approach and produce

more reliable CEAC, regression techniques have been regarded as an alternative to traditional

IB methods. Through their curve fitting process, regression techniques improve accuracy of the

CEAC, especially as they may use a combination of EVM data with Earned Schedule (ES) data

and provide more reliable forecasts early into the project life.

However, reported literature reveals that little advancement has been made in the area of

improving reliability of the IB approach via its refinement by regression techniques (Lipke et

al., 2009; Marshall et al., 2008; Tracy, 2005). Most studies integrating regression concepts into

IB approaches concern U.S. defense projects, which are complex in nature with large budgets

and long durations (Christensen et al., 1995 ; Lipke et al., 2009 ). In addition, within the EVM

framework, available regression-based methods to compute CEAC do not consider schedule

progress in cost estimates (Lipke, 2003 ).

To fill these gaps, a new regression methodology is proposed to provide more reliable

CEAC. The developed model overcomes the limitations inherent to traditional IB approaches.

In addition, the model regards project schedule as a factor of cost performance and, hence, takes

into account for the schedule progress, measured via the ES concept, to calculate CEAC. The

model equation is a classical IB formula modified with a Gompertz growth model function and

it integrates an ES-based factor to indicate the expected completion time used into the model.

The paper is structured as follows. Section 2 frames commonly used IB formulae for CEAC,

introduces a regression approach for cost S-curve fitting, and formulates a Gompertz growth

model to implement it to the proposed methodology. Section 3 designs the methodology and

establishes a framework for evaluating the model and comparing its estimated results with those

of IB formulae. In Section 4, we apply EVM data from nine projects to show application of the

proposed model, derive the study results, and present the role of ES in the developed

methodology. Section 5 explores the findings of the research and associated implications.

Section 6 presents the work contributions in advancing the body of knowledge and draws

conclusions and suggestions for future research.

2. Cost estimate at completion methods and framework

2.1. The index-based approach

In the EVM theory and practice, the calculation of the CEAC entails summing up two factors

(Eq. (1) ), namely: the Actual Cost (AC) of perform ed work to the Actual Time (AT), and the

estimated cost of the remaining work. The second factor is a difference between the Budget at

Completion (BAC) and the Earned Value (EV) adjusted by a Performance Index (PI – a

measure of cost efficiency of budgeted resources) (PMI, 2011 ).

)))/PI(EV(-(BAC)AC()CEAC( xxxx  (1)

The choice of a desirable PI depends on the project status and associated risks. Zwikael et al.

(2000) relate this choice to premises set by Project Managers in selecting the PI, from the belief

that all past cost deviations cancel into the future so that their projects can be accomplished

within the BAC to a pessimistic argument that the deviations will continue at the rate observed

so far. PMI (2011) provides four PIs to correct the remaining BAC (Table 1 ) with different

assumptions associated with actual project performance. Among these indexes the most

commonly used is the Cost Performance Index (CPI), which assumes that past cost performance

is the best available indicator of future cost outcome as a reasonable floor estimate. Anbari

(2003) states that an estimate obtained using a product of CPI and Schedule Performance Index

(SPI) is an indicator of the overall project health and is a ceiling CEAC to reflect both cost

deviation and schedule progress. Fig. 1 presents the EVM metrics addressed above and used in

this research.

Insert Table 1

Insert Fig. 1

Since this IB approach only relies on past information, it requires stability of the PI to

provide for reliable CEAC. In this regard, previous research carried out on defense projects

found that a cumulative value of CPI stabilizes by the time the project is 20 percent complete

and the forecast value does not vary by more than 10 percent from that point in time to

completion. The EVM community received this finding as a rule of thumb and generalized it as

being applicable for all types of projects. However, recent studies challenged this finding

attributing it to large-scaled and long duration defense and energy projects only ( Henderson and

Zwikael, 2008; Lipke et al., 2009). They questioned whether the PI stability existed and found

that most projects from other industries (e.g., construction, software) with relatively small

budgets and short durations, achieved the PI stability by the second half portion of the project

life.

2.2. The regression-based approach and S-curve fitting

To overcome such limitations of conventional IB techniques, regression-based techniques

have been gaining acceptance by practitioners. The main feature of these methods is that they

describe a linear or nonlinear statistical relationship between a predictor (input) and response

(output) variables through their parameters (Bates and Watts, 1988 ). Parameters of a regression

model represent the behavior of project cost over the whole lifecycle.

Efforts put to apply regression models are greater than those needed for relatively simple IB

cost forecasting methods. However, claims have been made that they yield better estimates early

in the project life, while the IB approach is likely to be unreliable (Tracy, 2005 ).

In Project Management, S-curves are used to graphically display cumulative progress of

work, expressed in units of costs, labor hours, progress percentage, etc., plotted against time

(PMI, 2008 ). The S-like shape of this curve represent s work progress which has lower rate at

the beginning and end (steady patter) and higher rate in the middle (steeper pattern). In EVM,

such curves are used to display AC, EV, and Planned Value (PV) of a project over the time axis.

Cioffi (2005) proposed a parameterized S-curve tool for managing cost of an ongoing project: it

is the derivation of a modified logistics equation with minor mathematical assumptions Project

Managers can easily set. The model was validated using two projects and showed flexibility in

generating a desired smooth cost profile by selecting the strength of the rise of the curve and the

point at which half the total cost was spent.

Depending on type, complexity, and nature of a project, the time-cost relationship can be

modelled using different mathematical equations (Warburton, 2011 ). Defining an equation for

the S-curve model requires considering some issues relevant to nonlinear regression analysis.

First, such models require defining initial values for their parameters and setting an algorithm

for the least squares (LS) approximation (Bates and Watts, 1988 ). In nonlinear regression, there

is no standard approach to specify initial values and one needs to know initial information (e.g.,

prior historical data, EVM data, variables relationship) in dealing with this task. This is because

a model's predictor and response variables have a nonlinear relationship.

Second, the most common assumption in nonlinear regression is that the observed data

points around the S-shaped curve follow a Gaussian distribution. With these concerns, nonlinear

curve fitting approximates values of the model parameters with LS method minimizing the sum

of squared errors of estimated and actual values. The proposed methodology applies the Gauss-

Newton algorithm for this iterative approximation, which converges not heavily depending on

initial values (Bates and Watts, 1988 ) of a nonlinear model within specified tolerance

thresholds.

2.3. The Gompertz growth model formulation

A Gompertz growth model (GGM) has found wide application in many fields associated

with population growth studies, such as biology, economics, marketing, etc. The model

describes phenomena inherent to data with a growth pattern. It is extensively used in curve

fitting and forecasting and belongs to a family of sigmoidal models.

The GGM generic function is given in Eq. (2). The α is a future value asymptote of the

model that represents the final cost (which is never attained) as time (x ) tends to infinity (Seber

and Wild, 1989). The β parameter is the y -intercept indicating an initial budget size and the γ is

a scale parameter that governs the cost GR.

