The paper proposes a new hybrid model for forecasting project total duration in earned value management that combines artificial neural networks, random number simulation, and statistical methods. The model uses an artificial neural network to forecast the next period's earned schedule value based on prior periods' actual values. It then uses the forecast along with statistical methods to calculate confidence intervals and point estimates for total project duration at each period. The model was tested on real project data and found to outperform traditional earned value management forecasting methods in terms of accuracy.

1. 402 Int. J. Networking and Virtual Organisations, Vol. 10, Nos. 3/4, 2012
Hybrid artificial neural network and statistical model
for forecasting project total duration in earned value
management
You Li* and Lu Liu
School of Economics and Management,
BeiHang University,
Beijing 100191, China
E-mail: lijinbi-sony@163.com
E-mail: liulu@buaa.edu.cn
*Corresponding author
Abstract: The paper proposes a new hybrid approach for forecasting project
total durations in earned value management, which combines artificial neural
network and random number simulation method to forecast the earned schedule
indicator of each period one step further based on several nearest finished
periods’ status and then employs statistical method to estimate the project total
duration and its intervals in each period of the project. Experiment results and
test show our hybrid model outperforms the classic method of earned value
management in both aspects of interval estimation and point estimation.
Keywords: project management; earned value management; EVM; artificial
neural network; ANN; earned schedule; ES; forecasting.
Reference to this paper should be made as follows: Li, Y. and Liu, L. (2012)
‘Hybrid artificial neural network and statistical model for forecasting project
total duration in earned value management’, Int. J. Networking and Virtual
Organisations, Vol. 10, Nos. 3/4, pp.402–413.
Biographical notes: You Li is a PhD student of information systems in the
School of Economics & Management at the BeiHang University of China. His
research focuses on decision support systems, complex social networks and
project management. He is working on papers employing complex social
network theory and project management methods to study the social network
effects on the decision process.
Lu Liu is a Professor of Information Systems in the School of Economics &
Management at the BeiHang University of China. She is the Director of the
R&D Center of Management and Information Systems. She is a member of the
General Council of China Association of Information Systems (CNAIS). Her
research area is e-commerce, including: web mining and decision support,
knowledge management, recommendation systems, trust and credibility in e-
commerce. Her papers have been published in journals such as Expert Systems
with Applications, System Research and Behavioral Science, The Journal of
Information and Knowledge Management Systems.
Copyright © 2012 Inderscience Enterprises Ltd.

2. Hybrid artificial neural network and statistical model 403
1 Introduction and overview
Earned value management (EVM) is a convenient and effective method of project
management. It cuts a project into several equal basic periods (generally the basic time
unit, e.g., month or day), and puts the cumulative planned workload (scaled in money
unit) into each period as planned value (PV); as the project is performing, the actual
finished PV of each period is filled into earned value (EV); plus the actual cost (AC) of
each period and several related derived indicators, e.g., CPI, SPI, CV, SV, etc., EVM
builds up a framework to weigh and forecast a project performance status. However, with
the development of EVM, researchers find that EVM performs poorly in the aspect of
weighing project schedule because the indicator SPI is defined by EV/PV and SV is
defined by EV – PV which makes them approach to 1 and 0 respectively in the latter part
of the project even if its performance is behind the planned schedule. This is
unacceptable when forecast the project total duration cause the result generally
approaches to the planned duration no matter if a project’s performance is good or bad
(Vandevoorde and Vanhoucke, 2006; Lipke et al., 2008); besides, the two indicators
cannot reflect the project performance status properly. Based on EVM, Lipke et al.
develops earned schedule (ES) method that it scales the workload in time unit and solves
the above problem, which is an extension to EVM. Based on ES method, Lipke et al.
(2008) apply statistical methods and their well established schedule performance
analysing technique-IEACt to predict total cost and total duration of a project.
Based on IEACt, the paper proposes a new hybrid method for project total duration
forecasting, which combines artificial neural network (ANN), random number simulation
method and statistical method. Experiments and test results show our hybrid method
outperforms the classic IEACt method in aspect of forecasting accuracy.
The paper’s structure is arranged as follows: Section 2 is a brief introduction to EVM,
and then our hybrid model is put force and experiments are carried out in Section 3,
Section 4 is accuracy test for the comparison of our hybrid model and classic IEACt and
conclusions are drawn in Section 5.
2 Review of EVM
An understanding of EVM is assumed in this paper. For convenience, we list the basic
EVM terminology including ES that portrays the project status and forecasts the total
duration.
We need to make an explanation that PV, EV, AC, ES with the performance indicators
CPI and SPI are all cumulative expressions in default situations, that is to say for each
period, these values are calculated by the cumulative values. The periodic expressions
can easily obtained by the difference of the adjacent two cumulative values. In this paper,
we denote periodic expressions of above terminology by adding suffix p and period
suffix t, e.g., the EV value of the 5th period itself is denoted by EVp,5. Earned schedule
framework is a recent extension to EVM, designed for providing reliable and useful
schedule performance information (Lipke et al., 2008; Cioffi, 2006). In earned schedule
framework, the basic metric is ES, which means the schedule duration earned, can be
calculated as follows:

3. 404 Y. Li and L. Liu
ESt = i + ( EVt − PVi ) ( PVi +1 − PVi ) (1)
In the above definition, the tth ES is described as the workload of already finished (i, time
unit) plus a linear interpolation value which is the amount of ES accrued within the
increment of i from PVi to PVi+1. Compared with EVM metrics, ES is specially designed
to cover the needs for time scale forecasting, which in traditional EVM metrics SPI
approximates to 1 no matter the performance of EV when a project is nearly finished;
hence the indicator SPI could not reflect the project performance properly. However, in
ES metrics, ES is calculated by the periodic actual finished proportion of planned
workload, wherever the project is performing, ES could properly express the performance
status of a project.
Table 1 Basic EVM and ES terminology
EVM ES
Status Earned value (EV) Earned schedule (ES)
Actual cost (AC) Actual time (AT)
Schedule variance (SV) Schedule variance (time) (SV(t))
SV = EV – PV SV(t) = ES – AT
Schedule performance index (SPI) Schedule performance index (time)
SPI = EV / PV (SPI(t))
SPI(t) = ES / AT
Cost performance index (CPI)
Cost variance (CV)
Forecasting Independent estimate at complete Independent estimate at complete time
(IEAC) (IEAC(t))
IEAC = BAC / CPI IEAC(t) = PD / SPI(t)
IEAC(t) = AT + (PD – ES) / PF
3 Methodology
According to the ES theory, the project total duration could be estimated by independent
estimate at completion time (IEAC(t)), it has two forms, short form and long form
respectively:
IEACt = PD / SPI (t ) (2)
IEACt = AT + ( PD − ES ) / PFt (3)
Where AT is the actual time, i.e., the current time; and PFt is the performance factor
which is generally SPI(t) for duration forecasting. IEACt provides us a convenient
forecasting method for project total duration. However, there is an underlying
assumption: the performance of future unfinished part of the project is equal to the
cumulative indicator SPI of finished part, i.e., the current SPI(t). Based on SPI(t), Lipke
et al. (2008) propose a statistical calculation method (Lipke et al., 2008; Lipke, 2002;
National Institute of Standards and Technology E-handbook of Statistical Methods,
2006), we summarise it as follows:

4. Hybrid artificial neural network and statistical model 405
CL = ln index(cum) ± Z * σ n * AF (4)
σ= ∑ ( ln index p (i ) − ln indexc )2 ( n − 1) (5)
AF = ( PD − ES ) ( PD − ES / n) (6)
IEACt = PD exp (CL) (7)
Where CL is the confidence limit, indexp refers to periodic index values and indexc refers
to cumulative index values. The index in our study refers to SPI, Z is the t distribution
value representing the level of confidence (95% in this paper), we use t distribution
instead of normal distribution because our data sample is less than 30. σ is the standard
deviation of SPI, n is the number of observations, and AF is the adjusted factors for finite
population, which is derived from the statistics formula (( N − n) / ( N −1)).
In this paper, we adopt this statistical method. However, we make a little change:
employing long forms instead of short forms; meanwhile, we make an extension to the
IEACt assumption as follows (the current time is t):
Assumption 1: The schedule performance index of future unfinished part of the project is
not exactly equal to the current cumulative SPIc,t as classic IEACt does, but equal to a
∧
forecasting value SPI c , t +1 , which could reflect the performance of unfinished part of the
project more properly than SPIc,t.
Assumption 2: The periodic EVp,t+1, ACp,t+1 and ESp,t+1 conform to normal distribution
respectively with parameters μ and σ2, where μ is the mean of the nearest T number of
periodic EVp,i, ACp,i, ESp,i (i = t – (T – 1,…,t) respectively, σ2 is their corresponding
deviation respectively.
The main idea of Assumption 2 lies in: we believe the performance of future unfinished
part of the project could be expressed by the nearest T number of EVp,i, ACp,i, ESp,i
(i = t – (T – 1,…,t) to it instead of the whole finished part from 1 to t, i.e., the latest
several periodic EV, AC, ES values could express better or have the greater possibility to
explain the future performance more than the whole finished periodic ones until t time.
Besides, we believe that for the periodic EV, AC, ES, the three metrics’ changing ranges
of future undone part (especially those of the next one period) have greater possibility to
fall in the regions formed by normal random numbers with the parameters of μ and σ2
respectively, instead of being simply equal to the means of t number of EV, AC, ES
respectively as traditional IEACt does.
For this consideration, we cut the whole forecasting process into two stages:
In the first stage we employ ANN back propagation algorithm to forecast the
next periodic earned schedule ESp,t+1 just one step further, and make
∧ ∧
SPI c ,t +1 = ( ES p ,t +1 + ESc ,t ) / (t + 1) as the future performance of the project. In Stage 2,
we put the forecasting value into the statistical framework to perform interval estimations
∧
for total duration; meantime, we make a replacement SPI c ,t +1 for PFt in formula (3) to
forecast the project total duration. The methodology of our hybrid model is summarised
as follows:

5. 406 Y. Li and L. Liu
1 Suppose the current time is t(t ≥ 3), set T =3.
2 Based on the available finished t number of periodic EVp,i, ACp,i, ESp,i (i = t – (T –
1,…,t), three groups of normal distribution random numbers EVp,R, ACp,R, ESp,R are
generated with their own parameters of μ and σ2 respectively.
3 Regard EVp,R and ACp,R as the input nodes, ESp,R as the output node, with the help of
∧ ∧
ANN to forecast ES p ,t +1 and then to obtain SPI c ,t +1 as the performance index of
future unfinished part of the project.
4 Employ formula (3) to (6) to make interval estimation and point estimation of the
project total duration standing at period t.
5 t = t + 1, loop Step (2) to (5) until the project is actually finished.
3.1 ANN forecasting procedure
Although traditional models outperform in terms of accurately describing the
phenomenon of long-term trends (Sallehuddin et al., 2009; Zou et al., 2007; Kayacan et
al., 2010; Yao et al., 2003), they require a large amount of observations to construct the
model. Unlike these forecasting requirements, forecasting within a project has much
fewer data, including the number of variables and observations. At the very beginning of
the project, we have only two to three month data and less than six indicators;
furthermore, related literatures suggest that detailed project analysis is a burdensome
activity. Thus, some widely used model like time series model and classic statistic
method do not match this type of forecasting.
In this paper, we employ two input nodes – one hidden layer – one output node
architecture ANN to forecast ESp,t+1. Training a network is an essential factor for the
success of the neural networks (Satish Kumar, 2006). Among the several learning
algorithms available, back-propagation is the most popular and most widely implemented
learning algorithm of all neural networks paradigms. In this paper, the algorithm of
back-propagation is employed and in the following experiment.
In order to construct the training set, based on the Assumption 2, we generate 1,000
normal distribution random numbers for the periodic EVp,t+1, ACp,t+1 and ESp,t+1
respectively. Each randomly selected corresponding ternary terms as a pattern (Satish
Kumar, 2006), then we have got 1,000 patterns as the training set. The 1,000 ternary
terms cover as much as possible combinations of periodic EV, AC and ES, which is a
simulation to actual performance situation. According to the cross validation theory, we
randomly select the learning set, the validate set and the test set from the training set,
where EVp,t+1, ACp,t+1 are the input nodes, ESp,t+1 is the output node, via pattern training
mode, after learning and validation, the test set is filled in the well-trained ANN, then the
∧ ∧
forecasting value ES p ,t +1 is obtained and so does SPI c ,t +1 .
∧
In view of the random nature of our training set, for each forecasting value ES p ,t +1 ,
we repeat the above forecasting process 100 times, and calculate its average value as our
∧
final forecasting value ES p ,t +1 . Since our ANN is not designed for the specific project,
the number of nodes in the hidden layer is not necessarily designed in details. We

