Construction Management
Duration Estimate at Completion: Improving Earned Value Management
Forecasting Accuracy
Solomon Sackey
a, Dong-Eun Lee
b, and Byung-Soo Kim
c aDept. of Civil Engineering, Kyungpook National University, Daegu 41566, KoreabMember, Dept. of Architectural Engineering, Kyungpook National University, Daegu 41566, Korea cMember, Dept. of Civil Engineering, Kyungpook National University, Daegu 41566, Korea
1. Introduction
Performance is one of three basic concerns in project management, along with schedule and cost. Once a project is underway, expectations are that activities will be carried out as planned. However, in project execution, things might not go the way management expected, because many internal and external factors influence project performance. Projects are expected to be completed on schedule and on budget, so in order to meet a project’s requirements and scope, the project’s progress must be measured. The Earned Value Management (EVM) method has emerged as one of the best quantitative approaches to project performance, measurement, and control. It is a project management technique used to measure a project’s progress at a certain date, and uses performance information, such as the actual cost of work performed and the corresponding estimated earned value, to forecast the total project length and cost at completion. Then,
the forecasted value (time/cost) estimate at completion is compared to baseline information so that corrective action can be taken if it is determined that the project is in trouble. The principles and application of EVM have been extensively studied by many researchers (e.g., Lipke et al., 2009; Mishakova et al., 2016; Willems and Vanhoucke, 2015; Kerkhove and Vanhoucke,
2017). Colin and Vanhoucke (2014), in a more detailed description and explanation, described EVM as a system that relies on a set of straightforward metrics to measure and evaluate a project’s overall performance. They noted that these metrics are used as early warning signals to identify problems in a project, and to provide corrective actions or to make productive use of opportunities.
Abba (1997) defined EVM in a different way, as a project management approach that relates resource planning to schedules and technical performance requirements. Abba explained that, as work is performed, value is earned based on the planned value, and the resulting schedule variance is the difference between this
ARTICLE HISTORY ABSTRACT
Received 11 March 2019 Revised 20 October 2019 Accepted 1 January 2020
Published Online 12 February 2020
KEYWORDS
Earned Value Management (EVM) has been established as a project management technique for project monitoring and control. The traditional EVM performs well in forecasting Cost Performance index and other cost metrics. However, in terms of schedule performance, the accuracy of the forecasted schedule metrics through the traditional EVM approach are always questionable. The schedule performance is not measured in time unit but rather in monetary units or uses cost information, which may cause misleading in the interpretation of the EVM schedule metrics. The schedule performance is not accurately forecasted, resulting in underestimating the estimate at completion (t). Even the renowned Earned Schedule also uses cost as a proxy to determine the earned schedule. This paper presents a new EVM tool, Duration estimate at completion (DEAC-model) developed to accurately forecast the time estimate at completion. DEAC-model uses the actual time spent on each activity, either in progress or upon completion, where the Performance is measured in time units. The benefits of DEAC-model to project management team and researchers are that it can be used: 1) to forecast schedule metrics accurately so that resources can be effectively allocated to complete the remaining activities, 2) as a gauge to assess if the project can be completed within the plan schedule, and 3) to apply time series and simple linear regression model concepts using excel worksheet syntax to forecast duration estimate at completion that is easily applicable.
Earned value management Forecasting
Performance measurement Project duration
Earned schedule
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planned value and the earned value. In their research comparing different project duration forecasting methods using earned value metrics, Vandevoorde and Vanhoucke (2006) described EVM as an approach used to measure and communicate the actual physical progress of a project, integrating scope, time, and cost. Their methodology used the work completed, the time taken, and the remaining estimated costs to complete the project to measure a project’s progress in monetary terms. EVM can be applied to all areas of a project; however, in construction site management practice, EVM application needs a systematic record of time and cost data (which could be updated once a week) in order to determine the earned value (the budgeted cost of work performed) and the actual cost of work performed (Czemplik, 2014). EVM predictions about the future performance of a project, based on its performance to date, are more accurate than the critical path analysis technique (APM, 2012). In order to improve project performance, several models and EVM extensions have been developed. Cheng et al. (2010) presented a complicated model that integrated a fast messy genetic algorithm and support vector machine to construct an evolutionary estimate at completion (EAC) support vector machine inference model. They developed the model to generate cost estimates. Chen et al. (2016) proposed a technique to provide management with unequivocal predictive information about earned value (EV) and actual cost (AC) by developing a modeling method that improved the predictive power of planned value prior to project execution. They also adopted a logarithm linear transformation, a method originally proposed by (Chen, 2014), which transformed the relationship between EV, AC, and planned value (PV) into a nearly linear relationship.