][ )(

)GGM( x

e

αex







 (2)

This model features with the position of the inflection point at approximately 1/3 of the total

growth (GGM(x )=α /e ) at time (x =β /γ ) when its growth rate (GR=αγ /e ) is the greatest. The

growth rate monotonically increases to a maximum before steadily declining to zero (Seber and

Wild, 1989). Fig.2 illustrates the S-shaped curve of the GGM.

Insert Fig. 2

With regard to the project cost growth, the GGM shapes such growth considering the cost

behavior as follows. During the project initial stage, work progress is typically slow, it speeds

up close to the middle stage increasing the cumulated cost accrual associated with the progress

and accelerating the GR. Finally, as the project reaches its completion, there is less work

remaining decreasing the GR to zero.

Recently, Trahan (2009) proposed to use the GGM as an industry proxy for future projects.

S-curves were developed using EVM data from a number of U.S. defense contracts. The

parameters of the S-curve model for complete projects were found by regressing normalized AC

values of the entire project life against respective time points. The majority of the sample

projects experienced cost overrun. Therefore, the normalization of AC and actual time values to

BAC and planned duration, respectively, produced the values for the S-curve model parameters

best suitable for overrun projects. Hence, the major finding was that the model is accurate to

compute CEAC of either overrun or overrun-close projects.

Trahan's work is one of the inspiring references of this proposed GGM. However, in contrast

with Trahan's work, the method proposed in this paper presents a comprehensive

methodological approach, greater validity, increased practicability for ongoing projects, and

extended applicability to various stages of a project life cycle.

3. Methodology

3.1. The Earned Schedule method

The CEAC methodology proposed in this paper integrates ES concepts into its equation to

take into account the project work progress. The ES technique overcomes limitations inherent to

the EVM method when it comes to computing Expected Duration at Completion (EDAC) of a

project (Lipke, 2003 ). It measures the schedule progress in time units and eliminates a

deficiency of EVM-based SPI, which tends to unity as the project approaches its completion,

regardless of any early or late finish. As far as the accuracy of the ES method in computing

EDAC is concerned, comparative studies with EVM methods show that the ES technique

provides more accurate estimates than SPI-based calculations (e.g., Vandevoorde and

Vanhoucke, 2006).

The value of ES is obtained by projecting to actual date the EV curve onto PV curve

assuming that the current EV should actually have been earned at that projected time

(Fig.1 ).Therefore, the ES is defined as per Eq. (3) .

ES(x )=C(x)+I(x ) (3)

Where C and the subscript c denote the number of total time units for which EV exceeds PV

and the incremental portion I(x ) = (EV(x ) - PVc)/(PVc+1 - PVc) which is more or equal to 0 and

less than 1.00.

As a consequence, a time-based SPIt can be defined as per Eq. (4) .

SPIt (x )=ES(x )/AT (4)

Thus, the resulting EDAC when the project is at time (x ) is the ratio of Planned Duration

(PD) to SPIt (x ). As the proposed approach utilizes the ES concept to consider schedule impact

in CEAC, the model uses the inverse of SPIt (x ), which is the ratio of EDAC to PD.

For the purpose of better understanding the proposed equation, this inverse ratio is referred

to as Completion Factor (CF). The CF indicates EDAC yielded to unity and it can also be

defined as inversely related to SPIt (x ) (Eq. (5) ).

1

t)(SPI)/PDEDAC()CF( 

 xxx (5)

If the value of the CF, based on work progress to date, is greater than 1.00 it indicates that a

project is likely to be delivered late, whilst less than 1.00 shows an early finish.

3.2. The proposed CEAC model

This section develops the new methodology following three steps. First, the values of the

three parameters of the GGM (Eq. (2) ) are found through nonlinear regression analysis.

Then, the new CEAC formula is introduced with integrating parameters of GGM to calculate

CEAC.

Finally, we further modify the CEAC formula with the purpose of reflecting schedule

progress on cost performance. To this end, the ES-based CF is integrated into the formula. Here,

the CEAC equation has two variants: a base one without integrating the CF, and an ES-based

one that interpolates the value of the defined CF.

Recently, Narbaev and De Marco (2013) provided comparative study on this CEAC

methodology integrating four growth models (Bass, Gompertz, L ogistic, and Weibull) into its

equation. They found that GGM is the best statistically valid model converging to approximate

values of its parameters in nonlinear regression curve fitting. In addition, the GGM generates

more accurate CEAC for early and middle stages of the project life. This work provides further

extended applicability and reliability of the previous model by providing accurate late estimates,

analysis of forecast precision, model timeliness, and integration of the influence of schedule

progress on the CEAC computation.

In particular, the proposed GGM is compared with four different index-based performance

indexes, is applied when the project is 80 percent complete, is tested the narrowness of the

forecast error, and is proven its reliability over time, which refers to as generating more accurate

and precise cost estimates in both the early and middle and late completion stages of a project.

The first step in developing the methodology is to find the three GGM parameters through

nonlinear regression curve fitting. For this, both time (a predictor variable) and cost (a response

variable) units are normalized to input into the GGM equation. The normalization of all the

values of time points to unity (1.00) assumes a project is 100 percent time complete (i.e.,

PD=1.00). Each next time point is a cumulated portion of this unity with the final time point

representing PD (1.00) of a project. These values represent a predictor variable (x ) of the GGM.

Each time point (x ), a value of the predictor variable, has a corresponding cost point, a value of

the response variable. These corresponding cost points are formed as follows. The values of AC

from time zero (x =0) to AT are normalized to unity (i.e., BAC=1.00) while the values of PV

from AT onto project completion with the final value of the normalization representing BAC

(1.00, i.e., 100 percent complete). Then, the normalized values of to date AC and PV are

combined to form the values of the response variable (y ) in the GGM.

Finally, each time point (x ) of the GGM equation (Eq. (2)) has its corresponding cost value

(y ) to run the nonlinear regression with the GGM. This allows finding the values for the three

fitting parameters. Both time and cost units have final values equaling 1.00 (PD=1.00 for time

and BAC=1.00 for cost).

The following requirements are taken into account for the GGM equation in the nonlinear

regression curve fitting: the normalization of the predictor and response variables and what the

three parameters represent an initial value for these parameters is 1.00 with the confidence level

95% and the approximation algorithm the Gauss-Newton (which converges the parameter

values not heavily depending on their initial values). Then, via running this regression

procedure, the values of the three parameters are obtained: the α asymptote, the y -intercept β ,

and γ -scale. The Minitab® software tool is used for this task.

The second step requires computing CEAC by using Eq. (6) . This equation is the refined

version of a classical IB formula as previously given in Eq. (1) . The difference is that Eq. (6)

calculates the remaining expected cost by regression analysis, while the IB formula adjusts it

with a PI. The second summand is an estimate to complete a project. It is equal to the product of

BAC times the difference of the two values of GGM (Eq. (2)): when a project is 100 percent

time complete (the result of the GGM function when time (x) is 1.00) and at AT (the result of

the GGM function when time (x) is at AT).