6. Hybrid artificial neural network and statistical model 407
uniformly set it to 20. A real-life project data from Fabricom Airport system
(Vandevoorde and Vanhoucke, 2006) is employed as the experiment data, the brief
information of which is listed in Table 1. The whole model is programmed with
Matlab 7.11.
Table 2 The brief project data of Fabricom Airport system
AT 1 2 3 4 5 6 7
PV 3023 5508 7828 10098 12158 13951 14205
EV 928 1904 2467 3414 4472 7152 7476
AC 1606 2766 4324 6138 7888 9835 10135
8 9 10 11 12 13 14
PV 15933 17902 19967 22208 24286 26331 26658
EV 9272 11441 13302 14699 15985 16753 17077
AC 13217 14755 16656 18768 20897 23364 23664
15 16 17 18 19 20 21
PV 28647 30989 33040 34909 36709 38016 38140
EV 20318 23061 26588 28681 30135 31487 32526
AC 26651 28437 30408 32012 34000 35554 37111
22 23 24 25 26
PV 38140 38140 38140 38140 38140
EV 33504 34513 36489 37630 38140
AC 38468 39798 41155 42600 43983
For the consideration of S-curve and the scarcity nature of samples of available
cumulative ESc,i(i = 1, 2,…,t), we also employ the Grey Verhulst rolling model (Kayacan
et al., 2010) to forecast ESc,t+1, the rolling cycle is also set to 3 (which is equal to T of our
method). However, the relative error percentage is larger than that of ANN method. The
forecasting results of two frameworks are listed below for comparison, where the actual
value is the actual cumulative parameters ESc,t+1 in each period.
The forecasting details are described as follows:
Set T = 3
At the very beginning of the forecasting, suppose only three month is performed, i.e.,
current time t = 3, so we have three true values for EVc,i, ACc,i, ESc,i (i = 1, 2, 3)
respectively, that is also mean we have got EVp,i, ACp,i, ESp,i (i = 1, 2, 3). Based on these
true values, we generate random numbers and training set according to the above
∧ ∧
framework, then forecast ES p ,t +1 just one step further, i.e., ES p ,4 , so the forecasting
∧ ∧
value ESc ,4 = ES p ,4 + ESc ,3 is naturally obtained. The comparative error percentage is
calculated by
∧
error % = ESc,t +1− ESc ,t +1 / ESc ,t +1 *100 (8)