Using fuzzy theory (Naeni et al., 2011) provided a fuzzy approach to EVM, with the objective of developing and analyzing the indices of EV, time, and cost estimates at completion in order to evaluate the progress of a project under uncertainty. Najafi and Azimi (2016) challenged traditional EVM methodology, which used past performance trends to predict the future, by showing that it had some weaknesses in analyzing the time performance of a project. Therefore, they presented two methods to improve the accuracy of schedule analysis results. The first of the two methods was a simple approximation method to reduce the errors in EVM analysis, and the second was an exact method that utilized EV and floating time concepts. Taking a different approach, (Acebes et al., 2015) described a new integrated methodology for project control under uncertainty, and improved methodologies of integrating EVM with risk analysis, by proposing a model called stochastic earned value analysis using Monte Carlo simulation and statistical learning techniques. Their proposed model provided probability of success, expected project duration, and cost.
Forecasting involves making projections about future performance using current and historical data (Kalekar, 2004). Trend-corrected exponential smoothing is a forecasting technique that uses time series analysis. It is a smoothing method for forecasting a time series that uses two smoothing constants, α and β. Exponential smoothing is a simple and pragmatic approach to forecasting where the forecast is developed from an exponentially
weighted average of past observations (Ostertagová and Ostertag,
2011). Exponential smoothing methods are powerful tools in time series analysis, used to predict future demand and decrease inventory cost (Tratar et al., 2016). The method is widely used, and its popularity can be attributed to its simplicity, its computational efficiency, the ease of adjusting its responsiveness to changes in the process being forecast, and its reasonable accuracy (Montgomery et al.,1990). In 1957, Holt expanded upon simple exponential smoothing to allow the forecasting of trend data.
EVM is an established project management technique for measuring project performance, monitoring, and control. The technique is applicable to various projects in different fields. Despite its acceptance and its applications, the technique has drawbacks. One of its major drawbacks is that EVM measures schedule performance and duration at completion in monetary terms. It estimates the schedule performance index (SPI) incorrectly, which results in underestimating the duration estimate at completion. A favorable or unfavorable schedule performance does not mean a project is ahead of schedule, nor does it mean schedule slippage. This is because EVM does not measure schedule performance in units of time, but in monetary units or cost. This may cause the interpretation of EVM schedule metrics to be misleading. Another issue with EVM schedule metrics is that the forecasted metrics become unreliable toward the end of a project, since the schedule performance is equal to one at the completion date. To overcome this problem, a new model was developed to forecast project duration estimate at completion (DEAC) using a trend-corrected exponential smoothing method. In this research, the authors demonstrate that a modified time series approach can forecast expected project duration at completion. The DEAC model applies the exponential smoothing method to forecast duration in construction projects. However, the only difference between the traditional exponential smoothing and the DEAC model is that, because it is applied to construction activities consisting of critical and non-critical activities, a weight factor of 0.5 is subtracted from both the trend and level equations. This factor of 0.5 results from the existence of any non-critical activity in the model divided by trend plus level, i.e., 1/2. The critical path method does not reveal the true criticality of activities, which is why some duration falls short. Because in reality the critical path may change and some non-critical activities may become critical. For this reason, this method does not consider the criticality of the activities but rather it captures the trend in the activities duration upon completion or in progress. It is a different approach to scheduling where activity relations matter most. It uses past performance data of the activities and utilizes trend and level concepts for prediction. This model is an improvement on EVM, and improves the accuracy of EVM schedule metrics.