)]BACGGM(-)[GGM()AC()CEAC( x1.00xx  (6)

Finally, the GGM is modified to consider possible influence of work progress on CEAC. The

main assumption of this refinement is that a favorable schedule efficiency tends to improve the

final cost, while a poor schedule progress may increase the final cost. To this end, in Eq. (6), the

value of x=1.00 (which implies that a project finishes on time) is replaced by the CF (the ratio of

EDAC to PD). This is less than1.00 if a project is ahead of schedule and greater than 1.00 if a

project is behind schedule. This modification represents a cost-schedule integrated approach

because the cost estimate considers the schedule impact as a determinant factor of cost behavior.

The refined CEAC formula is given in Eq. (7) .

)]BACGGM(-))[GGM(CF()AC()CEAC( xxxx  (7)

3.3. Evaluation of the model

This section provides the framework for assessing the quality of the proposed methodology

and analyzing the influence of schedule progress through ES-based CF on CEAC. The

evaluation of the forecast is based on two criteria: accuracy and precision.

Among the two criteria to assess the quality of a cost forecasting method, accuracy is

regarded as the most often used and important one (Yokum and Armstrong, 1995 ). This study

measures CEAC accuracy by a percentage error (PE) and the mean absolute percentage error

(MAPE) for early, middle, and late stages. PE is the difference between CEAC and Cost at

Completion (CAC) expressed as a percentage of CAC with a negative value suggesting

underestimation and a positive value the overestimation. MAPE is referred to as the average of

the absolute values of differences between CEAC and CAC over the number of projects tested

(Bates and Watts, 1988 ). Eq. (8) and Eq. (9) are used to compute these measures:

%100

CAC

CAC-CEAC

PE%  (8)

%PE

1

CAC

CAC-CEAC

100%

MAPE% 11  



n

i

i

n

ii

ii

nn (9)

Where CAC – Cost at Completion; n – number of projects.

The second criterion of the model is precision, defined as the narrowness of a forecast error.

It is measured by the Standard Deviation (SD), which is an indicator of a statistical dispersion of

the values of prediction errors from the average forecast within the population (Seber, 1989).

SD is computed by Eq. (10), which takes the square root of the variance (the average of the

squared differences between the PE of an individual project and mean of the PEs). A smaller

value of SD indicates that cost estimates calculated by a particular model are closer to its MPE

and, hence, produce more precise CEACs.

%

)MPEPE(

SD% 1

2

n

n

i

i







 (10)

The accuracy of EVM cost forecasting methods should also be reliable over a certain period

or the entire project life. This property of cost forecast is defined as timeliness and shows

reliability in accuracy of cost forecasting (Kim, 2007 ). From a practical perspective, Project

Managers may be more concerned about timeliness in cost forecasting as it implies reliability in

cost forecasting and provides a project team with warning signals about the final cost outcome

(Kim, 2007; Kim and Reinschmidt, 2011 ). Teicholz (1993) defines it as accuracy of estimates

during the first half of project duration. Vandevoorde and Vanhoucke (2006) evaluate it

correlating to changes in EDAC accuracy over the project's final stage. These works report

timeliness analysis with regard to accuracy of estimates. This paper adds also analysis of the

precision timeliness. In this regard, this paper defines the timeliness of the proposed CEAC

methodology as a property describing more accurate and precise CEAC over the three forecast

stages. From a practical perspective, this may be of great importance to Project Managers as it

suggests reliability of the cost forecast process.

Finally, based on these two criteria, estimates using the proposed model are compared with

the four IB methods according to PI values and assumptions given in Table 1 .

As discussed earlier in the paper, another important advantage of the proposed methodology

is the ability to appropriately capture the influence of the schedule progress into CEAC. The

EVM approach is known as an objective method that assists project managers in the task of

monitoring and controlling projects through an integrated cost-schedule-scope measurement

system (PMI, 2008 ). This implies that changes in one element of this triangle may cause

changes in the other/others. One of basic prerequisites of EVM approach is that work scope

remains as it is throughout the project life. On the contrary, the scope of work is revised when

complimentary activities are added into a project upon approval of change orders from a project

owner. Such scope change is subject to project's rescheduling leading to potential changes in all

components of the measurement system including a work breakdown structure, the performance

measurement baseline and so forth. In such a case, the EVM system is revised according to

these changes.

In line with these considerations, the proposed CEAC model considers the possible influence

of work progress on CEAC. This relation is reflected through the integration of ES-based CF

which is related to SPIt and, hence, a measure of time-based schedule efficiency (PMI, 2011).

For this, at some time(x ) if the project schedule efficiency is favorable (CF<1.00) this shows

that the final cost tends to improve, while a poor efficiency (CF>1.00) would influence increase

of the final cost. However, it is noted that this cannot be generalized for those ongoing projects

that are subject to adjustments and corrective actions as measures to speed up the work

progress, such as in the case of activity crashing or fast tracking. This usually results in cost

increase or significant changes to the original scope and schedule network (e.g., re-baselining),

which in turn needs the EVM system to be reset.

The model considers this relationship by replacing the 100 percent time completion value

with the value of the CF in its equation (Eq. (7) ). In other words, the model generates more

accurate and precise estimates when it takes into account for the schedule progress.

4. Application and results

4.1. Sample application

This study uses EVM data of nine construction projects selected from qualified reported

literature. Five out of nine projects are delivered with cost overruns and six report schedule

delays. They all are small to medium-scale projects with average BAC close to 8 million US

dollars and PD varying from 6 to 27 months.

As the number of time points and values of reported EVM data differs from project to

project, a percent value for the budget completion at early, middle, and late stages cannot be a

predetermined percentage. As a consequence, we define the range for these stages as 10-25%,

45-65%, 70-95%, respectively (Narbaev and De Marco, 2013). Below we demonstrate the

stepped procedure using EVM data of Project 1 to forecast CEAC when the project is in its

early stage.

The first step is to determine values of the three GGM's parameters through the nonlinear

regression curve fitting. Table 2 provides initial absolute values for time (column Time point)

and cost data (column PV and AC). Then these time points are normalized to unity (assuming

PD=15 is 1.00) and PV and AC values to unity (assuming BAC=3,725,000 euro is 1.00). These

normalized time (variable x ) and cost (variable y ) points are reported down on the column

Predictor and Response in Table 2 and are input data for the GGM equation to run the fitting

process. The AC-PV values are combined values of AC from time zero (x =0) to AT and of PV

from AT to BAC=15. To compute the early stage CEAC for Project 1, month 4 is chosen as

time for the early stage estimation time when 20.90% of the BAC is earned. The requirements

one should take into account when running the nonlinear regression are considered in Section

3.2 above.

Insert Table 2

The GGM equation generated by Minitab® for EVM data of Project 1 (Table 2) is given in

Eq. (11). To calculate CEAC for the early stage, four months into the project execution when x

is 0.267 (in Table 2), this GGM equation result is 0.241 (or 24.10% of the project BAC). The

interpretation of the values of the three parameters (addressed in Section 2.3) is as follows. The

ratio of the β parameter to the γ parameter gives time percent complete point (x=β /γ ) when the

cost growth rate is maximum which is 43.70% for Project 1with resulting cumulative cost of

44.20% (GGM(x )=α /e ) of the BAC. Finally, the α asymptote value of 1.202 implies that, as

Project 1 tends to infinity, it will experience 20.20% cost overrun.