2. Methodology and Procedure
2.1 Time Series Analysis
forecasting technique that uses a model to predict future outcomes by using historical data. There are two basic components of the observed data used in time series forecasts, a random component and a systematic component. The random component exists because there is always randomness whenever something is forecast, but it is not easy to forecast its randomness. However, the systematic component can always be forecasted using data from past performances. The systematic component reveals whether there is a trend or seasonality in the data. If there is an increase in the data, it means there is an increase in the trend. Therefore, the systematic component includes trends and levels. The trend-corrected exponential smoothing method captures the trends in data. The actual time for activities to complete may differ from period to period, and as activities are started or completed, there is an increase in the project duration until all activities cease and the project is finally completed. Therefore, the systematic component now includes the trend and the level. In such cases, the trend-corrected exponential smoothing method can better forecast project DEAC by capturing these trends and levels.
2.2 Algorithm and Computation of the Duration
Estimate at Completion Model
To develop the DEAC model, the actual activities duration measured at the end of the status date were used. These are the
durations of every activity that was either started, in progress, or completed by the end of the status date. As the project progressed, the last activity in the model, which consequently determines the total project duration at completion, is forecasted based on the trend and level of the individual activities. Fig. 1 depicts the algorithm and the process of the DEAC model, followed by the steps describing in details how the model was developed.
Step 1. Extract the actual activity duration
By the end of the status date, the actual activity time spent on each activity was collected. This corresponded to the periods in which the measurement was done. In this case, the periods represented individual activities in the project, the periods within which the activities were performed. The first period corresponded to the first activity, the second period to the second activity, and so on in sequential order.
Step 2. Initialize the Trend and Level
Trend and Level values were determined based on regression analysis. Regression analysis was conducted using the cumulative duration from the start of the project up to the time of the performance measurement. The use of the cumulative duration was based on the assumption that the activities are independent. The initialization was performed using the following equation:
(1)
t
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where, a= the initial trend (slope) of the series at time t b = the initial level at time t
Yt= Forecast equation
From the output of the regression analysis, the y-intercept value is the initial Level value, while the X variable (slope) is the Trend value. i.e., b = y-intercept value and a = X variable (slope). These are used because the initial smoothing constants are unknown.
Step 3. Determine the smoothing constants, Alpha (α) and Beta (β)
In the exponential smoothing model, these smoothing constants are necessary to determine the Trend and Level of the activities with measured performance records. Alpha and Beta are random numbers between zero and one, and in this study 0.2 and 0.3 were chosen as α and β, respectively, to update the initial Trend and Level values.
Step 4. Determine the actual Trend and Level in each period With the initialization and the smoothing constants known, Level and Trend values were determined from these equations:
(2) (3) where Lt is the Level in the current period (activity), yt is the
cumulative time of the current activity, and Lt-1 and Tt-1 are the
previous Level and Trend.
Step 5. Determine the DEAC forecast
Once Level and Trend values are determined for each period, the project DEAC is forecast. Similarly, the duration at completion for subsequent periods can be forecasted using these equations:
(4) (5) where Ft is the duration forecast at period t, t representing each
activity, Ft+nis the duration forecast for the next activity in the
network, and nTt is the Trend for the next activity, without
historical performance measurement data.
Step 6. Optimizing α and β to minimize the error rate
Initially, the Alpha and Beta values were randomly selected for forecast analysis and error determination. However, to optimize the smoothing constants, Excel Solver was utilized to minimize the error in the forecast. Excel Solver is a genetic algorithm tool used to determine an optimal (minimum or maximum) value for a given formula in an objective cell, subject to constraints.
To simplify and automate the computation of the schedule metrics of the DEAC-model, the authors developed a Graphical User Interface, GUI in Matlab. In this way, the user only enters the input values of the BDAC (which is the CPM-based initial schedule), the estimated DEAC result from the DEAC-model, and the PT (time at which the performance measurement was done). With only these 3 inputs, the schedule metrics are computed automatically by clicking on each schedule metrics. Eqs. (6) − (9) were used to determine the schedule metrics.
(6)
SPI = (7)
The Earned duration, ED was computed as:
(8) In predicting the schedule, Eqs. (9) and (10) are used to answer these questions:
1) Can the project be completed within the initial planned schedule?
(9) 2) Can the project be completed within the predicted duration, DEAC?
(10)
Where,
BDAC = Budgeted duration at completion DVAC = the duration variance at completion,
PT = Time at which project performance measurement was done (status time)
SPI = schedule performance index
TSPI = To Complete Schedule Performance Index
3. Applying the Duration Estimate at Completion
Model to an Actual Construction Project:
A 3-Unit Classroom Block
3.1 Project Information
The project in this case study is a 3-unit classroom block project located in Adiewoso in the Western Region of Ghana. It is a
(
1)
(
1 1)
0 5 t t t t L =αy +⎣⎡ −α L− +T− ⎤⎦− .(
1)
(
1)
1 0 5 t t t t T =β L −L− +⎣⎡ −β T− ⎤⎦− . t t t F L T= + t n t t F+ = +L nTDVAC BDAC DEAC= − BDAC DEAC ED SPI PT= × BDAC ED TSPI BDAC PT − = − BDAC ED TSPI DEAC PT − = − 1, 1, TSPI Achievable I TSPI Unachievable
f
∫
<>Table 1. Estimation of Activities Duration for the Case Study Project Activity Predecessor
activity Activity duration (Days)
classroom block built to serve pupils between the ages of 5 to 10 years from Junior Secondary School, JSS 1 to JSS 3. The project started on June 15, 2018, and was expected to be completed on January 14, 2019. The total cost of the project was GH¢285,958, approximately $63,265, with a project duration of 151 days. The progress was measured at the end of July, on the 46th day, and the PV and EV were determined to be $35,852.90 and $34,680.60, respectively. At the time of the report, activities A through H had been completed, activities I and J were in progress, and activities K and L were not yet started. Table 1 presents the estimated duration, in days, for each activity. Fig. 2 depicts the network diagram of the case project, using the precedence diagramming method.
3.2 Duration Estimate at Completion Forecast Analysis
and Results
Using the actual days spent on each activity as of the status date,
a regression analysis was performed to set up the initial Trend and Level values. The summary output of the regression analysis
Fig. 2. Network Diagram of the Case Project
Table 2. Regression Analysis of the Actual Cumulative Duration of Activities SUMMARY OUTPUT Regression Statistics Multiple R 0.988379331 R Square 0.97689702 Adjusted R Square 0.974005415 Observations 10 Coefficients Intercept 2.200 X Variable 1 15.054545
Table 3. Project DEAC Forecast
Period Actual timeAt Cumulativetime Ct LevelLt TtTrend DurationForecast Ft Error Error2 Abs (Ft − At)/At
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for the initialization of the Trend and Level variables is presented in Table 2, where the only focus is the y-intercept and the slope (X variable 1) values. The initialization values from the regression analysis were 2.200 and 15.0545 for Lt and Tt, respectively.
The Forecast equation, Yt = 2.200 + 15.0545t. Table 3 presents
the complete analysis of the DEAC forecast. The number in the first column represents the activities (i.e., activity 1 to activity 12). The second column represents the actual days spent on each activity through the status date on the 46th day. The Trend and Level were forecasted for all activities using the initial Trend and Level. Then, using Eqs. (4) and (5), the duration estimate at the completion of the project was forecast to be 167.2353 days. This value is the expected time to complete the project, should the project continue at its current pace.
The (Ft − At)/At in Table 3 is the Absolute Percentage Error,
which is used to determine the Mean Absolute Percentage Error (MAPE) as explained in Eq. (13). Ft and At are the forecasted and
actual activities duration.