][ )77322121(

2021)GMM( x..

e

e.x 



 (11)

Step 2 computes the project CEAC for its base case using Eq. (6) . For this purpose, we

additionally compute the value of GGM equation when x =1.00 (100% time complete). As

previously explained, the remaining of the project BAC must be adjusted by the difference of

the two values of GGM: when a project is 100 percent time complete and at AT. From this,

GGM(1.00 )=0.974 and we use the refined version (Eq. (6) ) to calculate CEAC of Project 1. The

methodology finds the project CEAC with PE=-6.96, which means that it is underestimating its

CAC.

Step 3 is about taking into account schedule progress based on the assumption that the

schedule is a factor of cost performance and, hence, it has its impact on the estimate. Therefore,

we include the projects CF into Eq. (6) . It is noted that the project has PD=15 months,

EDAC=16 months at AT=4, and actual duration (AD) of 16.25 months. At month four, CF

equals 1.083 and it replaces x =1.00, as given in Eq. (7) . It produces a new CEAC that considers

work progress: it is closer to CAC value with PE=-2.91 (4.05% of improvement over PE=-6.96

of the base case).

4.2. Accuracy and precision

This section presents the CEAC computations for the nine sample projects and provides an

analysis of accuracy and precision of the estimates together with an assessment of the role of the

ES influence in the early, middle, and late stages.

Table 3 allows an evaluation of the projects' CEAC accuracy in PE for the early stage

computed applying the proposed method (Eq. 6 and Eq.7 for base and ES-based cases,

respectively) in comparison with the IB method (Eq. 1). It adjusts the remaining portion of BAC

by the four PIs (CPI, CR, CI, and MA) introduced in Table 1. Accordingly, the IB method

produces four different CEACs, which vary in assumptions associated with future cost

performance (Anbari, 2003; PMI, 2011). The detailed information on how these PEs are

computed is provided in Appendix A for Project 1. In five cases (Project 1, 2, 4, 7, and 8)

CEAC results calculated by GGM (either base or ES-based cases) are more accurate than those

computed by four IB formulae. When comparing the cost estimates of two GGM cases, it

appears that the integration of CF into the model improves the model's forecasting capability

(Project 1, 2, 3, 5, 7, 8, and 9). Overall, GGM allows overcoming the critical limitation of

traditional IB formulae to accurately determine early CEAC. The IB methods generate mixed

results difficult to interpret. However, the following can be concluded: all of the traditional

formulae provide PE above 10.00 for Project 2 and 7 and above 5.00 for most of the cases.

Insert Table 3

Table 4 provides results of the estimates' accuracy (computed by Eq. 9) and precision

(computed by Eq. 10). Overall, the results show that the proposed model's estimates are more

accurate (in MAPE) and precise (in SD) than those of the index-based formulae. Also, the

integration of the schedule progress into the model equation leads to improving the CEAC

accuracy. Therefore, the ES-based GGM appears to be the most accurate and precise model in

all the execution stages. This allows concluding that schedule is a factor of cost behavior and

delay/advance in the work progress has its respective influence on the project cost outcome.

Insert Table 4

With regard to the model timeliness, as addressed in Section 3.3, it implies providing for

more accurate and precise CEAC in early, middle, and late completion stages. The results of

both accuracy and precision suggest that the ES-based GGM meets this criterion producing

more accurate (Fig. 3a ) and precise (Fig. 3b ) estimates in all of the stages. Finally, another

pattern noticed is that all the compared models (except the GGM base case) improve both

CEAC accuracy and precision as projects tend to completion.

Insert Figure 3

4.3. The role of ES in the cost forecasting

This section aims to test the effect of the schedule impact on the CEAC accuracy and to find

out if there is a relation between the work progress and the estimate accuracy. To accomplish

this analysis, we calculate CEAC for both cases (both without and with the CF). Then, the study

analyzes possible existence of a relationship between CEAC and project cost outcome

(underrun, on budget, overrun). Table 5 reports the results of the analysis: values of CF

computed at the forecast time, PE of CEAC for the two cases, and the projects' cost outcome. A

CF greater than 1.00 indicates the project is experiencing a schedule delay at the time of

estimation and warns that this poor schedule efficiency may be influencing increase in the final

cost.

Insert Table 5

Overall, the ES-based case appears to be more accurate in all three stages than the case when

the work progress is not considered. From this table it can be drawn that the integration of the

CF into the forecasting model results in more accurate cost estimates. In particular, this

improves the estimates accuracy of seven projects in the early, five in the middle, and six in the

late stages.

Additionally, the valuable contribution of the ES method to enhance accuracy of the

proposed CEAC methodology for the early, middle, and late stages is provided in Fig. 4a, b, and

c, respectively. Closer to zero line values of PE in the chart implies more accurate estimates. On

average, integration of CF into the GGM (Eq. (7) against Eq. (6)) improves the cost estimates

from MAPE=7.28 to 4.20, 5.11 to 3.47, and 5.48 to 3.22 in the early, middle, and late execution

phases, respectively.

Insert Fig. 4

5. Discussion

Three main findings of the proposed CEAC model can be highlighted with regard to its

accuracy, precision, and the influence of schedule progress on CEAC.

First, the comparative analysis (Section 4.2) of CEAC found by the proposed nonlinear

GGM and the four simple IB formulae proves that the proposed model generates more accurate

CEAC (Table 3). The cost estimates provided by the ES-based GGM are the most accurate:

4.20, 3.47, and 3.22 for the early, middle, and late stages, respectively. CEAC generated by

Base GGM and the traditional approach with CPI, CI, and MA produced the same results

between these four cases (Table 4). Lastly, the estimates computed by CR-based method are the

worst among the methods (MAPE=16.22, 10.19, and 5.72 for the three stages, respectively).

Overall, with regard to accuracy of CEAC the following concerns are worthwhile to note. The

test results show that a pure and simple traditional IB approach to forecast the expected project

final cost might be inadequate. CEAC comprises a sum of two components: to date actual cost

and the remaining portion of cost to complete. The first limitation is associated with the

assumption that a traditional IB technique is backward looking and relies on past EVM

information only. Therefore, the index-based approach adjusts the remaining BAC by PI

proposing a project will continue in its current progress until its completion. This forces Project

Managers to accept the belief that cost performance is stable for the rest of the project life.

However, the project implementation environment has uncertainty and changes in project cost

outcome that decrease as a project tends to completion. This change is reflected in the

cumulative value of CPI, which gets stabilized as a project progresses. This indicates stability in

project execution and, subsequently, ensures for more stable values of CEAC by the end of a

project. This leads to integrate the interpretation of the first finding with the second limitation of

traditional IB approaches. For a project in its early life, when few EVM data are at hand, this

technique is unreliable as it makes extrapolations from few time points for the rest of the

project: this is risky and provides inaccurate estimates.