Table 4 shows the forecasted duration, the predicted duration from the analysis, and the percentiles of the forecasted duration for each activity. In Table 4, the observation represents the activity, and the Y is the forecasted duration from the model, while the predicted Y values represent the values that should have been predicted instead of what the model forecast. It is apparent that sometimes the forecast value is too high while the predicted value of the forecast is too low, and vice versa. At the end of the project, the project duration forecast was 167.2351 days, and it was predicted to be completed in 166.947365 days. There was no significant difference between these two values; the forecast was almost the same as what should have been predicted. This indicates that the forecasted values are accurate enough to rely on. Fig. 2 shows the residuals, which are the error rate. The largest residual, or error, of 2.468 days was for activity D, while the smallest error, 0.00287 days, was for activity A.
Fig. 3 presents the line fit of the observations. The X variable 1 in Fig. 4 represents the activities from A to L. From the graph, it can be seen that, close to the end of the project, the predicted Y
line was below the forecast Y line, which denotes that the predicted Y value was less than what was forecast. Because the values are extremely close, the forecast Y graph that is beneath the predicted Y is not evident and cannot be seen. Fig. 5 displays the normal probability of the forecasted values. The smallest probability occurred in the forecast for activity A, which had a 4.17% chance. There is a 95.83% chance that the project will be completed within the forecast duration at the end of the project, 167.235 days.
3.3 Measures of Accuracy Calculations of the Duration
Estimate at Completion Model
3.3.1 R-Square or Coefficient of Determination
In order to determine if the model was a better fit, a regression-based measures analysis was conducted on the forecasted duration of the activities to determine the R-square and the significant F, or probability. R-square, also called the coefficient of determination, is a statistical measure of how closely the data fit the regression line. R-square is a number between zero and one, 0 ≤ R2 ≤ 1, and
the closer R-square is to one, the better the model fits. Table 5
presents the output of the regression analysis on the forecasted duration. The table also shows multiple R, Adjusted R, and
Table 4. Comparison of Forecasted Duration and Predicted Duration Observation Y Predicted Y Residuals Percentile for
Y (%) 1 17.254545 17.257417 -0.002872 4.1667 2 32.652909 30.865594 1.787315 12.5000 3 45.302425 44.473772 0.828654 20.8333 4 55.613893 58.081949 -2.468056 29.1667 5 70.616233 71.690126 -1.073892 37.5000 6 86.031132 85.298303 0.732829 45.8333 7 98.431183 98.906480 -0.475297 54.1667 8 112.53535 112.514657 0.020695 62.5000 9 126.59657 126.122834 0.473733 70.8333 10 138.27974 139.731011 -1.451266 79.1667 11 154.6795 153.339188 1.340314 87.5000 12 167.23521 166.947365 0.287843 95.8333
Fig. 3. Residuals of the Observations
Fig. 4. Line Fit of the Observations
significant F values.
The R-square value of 0.999392, which is close to one, suggests that the fit of the model is better. The small significance F value of 2.03799E-17 indicates that the forecast results are significant.
3.3.2 Theil’s Forecast Accuracy Coefficient
Theil’s Forecast Accuracy Coefficient, simply called Theil’s U, is a method used to determine the accuracy of a model’s forecast. In order to be better than pure guessing, the Theil’s U value should be less than one.
(11)
The Theil’s U for the model was 0.1005, which is far below one, and suggests that the model provides an estimate that is statistically better than guessing.
3.3.3 Root Mean Square Error and Mean Absolute
Percentage Error
Root mean squared error (RMSE) is a measure of the amount of error that exists between data points; it measures how closely the data points are concentrated around the best fit line. Mean absolute percentage error (MAPE) is a common measure of forecast error; it is the average of the absolute percentage errors of the forecasted values.
(12)
(13) With these forecast error measures computed, Excel Solver optimized the initial Alpha and Beta values to minimize error, especially the MAPE, as summarized in Table 6 below. Fig. 6
shows the Excel Solver input parameters, where the constraints are the randomly chosen initial Alpha and Beta values. The Solver method used to provide a locally optimal solution to the
problem was a Generalized Reduced Gradient (GRG), which is a nonlinear optimization algorithm.
After optimization, the DEAC for the project was forecast to be 167.2774 days. This means that if the project continued at its current pace, then the expectation was that the project would be completed in 167.2774 days. The Theil’s U value of 0.1005 suggests that the model provided an estimate that is statistically far better than guessing. A MAPE of 0.1296 (12.96% error) suggests that the forecast model was about 87.04% accurate. This does not mean that the model is poor, but since MAPE only measures the deviations of the actual from the predicted, it is better to combine it with other accuracy measures that can help provide a better understanding of the model’s accuracy. The low value of Theil’s U is enough to suggest that the model is not biased.
With the DEAC forecasted, the schedule metrics are then forecasted and the results are summarized in Fig. 7 of the Matlab GUI interface.
The DEAC-model estimated the SPI to be 93% (0.93). The 93% efficiency rate is a true reflection of the fact that the performance measurement was done in terms of time not in cost unit. With the current efficiency rate of 93%, the TSPI was computed as 1.03 >1, suggesting that the project is not achievable within the planned schedule of 156 days, but is achievable with the estimated DEAC schedule. The Theil’s U value of 0.1005 < 1
(
)
2 1 2 1 1 2 2 1 / n i / n i t t t F A U A = = ⎡ − ⎤ ⎢ ⎥ ⎣ ⎦ = ⎡ ⎤ ⎢ ⎥ ⎣ ⎦∑
∑
(
)
2 1 n t t i F A RMSE n − = =∑
(
)
1 t t 100 t F A MAPE An
⎡ − ⎤ =⎢ ⎥× ⎢ ⎥ ⎣ ⎦∑
Table 5. Comparison of Forecasted Duration and Predicted Duration SUMMARY OUTPUT Regression Statistics Multiple R 0.999696167 R Square 0.999392427 Adjusted R Square 0.99933167 Significance F 2.03799E-17 Observations 12
Fig. 6. The Excel Solver Parameters Interface
Table 6. Optimization and Summary of the Measures of Accuracy Calculations
When α = 0.2, β = 0.3 Optimization α = 0.29, β = 0.12 Error DEAC Error DEAC Theil's U 0.10894 Theil's U 0.1005
RMSE 11.03537 RMSE 10.5533 MAPE 0.13485 MAPE 0.1296
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suggests that the model provides an estimate that is statistically far better than just guessing, which further suggests that the model is not bias.
4. Time Estimate at Completion Analysis Using
Two Existing Models
4.1 The Traditional Earned Value Management Method
The three basic components of the earned value management (EVM) method include the PV, also called the budgeted cost of work scheduled, AC, and EV, often called the budgeted cost of work performed. For each activity, the EV is calculated by using the actual percentage of work performed out of what was budgeted. The EV expresses how efficiently project resources are used. In this technique, schedule metrics are forecast in monetary units; the model uses cost performance measurement data for its forecasts. The cost and schedule information in section 3.1 of this study were used in this analysis. The schedule performance index, SPI, and the time estimate at completion, EACt, were forecast
using these equations:
(14) (15) Where, DAC is the estimated duration at completion.
Thus, the metrics were forecast as:
SPI = = 0.97 (16)
EACt = = 155.7 days (17)
Using the traditional EVM approach to analyze project performance, the time estimate at completion was forecast to be 155.7 days.
4.2 The Earned Schedule Method
The ES approach was first developed by Lipke et al. (2009) as a
new management method for forecasting an independent estimate at completion time, IEAC(t), which has been accepted and established as a valid extension of EVM. It is based on determining the actual time during the project at which the earned value was achieved, or the moment in the project at which the PV should have been equal to the current EV. It uses the concept that the ES occurs where the EV curve meets the PV curve on the EVM graph, and measures project performance in time units. The PV and EV values are calculated first, and the ES is determined by tracing the meeting point of the EV and PV curves to a location on the horizontal time axis. The ES method determines the schedule performance index, SPI(t), ES, and IEAC(t) from these equations:
(18) (19)
(20) Where, AT is the actual time (the status date or current time), PD is the baseline total project duration, C is the cumulative EV of the previous period, and I is the cumulative EV of part of the next period. Fig. 8 illustrates the Earned Schedule concept, where C is 40 days and I is 1.7 days.