Second, the proposed model provides more precise estimates. Precision refers to the

narrowness of the forecasting error. On average, the cost estimates provided by the ES-based

GGM are the most precise: MAPE=5.27, 3.42, and 3.17 while the worst estimates are produced

by the CR-based method as MAPE=11.82, 5.41, and 4.77 for the early, middle, and late stages,

respectively (Table 4). Overall, unlike the IB approach, the developed CEAC model gives more

accurate and precise estimates as it adjusts the remaining portion of CEAC (second summand of

Eq. 6) by the GGM via nonlinear curve fitting, whereas the IB method achieves this adjustment

by PI (Eq.1). It is a refinement of IB approach via nonlinear regression. The new technique

interpolates intrinsic properties inherent to growth models into its formula (Eq. 6 ) and takes into

account for a combination of AC (from a project start to AT) and PV (from AT onto

completion) reflected in the three GGM parameters.

Another point to remark is about the GGM property to maintain more accurate and precise

estimates in all the three stages compared to the traditional approach, as it means reliability in

the forecasting. We defined this property of the model as timeliness, referred to as the ability to

give warning signals about the final cost outcome of a project. The timeliness of accuracy and

precision means reliability in CEAC forecasting. Moreover, in the ES-based GGM case,

accuracy (Fig.3a) and precision ( Fig.3b ) appeared to improve over time from early to late stage

estimation, with decreasing values of MAPE (4.20, 3.47, and 3.22) for accuracy and SD (5.27,

3.42, and 3.17) for precision (Table 4 ). The characteristic of this decrease in the estimates'

errors proves the model to be considered as viable. This feature of the model suggests that the

observations in MAPE and SD tend to converge to the actual result at completion. In addition,

the explanation of this tendency lies in the nature of the ES approach suggesting improvement

of duration estimates as SPIt stabilizes and a project approaches its completion. In addition to

this, it makes use of nonlinear regression. The growth model via the regression combines to date

AC data with future PV for which its three parameters show the relationship between past,

current and future project performance and progress. This second finding collaborates with the

previous research (Christensen et al., 1995; Marshall et al., 2008; Tracy 2005) which reported

the advantage of the nonlinear regression modelling over the conventional IB methods in EVM

system. Our comparative analysis shows that CEAC computed by the four IB formulae produce

abrupt and, hence, unstable estimates. The values of MAPE of these four formulae vary from as

small as 4.32 to as large as 16.22 and SD ranging from 5.92 to 20.2. Therefore, the proposed

model's timeliness property is another practical advantage over the IB approach. We remark

that, in most projects regardless of their nature, budget, and duration, estimates by a traditional

approach stabilize by the second half of the project life or at late stage. The results of timeliness

of accuracy and precision are in accordance with the findings of previous research in the field.

For example Henderson and Zwikael (200 8) showed that the PI values (CPI and SPI(t))

converged to their respective final values as the project gets closer to completion.

A third finding of this study is that asserting schedule progress as a factor of future cost

improves both accuracy and precision of the developed model. EVM is a system that integrates

project cost, schedule, and scope. In this regard, schedule is known as a factor of project cost

performance. Advance/delay in work progress has its relative influence on cost behavior. The

majority of projects experience impact of schedule progress on their final cost. Therefore, our

methodology makes explicit use of ES concepts in calculation of CEAC. This practical

contribution of the ES method into the forecasting formula reflects schedule impact and, hence,

provides more reliable CEAC (Fig. 4 and Table 5 ).

In addition, this research provides a novel and extended contribution toprevious research on

the development of the GGM. In particular, the research conducted by Narbaev and De Marco

(2013) provided for information about adapting the GGM to EVM, comparing it with other

growth models in the field, constructing the best fit S-curve for CEAC with the integration of

ES concepts for early and late stage estimates, and, finally, applying the model to compute

CEAC of a set of construction projects. This paper continues that work as part of its future

research and provides a comparison with the four IB methods, the calculation of CEAC for a

late stage, the analysis of precision of CEAC, and finds the model timeliness property as being

reliable in providing most accurate and precise estimates throughout project life.

Finally, this study aims at the diffusion of the GGM for a variety of projects and various

industries.

6. Conclusion

Reliability in forecasting CEAC has long been a focus of many comprehensive research and

comparative studies. This is because accurate and precise CEAC forecasts throughout the

project life equip the project team with essential information in taking prompt preventive

actions and assisting on timely completion within available budget. The traditional approach

using PI in EVM has been in use to assist in this task for over four decades with little change.

However, this technique relies on EVM data only and merely calculating CEAC by adjusting

the remaining BAC by a PI (Kim and Reinschimdt, 2011; Lipke et al., 2009 ). In addition, IB

method may produce inaccurate and unreliable CEAC in the early stages of projects due to little

EVM data available.

This paper proposes a new CEAC methodology to forecast the final cost of ongoing projects.

It is a combined index-regression approach. The method is based on an ES-based IB equation

modified by integration of the GGM via a nonlinear regression analysis. This combined

approach produces more accurate and precise CEAC effective for all stages of the project life

because it meets the property of timeliness. The proposed methodology overcomes the reported

limitations inherent with traditional linear IB methods.

Practical implications arise from the proposed CEAC model as a tool for Project Managers

to better incorporate the progress status into the task of forecasting the final cost of an ongoing

project. In particular, the inclusion of the ES-based CF, which indicates the expected

completion time, takes into account for any schedule advance or delay into the estimate. This

implies that schedule is a factor of cost performance and has large influence on CEAC. The

results of comparative analysis without (the base case) and with (the ES-based case) CF in the

model equation show that the second case generates more accurate and precise forecasts in all

three completion stages of a project. This cost-schedule relationship represented in the model

equation is a contribution to extending the EVM research and practice to better capture the

inherent relation between cost and schedule forecasts.

In addition, the field literature reports that application of traditional IB methods (originally

developed as a tool to manage complex and large projects) is questionable when it comes to

CEAC of small-sized and short-duration projects. On the contrary, the proposed forecasting tool

demonstrates applicability to small and medium-sized projects, such as those used for the

sample test.

Moreover, it is an effective and practicable method for early CEAC when as few as three

time points are available. Thus, it is effective for short lifespan projects with small-sized

budgets.

To pursuit the advantages of this methodology, future research is directed toward evolving

the theoretical framework and providing for extended applicability. On the one hand, with the

purpose of understanding the model behavior in a dynamic project environment, it might be

opportune to integrate the given CEAC calculation method with uncertainty and risk analysis

able to capture major exceptional risk events into CEAC formulation, as well as include expert

managerial belief as a potential source of corrective actions affecting future project performance

and CEACs. With this regard, it should also be comprised within the framework of the system

behavior theory.

Another prospective research direction drives towards understanding the impact of reducing

the number of the parameters for the GGM, as it will ease understanding the time-cost/schedule

relationship being described by the model, as well as it will make the model easier-to-adopt by

field practitioners.

Finally, the method is proposed to practitioners for application to a larger variety of projects

at different progress stages and for diffusion in various industries.

Appendix A. Calculation of CEAC for a sample project.

Should it be a separate file uploaded in the system? Or to add here?

Glossary

Actual Cost (AC). The realized cost incurred for a project during a specific time period.

Actual Time (AT). The number of time periods from the start of a project to a project status

date.

Budget at Completion (BAC). The sum of all the budgets established for the work to be

performed on a project. The total Planned Value for the project.