The schedule metrics were forecasted as:
= 0.91 (21)
= 171.4 days (22)
Using the original ES method, the project is expected to be completed in 171.42 days if the current performance continues.
In Table 7, the time estimate at the completion of the project
using the DEAC-model, EVM technique and ES method is summarized. Using the baseline plan of 156 days to complete the project, the percentage variance of this baseline duration using
EV PV SPI = t DAC EAC SPI = 34 680 6 35 852 9 , . . . 151 0.97 ES C I= + ES AT SPI(t)= PD SPI( t ) IEAC(t)= 41 7 46 . SPI(t)= 156 0 91. IEAC(t)=
Fig. 7. Computational Results of Schedule Metrics in GUI
the original EVM was forecasted as just 3.09%, 7.23% variance using the DEAC-model and 9.88% using the ES method. The original EVM forecast for a time estimate at completion was only 160.82 days, which is underestimated when compared to the forecast using the DEAC-model and the renowned ES method of 167.277 days and 171.4 days respectively. The forecast using the DEAC-model is 4.14 days error, representing just 2.4% error when compared to the ES method.
Using the baseline plan of 156 days to complete the project, the percentage variance of this baseline duration, according to the original EVM forecast, was just 3.1%. Using the DEAC model, the variance was 10.78%, and using the ES method, it was 12.74%. The original EVM forecast for a time estimate at completion was only 155.7 days, which is an underestimate compared to the forecasts, using the DEAC model and the ES method, of 167.28 days and 170.24 days, respectively. Since the renowned ES method measures project performance in unit of time, its result was used as the actual against which the EAC models developed in this research were compared and validated
As depicted in Fig. 9, which shows the time estimate at completion, the EVM method has 14.54 days’ error, representing an error rate of 8.54%. On the other hand, the DEAC model has just 2.96 days’ error, representing an error rate of 1.74%. This suggests that the DEAC model developed provides a more accurate forecast of the time estimate at completion than the typical EVM method. In other words, the DEAC model is 98.26% accurate when compared to the standard Earned Schedule approach.
5. Conclusions
Projects today continue to be delivered behind schedule, despite the existence of project control techniques. This research identified the most critical issues underlying this trend as an over-emphasis
on cost information, inaccuracy in the forecasts of project performance metrics, and the use of cost as the basis for measuring the schedule-based performance of projects, as in traditional EVM. Realizing that there is a trend in activity duration upon or during the completion of a project, this study developed a model that captures these trends, in time units, in order to forecast the DEAC better. This novel model not only helps avoid using cost as a proxy to measure schedule performance metrics, it also improves the accuracy of the time estimate at completion forecast. Using activity time information, i.e., the actual time spent on activities, to measure the schedule performance of a project is especially advantageous in relation to the Earned Schedule method, which uses cost information about the activities as a proxy to establish the earned schedule as units of time. This new model helps one to understand that the forecast of the time estimate at completion of a project is a true reflection of the fact that schedules are measured in units of time. When applied to a real project, the results of the model showed an error rate of just 1.74%, suggesting an accuracy rate of 98.26% compared to the ES approach. Underestimating the EAC(t) will lead to schedule
overruns, while overestimating it will lead to resource waste. Hence, while this new DEAC model can be used independently, it can also be used in conjunction with the traditional EVM method to help project managers make informed decisions and allocate resources efficiently to meet project milestones.
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.NRF-2018R1A5A1025137).