Completion Factor (CF). The Earned Schedule (ES)-based factor which is the ratio of

Expected Duration at Completion to Planned Duration (PD). It is inversely related to the time-

based Schedule Performance Index (SPIt ). The value of CF less than 1.00 indicates a project is

ahead of schedule (favorable condition), more than 1.00 – behind schedule (unfavorable

condition), and equal to 1.00 – according to schedule.

Composite Index (CI) – a Performance Index (PI) expressed as the sum of the portions of

Cost Performance Index (0.8*CPI) and Schedule Performance Index (0.2*SPI).

Cost at Completion (CAC). The realized cost incurred for a whole project. Actual Cost

(AC) of a finished project.

Cost Estimate at Completion (CEAC). The expected total cost of completing a project. It

is expressed as the sum of the Actual Cost (AC) to date and the remaining portion of Budget at

Completion (BAC minus AC) adjusted by a Performance Index (PI) or Gompertz Growth

Model (GGM).

Cost Performance Index (CPI) – a Performance Index (PI) expressed as the ratio of Earned

Value (EV) to Actual Cost (AC).

Critical Ratio (CR) – a Performance Index (PI) expressed as the product of Cost

Performance Index (CPI) and Schedule Performance Index (SPI).

Earned Value (EV). The cumulative to date measure of the work performed, expressed in

terms of the budget authorized for that work.

Expected Duration at Completion (EDAC). The expected total time for completing a

project. It is expressed as the ratio of Planned Duration (PD) to the time-based Schedule

Performance Index (SPIt ).

Gompertz Growth Model (GGM). An S-shaped model represented by a sigmoid function

which accounts for the slow initial growth of cost accrual, accelerating the growth rate on the

middle stage, and slowing down again by the end of a project.

Index-Based (IB) method. A method to compute Cost Estimate at Completion (CEAC) that

adjusts the remaining portion of Budget at Completion (BAC) by a performance index.

Least Squares (LS) method. A method that determines the best fit of the observed values in

the data fitting. The method minimizes the sum of the squared forecast errors; the error which is

the difference between an observed value and the fitted value generated by the Gompertz

Growth Model (GGM).

Mean Absolute Percentage Error (MAPE). The average of the absolute values of

Percentage Errors (PE) on the number of projects tested.

Moving Average (MA) – a Performance Index (PI) expressed as the averaged CPI which is

the ratio of sums through three periods beginning with the most recent period and going

backwards.

Percentage Error (PE). A measure of forecast accuracy which is the difference between

Cost Estimate at Completion (CEAC) and Cost at Completion (CAC) expressed as a percentage

of CAC with a negative value suggesting underestimation and a positive value – overestimation.

Performance Index (PI). A measure of cost efficiency of budgeted resources. Four types of

PI are used in the research.

Planned Duration (PD). The planned duration for a project.

Planned Value (PV). The authorized budget assigned to scheduled work.

Standard Deviation (SD). A measure of a statistical dispersion of the values of Percentage

Errors (PE) from the Mean Absolute Percentage Error (MAPE) which is computed by taking the

square root of the variance (the average of the squared differences between PE of an individual

project and mean of PE). A smaller value of SD indicates that cost estimates calculated by a

particular model are closer to its mean forecast error and suggest more precise estimates.

The α parameter. A parameter of the Gompertz Growth Model (GGM) that represents the

never attained final cost as time (x ) tends to infinity.

The β parameter. A parameter of the Gompertz Growth Model (GGM) that is the y-

intercept which indicates an initial budget size of a project.

The γ parameter. A parameter of the Gompertz Growth Model (GGM) that governs the cost

growth rate.

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Cost, $

PV

CEAC

BAC

Cost

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Schedule

ES

Time

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10

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14

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18

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3b

0

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4b

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... Soma-se a isso, a discussão sobre a natureza do sucesso de projetos. O PMI realizou uma conferência totalmente dedicada a debater a natureza multifacetada da ideia de sucesso aplicada a projetos (DE WIT, 1998). Entretanto, essa discussão desconsidera o fato de que os projetos não estão isolados no tempo e no espaço. ...

... Alguns pesquisadores divergem sobre qual abordagem de gerenciamento de projetos é mais efetiva: a aplicação da abordagem prescritiva de natureza rígida, que normalmente é feita por meio da adoção de metodologias tradicionais de gestão de projetos ou a abordagem adaptativa com um viés mais flexível e adaptável às mudanças e aos aspectos do ambiente do projeto (NERUR; BALIJEPALLY, 2007;COHN, 2006;DE WIT;MEYER, 2010;KERZNER, 2016). O debate da superioridade de uma abordagem sobre a outra não está resolvido. ...

... Está diretamente relacionada à satisfação e à maneira pela qual o resultado é percebido em termos de benefícios MOHAMED 1999;BELASSI;TUKEL 1996;DE WIT, 1998;ATKINSON, 1999 Linkedin. ...

• Ralf Luis de Moura

O alto índice de projetos que não conseguem atingir as metas e resultados previamente estabelecidos é um desafio persistente na área de gestão de projetos. Para minimizar estes desafios, as organizações adotam metodologias de gestão de projetos que se sustentam no pressuposto de que um único meio é capaz de ajudar no alcance dos resultados em quaisquer situações (one size fits all). Grande parte das metodologias defendem que somente é possível atingir a excelência na gestão de projetos por meio do planejamento rígido, baseado na aplicação de métodos dotados de rigor lógico e objetividade, o que direciona à aplicação de uma abordagem prescritiva na implementação dos projetos. Entretanto, nem todos os projetos são iguais e alguns destes, em função do ambiente em que estão inseridos, podem depender de uma abordagem adaptativa para alcançar o sucesso, pois as características ambientais adversas do projeto representadas pelos elementos: dinamicidade, incerteza, diversidade técnica e ambiguidade podem influenciar seu sucesso tanto em relação ao alcance das metas estabelecidas quanto à satisfação com os resultados do projeto. Por meio de um arcabouço teórico, este estudo teve por objetivo propor e testar um modelo de classificação de projetos que indica a abordagem de implementação mais ajustada às características ambientais adversas do projeto com capacidade de propiciar maior probabilidade de sucesso. Para tal, por intermédio de uma pesquisa empírica com 332 profissionais envolvidos em projetos, este estudo propôs um modelo estrutural que foi validado e testado. A partir dos resultados do modelo testado, criou-se um modelo de classificação de projetos que permitiu a indicação da abordagem de implementação com maior probabilidade de auxiliar o projeto a alcançar o sucesso. Os resultados mostraram que, contrapondo o que afirmam muitos estudos, nem todos os projetos no qual as características ambientais adversas têm grande influência, têm maior probabilidade de sucesso quando adotam abordagens adaptativas. Ademais, nem todos os projetos em que as influências ambientais têm baixa influência tendem a apresentar melhores resultados quando adotam abordagens prescritivas. O que denota que é necessário entender previamente o contexto ambiental ao qual o projeto está inserido e a partir deste entendimento optar pela abordagem de implementação com maiores chances de sucesso. Mostrando evidências de que um único meio não é capaz de endereçar todos os tipos de projetos (one size does not fit all).

... While Tuman [27] focuses on requirements and resources in his definition, "having everything turn out as hoped…anticipation all project requirements and have sufficient resources to meet needs in a timely manner". De Wit [28] has a more comprehensive definition of success with focus on both performance and satisfaction and define success as, "the project is considered an overall success if the project meets the technical performance specifications and/or mission to be performed, and if there is a high level of satisfaction concerning the project outcome among: key people in the parent organization, key people in the project team, and key users or clientele of the project effort". De Wit point out that a project can be a success for one party and a disaster for another, simultaneously success is time dependent [28]. ...

... De Wit [28] has a more comprehensive definition of success with focus on both performance and satisfaction and define success as, "the project is considered an overall success if the project meets the technical performance specifications and/or mission to be performed, and if there is a high level of satisfaction concerning the project outcome among: key people in the parent organization, key people in the project team, and key users or clientele of the project effort". De Wit point out that a project can be a success for one party and a disaster for another, simultaneously success is time dependent [28]. Certain factors have been worked out as more critical to project success than others. ...

Approximately 80% of the current Norwegian building stock is expected to still be in use in 2050. Norwegian government demands that the refurbishment and modernization of these buildings should be sustainable. According to the authors the early phase planning should therefore be improved in order to be able to fulfill the sustainability requirements. A great deal of the potential for a successful project lies in the early phase, but there seem to be no clear definition of when it starts or when it finishes. This paper investigates different definitions of "early phase" and what this phase of the project should contain to facilitate a successful rehabilitation. Economy is important when defining if a project has been successful or not, but budget overrun is an everyday problem in refurbishment projects. This paper will see if it is possible to determine a more secure economic framework in the early phase. The research has been conducted as a case study approach, based on a literature study, ten interviews and a survey. The first case study was a refurbishment with both technical and financial challenges. The other case study consisted of an investigation of how two municipalities in Norway decide whether to refurbish or demolish their school buildings. The interviews and the survey have been carried out with major stakeholders such as building owners, architects, consulting engineers and contractors. There seems to be no unanimous agreement of what the content of the early phase in refurbishment projects should be. The interviewees have individual definitions, depending on their role. Another notable finding is that all the respondents mean that they have more to contribute with, if they were contracted at an earlier stage in the project. The results will hopefully enable stakeholders in refurbishment projects to improve the structure of their activities. This will support the shareholders to get better and more sustainable end results.

... After the completion of a project, Wit (1988), Munns and Bjermi (1996) and Belout and Gauvreau (2004) say that its success can be verified by attending their objectives. They also present some factors that project managers must pay attention in order to better conclude it, such as: ...

• Ernany Daniel de Carvalho Gonçalves
• Carlos E S Silva

Due to the race in search for innovation, organizations from Brazil and around the word face constant challenges to maintain themselves relevant in the market, looking for better ways of managing their projects and using the existing and scarce resources with the objective of maximizing a utility measure or benefit and, in some cases, minimizing the risk or costs of their projects. According to a systematic review of 61 articles, written from 1970 to 2018, which use Multi-Criteria Decision Making (MCDM) methods to select Research Development (R&D) projects, only 19 of them give a proper explanation of the used criteria. Thus, in order to contribute with the project selection process, the main goal of this work focuses on showing which types of criteria have more importance over the others. The whole process is done thorough a systematic literature review: since the articles selection, the criteria grouping and their evaluation by two specialists using the Analytic Hierarchy Process (AHP) method. By the end, it is noticed how important the financial benefit is to specialists, and that innovation is not considered as relevant to them and to the majority of the analyzed articles.

... Secondly, we found the concept of project management success was poorly defined within the literature. Some authors discuss project management success as the acceptable completion of the technical aspects of the project as evidenced by the traditional positivist metrics (Atkinson:1999, Stretton:2014 that includes a review of the project after it has been operational for a certain period of time (De Wit:1988). Others use project success and project management success almost interchangeably to describe a wide range of evaluation criteria including: measurement against strategic objectives (Cooke-Davies:2004, Jugdev and Mathur:2006, Killen et al.:2012; whether the final project outcomes work as expected (Karlsen et al.:2005); meeting project participant's expectations (Hoffman:2007); and meeting the psychological expectations of the project participant's in relation to interpersonal relationships (Chan and Chan:2004). ...

Our research applies paradox theory to a project management construct to help project management researchers and practitioners understand the tensions that can exist between project success and client satisfaction. Our research highlights that although project success and client satisfaction are both present within a project management construct, they also belong to different functional systems. Project success and client satisfaction have different systemic-discourses and use different language games to convey information. These distinctions can create latent and sometimes salient tensions within the project management construct that project managers must understand, embrace, and work with.We have used a Grounded Theory (GT) methodology to explore the lived experience of project managers, and from this have identified a phenomenon which we have termed project management yinyang.Project management yinyang is the state that exists when both project success and Client satisfaction are tightly coupled within the project management construct. Project management yinyang highlights that these two phenomena cannot be viewed as separate elements because the 'seed' of each exists within the other. And to truly achieve one, you must also achieve the other.Our findings indicate that in order to create project management yinyang the project manager must embrace a paradoxical yet holistic philosophy. They must understand the complementarity, interdependency, and structural coupling that exists between the positivist and interpretivist paradigms within the project management construct. They must understand how satisfaction (Yin) and success (Yang) are created through focus. Furthermore, they must understand how project management yinyang is separate from, but borne from, the convergence of the other two elements.

... Una buena gestión puede influir en el éxito del proyecto pero no es probable que sea capaz de prevenir su fracaso. Asimismo, el grado en que se han cumplido los objetivos previstos es una medida determinante del éxito o de fracaso de un proyecto (13). ...

... Альтернативная система показателей ( не получившая в дальнейшем распространения) предлагалась в[120]. ...

• Елена Валерьевна Колосова
• Dmitry A. Novikov
• Александр Васильевич Цветков

Работа содержит описание методики освоенного объема – совокупности методов управления проектами, использующих показатели освоенного объема, и механизмов принятия оперативных управленческих решений. Значительное внимание уделяется изучению практически важных случаев использования методики освоенного объема в рамках существующих программных средств по управлению проектами. Работа рассчитана как на специалистов-теоретиков по управлению сложными системами, так и на руководителей проектов.

Communications serve as the environment for integrating project participants, transforming them from individual office players into the cohesive project team. From the perspective of project management practitioners, communications and relations between project participants turn into essential project success factors. Taken together, formal and informal social ties of project network participants compose communication environment of the project. Connections' character and structure influence project management performance and therefore can be potentially seen as indicators of project success. In the present paper the approach based on social network analysis techniques is applied for assessing possible impact of social communications on performance of engineering projects.

• Kashif Saeed
• Georg Ziegler
• Muhammad Kashif Yaqoob

This chapter is divided into three main sections; project management, HSE management, and quality management. A focus description of the different elements of exploration and production industry along with implementation of management practices on each of these elements including asset/portfolio, resources, time, project planning and scheduling, and proactive risk management are presented. Health safety and environment and quality management are dealt with as separate sections.