ORCID
Solomon Sackey http://orcid.org/0000-0002-1367-857X
References
Abba WF (1997) Earned value management-reconciling government and commercial practices. Program Manager 26:58-63
Acebes F, Pereda M, Poza D, Pajares J, Galán JM (2015) Stochastic earned value analysis using Monte Carlo simulation and statistical learning techniques. International Journal of Project Management 33(7):1597-1609, DOI: 10.1016/j.ijproman.2015.06.012
APM (2012) Association for project management body of knowledge. Imprint Digital, Buckinghamshire, UK, 162-168
Chen HL (2014) Improving forecasting accuracy of project earned value metrics: Linear modeling approach. Journal of Management in Engineering 30(2):135-145, DOI: 10.1061/(ASCE)ME.1943-5479. 0000187
Chen HL, Chen WT, Lin YL (2016) Earned value project management: improving the predictive power of planned value. International Journal of Project Management 34(1):22-29, DOI: 10.1016/j.ijproman. 2015.09.008
Cheng MY, Peng HS, Wu YW, Chen TL (2010) Estimate at completion for construction projects using evolutionary support vector machine
Table 7. Comparison of Different Time Estimate at Completion Techniques Technique Used Time Estimate at Completion, TEAC Time Variance at Completion, TVAC % Variance of Planned Duration Original EVM 160.82 days 4.82 days 3.09% DEAC-Model 167.277 days* 11.28 days 7.23% (ES) Model 171.42 days 15.42 days 9.88%
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inference model. Automation in Construction 19(5):619-629, DOI: 10.1016/j.autcon.2010.02.008
Colin J, Vanhoucke M (2014) Setting tolerance limits for statistical project control using earned value management. Omega 49:107-122, DOI: 10.1016/j.omega.2014.06.001
Czemplik A (2014) Application of earned value method to progress control of construction projects. Procedia Engineering 91:424-428,
DOI: 10.1016/j.proeng.2014.12.087
Kalekar PS (2004) Time series forecasting using holt-winters exponential smoothing. Kanwal Rekhi School of Information Technology 4329008(13):1-13
Kerkhove LP, Vanhoucke M (2017) Extensions of earned value management: Using the earned incentive metric to improve signal quality. International Journal of Project Management 35(2):148-168, DOI: 10.1016/j.ijproman.2016.10.014
Khandare Manish A, Vyas Gayatri S (2012) Project duration forecasting using earned value method and time series. International Journal of Engineering and Innovative Technology 1(4):218-224
Lipke W, Zwikael O, Henderson K, Anbari F (2016) Prediction of project outcome: The application of statistical methods to earned value management and earned schedule performance indexes. International Journal of Project Management 27(4):400-407, DOI: 10.1016/j.ijproman.2008.02.009
Mishakova A, Vakhrushkina A, Murgul V, Gardiner AS (2016) Project control based on a mutual application of pert and earned value
management methods. Procedia Engineering 165:1812-1817, DOI: 10.1016/j.proeng.2016.11.927
Montgomery DC, Johnson LA, Sazonova T (1990) Forecasting and time series analysis. McGraw-Hill, New York, NY, USA, 138-156 Naeni LM, Shadrokh S, Salehipour A (2011) A fuzzy approach for the
earned value management. International Journal of Project Management 29(6):764-772, DOI: 10.1016/j.ijproman.2010.07.012
Najafi A, Azimi F (2016) An extension of the earned value management to improve the accuracy of schedule analysis results. Iranian Journal of Management Studies 9(1):63-75, DOI: 10.22059/ijms.2016.55035
Ostertagová E, Ostertag O (2011) The simple exponential smoothing model. The 4th international conference on modelling of mechanical and mechatronic systems, Technical University of Košice, Herľany, Slovak Republic, 380-384
Tratar LF, Mojškerc B, Toman A (2016) Demand forecasting with four-parameter exponential smoothing International Journal of Production Economics 181(Part A):162-173, DOI: 10.1016/j.ijpe.2016.08.004
Vandevoorde S, Vanhoucke M (2006) A comparison of different project duration forecasting methods using earned value metrics. International Journal of Project Management 24(4):289-302, DOI: 10.1016/ j.ijproman.2005.10.004