• Walt Lipke

The most frequently used Earned Value Management formulae for calculating the Independent Estimate at Completion (IEAC), which is significant to project management, are discussed. Some of the formulae appear to be inconsistent with the determinations from the studies of the Cost Performance Index (CPI). An alternative method of calculating IEAC is also presented, which is in agreement with the generalizations and conclusions from the IEAC and the CPI studies. It the CPI for each performance period of the project behaves independently from when it occurs, then the alternative method should yield very good results.

Reliable cost estimates are essential for effective project control and the management of cash flows within the project and at the company level. Conventional approaches to project cost forecasting, which rely on detailed information developed for a specific project (the bottom-up estimate or inside view), often result in cost overruns. It is argued here that the inside-view project cost estimates should be adjusted by combining them with the outside (or top-down) view of the project, which is based on statistical models of historical project data. This paper presents a probabilistic cost forecasting method and a framework for an adaptive combination of the inside view and the outside view forecasts of project cost using Bayesian inference and the Bayesian model averaging technique. During the project execution phase, the Bayesian adaptive forecasting method incorporates into the predictions the actual performance data from earned value management and revises preproject cost estimates, making full use of the available information. Qualitative examples are presented to demonstrate the validity of the proposed method as a tool for effective project cost prediction and control.

To improve the accuracy of early forecasting the final cost at completion of an ongoing construction project, a new regression-based nonlinear cost estimate at completion (CEAC) methodology is proposed that integrates a growth model with earned schedule (ES) concepts. The methodology provides CEAC computations for project early-stage and middle-stage completion. To this end, this paper establishes three primary objectives, as follows: (1) develop a new formula based on integration of the ES method and four candidate growth models (logistic, Gompertz, Bass, and Weibull), (2) validate the new methodology through its application to nine past projects, and (3) select the equation with the best-performing growth model through testing their statistical validity and comparing the accuracy of their CEAC estimates. Based on statistical validity analysis of the four growth models and comparison of CEAC errors, the CEAC formula based on the Gompertz model is better-fitting and generates more accurate final-cost estimates than those computed by using the other three models and the index-based method. The proposed methodology is a theoretical contribution towards the combination of earned-value metrics with regression-based studies. It also brings practical implications associated with usage of a viable and accurate forecasting technique that considers the schedule impact as a determinant factor of cost behavior.

Accurate forecasting of a project's Cost Estimate at Completion (CEAC) based on current performance and progress is one the main issues in project monitoring and control. For decades, Earned Value Management (EVM) has been proved itself as a valuable tool to fulfill this task and cost estimates calculated by its Cost Performance Index (CPI) are widely applicable for projects of any type and size. However, recent studies show that the CPI-based method may be valid only for large projects with long durations. As an alternative to the index-based method, techniques with regression analysis gained a great insight in this direction. The purpose of this work is to propose a new regression-based nonlinear CEAC methodology which integrates Earned Schedule (ES) concept to assume a project progress in calculating CEAC as early as when a project is 20 percent complete. The paper sets three objectives to achieve the research purpose: development of the new equation based on a nonlinear regression modelling and ES method; validation of the new technique through case study application; and, providing a comparison with CPI-based estimates to determine the best performing equation. Testing the prediction accuracy of the proposed and index-based formulae is performed by comparing values of Percentage Error (PE) and Mean Absolute Percentage Error (MAPE). Based on six case studies from construction industry, the comparison reveals that the new methodology generates better estimates (MAPE=2,88 percent) than those calculated by traditional index-based equation (MAPE=9,98 percent)

Purpose - To contribute to the diffusion of Earned Value Management (EVM) as a practicable methodology to monitor facility construction and renovation projects in the context of the European industry. Design/methodology/approach - Firstly, a review of the literature reveals how EVM evolved as a tool for facility construction project monitoring together with specific concerns for its application. Then, a review of EVM practice and trends in Europe are provided and, finally, applicability and viability of the method is proved through a case demonstration. Findings - The EVM practice in the European construction industry is found to be lagging behind other experienced countries and industries despite EVM is found to be applicable, adaptable, and predictive of integrated final cost and schedule of facility construction projects. In particular, cost estimate at completion is forecasted by a simple Schedule Performance Index (SPI) while for the time estimate at completion the Earned Schedule concept is revealed as an accurate predictor. Research limitations/implications - The paper urges the need for research of a European standard as a primary factor for successful diffusion of EVM usage in architecture, engineering and construction projects. Practical implications - This paper helps practitioners to understand the adaptability of EVM practice in the European construction industry and to apply EV tools for effectively monitoring the performance of their projects. Originality/value - Current trends of EVM practice in the European construction context are presented and suggestions for sustaining the diffusion of EVM are given

In this paper we propose two new metrics that combine Earned Value Management (EVM) and Project Risk Management for project controlling and monitoring. We compare EVM cost and schedule variances with the deviation the project should have under the risk analysis expected conditions.These two indexes allow project managers to analyse whether the project over-runs are within expected variability or there are structural and systemic changes over the project life cycle. The new monitoring indexes we present are the Cost Control Index and the Schedule Control Index.

• Paul M. Teicholz

This paper describes a computational approach to calculating the final cost and budget of a construction project, which is based on the data normally developed by a cost system during the life of the project. While most cost systems are able to collect total budget and to-date cost, budget, and quantity data, there is often less capability to use this data to forecast the final cost of a project. In many cases, the cost forecast for unstarted work does not reflect the overruns or underruns that are recorded early in the life of a project. This paper presents an algorithmic approach that has been tested using the data from 121 completed construction projects, which calculates reasonably good cost and budget forecasts over a wide range of project types and changed conditions. The proposed method is compared to two other methods and is found to be superior in accuracy, timing, and stability. The forecasting method, sliding moving average, is general in its approach and may be useful for other situations in which predictions of limited duration time-series data are desired.

• Ofer Zwikael
• Shlomo Globerson
• Tzvi Raz

This paper addresses how to estimate the final cost of a project and when the estimate becomes accurate. The performance of five forecasting models drawn from literature was evaluated with data from a sample of actual projects. A stability analysis was carried out in order to identify when the forecasts become stable and accurate for the model that emerged as the most accurate.

• Denis F. Cioffi

The solution to a differential equation used frequently in ecology is found to reproduce the well-known S-curve seen in various aspects of project management. The solution is modified in a minor way to fit project management boundary conditions. An excellent fit of this theoretical curve to two samples of project cost data shows the utility of the formula. Numerical approximations valid under typical project conditions are utilized to produce an analytic expression that can easily generate classic project management evolution curves under a variety of conditions. The curves are normalized to two basic parameters: the total of the relevant quantity (e.g., project costs) and the duration of the project. The user can choose the steepness of the climb and the point in time at which half the total has been accumulated.

• Denis F. Cioffi

A new formalism and a corresponding new notation for earned value analysis are presented. With compact, consistent, mnemonic notation, earned value calculations become more transparent and flexible, leading to insights about standard quantities and advances through new measures. As an example of the notation's utility, it is used to generate a modified earned value approach that weights quantities according to their position in a project's timeline.

Source: https://www.researchgate.net/publication/260292210_International_Journal_of_Project_Management

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