7. 408 Y. Li and L. Liu
Table 3 ES forecasting results of two models
GM(1,1) Verhurlst model ANN model
Actual value
AT ∧ ∧
(ESc,t+1) Error (%) Error (%)
ESc ,t +1 ESc ,t +1
4 1.1573 0.86 26 1.09 6.12
5 1.5831 1.87 18.27 1.45 8.63
6 2.7086 2.06 23.77 1.90 29.82
7 2.8483 7.12 149.93 3.23 13.58
8 3.6361 2.84 21.85 3.33 8.46
9 4.6519 5.52 18.65 4.15 10.87
10 5.6380 5.94 5.44 5.21 7.54
11 7.2859 6.49 10.94 6.25 14.28
12 8.0264 10.30 28.36 8.03 0.008
13 8.4165 8.24 2.06 8.77 4.14
14 8.5810 8.59 0.1 9.12 6.32
15 10.1566 8.64 14.94 9.27 8.74
16 11.4105 11.51 0.88 10.93 4.20
17 13.7859 12.30 10.81 12.22 11.39
18 15.0145 18.62 24.01 14.71 2.04
19 15.6354 15.49 0.91 15.96 2.08
20 16.2428 15.90 2.11 16.57 2.03
21 16.7494 16.83 0.50 17.16 2.43
22 17.2483 17.16 0.50 17.65 2.35
23 17.7881 17.74 0.28 18.13 1.90
24 18.8778 18.37 2.67 18.64 1.25
25 19.7047 20.89 6.01 19.75 0.23
26 21 20.30 3.33 20.56 2.10
RMSE 1.41 0.57
MSE 2.0 0.32
MAPE(%) 16.19 6.55
MAD 0.89 0.45
In the next forecasting process t = 4, we use the nearest T (= 3) true values of EVc,i, ACc,i,
∧
ESc,i (i = 2, 3, 4) to forecast ESc ,5 . The process is performed until the project is finished.
We list the detail forecasting values of every forecasting period guided by two
forecasting frameworks based on the experiment project data in Table 3. To evaluate the
two forecasting metrics, four statistical test indexes [formula (9) to (12)] are carried out:
root mean square error (RMSE), mean square error (MSE), mean absolute percentage
error (MAPE), mean absolute deviation (MAD). In all the four aspects of basic
forecasting performance indexes, the designed ANN model outperforms the GM(1,1)

8. Hybrid artificial neural network and statistical model 409
Verhurlst rolling model. Hence, in the first stage of forecasting, we employ ANN instead
of GM(1,1) Verhurlst rolling model.
n
1
RMSE =
n ∑ (observed − predicted )
t =1
t t
2
(9)
n
1
MSE =
n ∑ (observed − predicted )
t t
2
(10)
t =1
n
observedt − predictedt 100
MAPE = ∑ observedt
×
n
(11)
t =1
n
observedt − predictedt
MAD = ∑t =1
n
(12)
3.2 Statistical estimation for total duration
In Stage 2, for each period, we make use of the latest one step further forecasting value
∧ ∧
ESc ,t +1 to calculate the schedule performance index SPI c,t +1 as the SPI of future
unfinished part, which is our Assumption 1. The benefit of doing this lies in:
Firstly, the classic IEACt method regards the current SPIc,t as the SPI of future undone
part. In essence, this is a kind of simple averaging process because the current
SPIc,t = ESc,t/t, that is to say, SPIc,t is the average performance ability of all t periods
∧
already finished. In comparison, SPI c,t +1 is a kind of fitting value by fitting the average
performance ability of the nearest T periods, which can better express the current
performance status of the project, which is an extension to SPIc,t as we employ random
number simulation method to construct a scene that can simulate the performance ability
trends (the trends are calculated by fitting many different ternary ties of EV, AC, ES,
which can cover more possible actual situations close to actual performance).
∧
Secondly, standing at the current period, due to the extra forecasting SPI c ,t +1 , the
sample number n in the formula increases compared to the classic based on n true
samples; besides, low error percentage forecasting could bring an effect that if we had
known the true value of the next period, according to the experiments provided by Lipke
et al. (2008), which proves that the logarithm of periodic indexes of SPI or CPI
approximates to a normal distribution and would become more and more stable after 30%
percent of the project. The above explanation enables our one step further forecasting to
produce an analogical effect as if we stood at the next period to forecast the total
duration, which has more possibilities to perform a comparatively better result in both
aspects of interval estimation and point estimation.
Based on the above explanations, we draw the result of total duration forecasting both
in our hybrid method and the classic IEACt method from the 4th period to the 26th,
including both interval and point estimation. The details for each forecasting round are
listed in Table 4, and shown in Figure 1.

9. 410 Y. Li and L. Liu
Table 4 Total duration forecasting results of two models
IEAC(t) Hybrid forecasting
AT
Value Lower Upper Error% Value Lower Upper Error%
4 78.749 61.466 96.033 202.882 77.049 66.197 87.902 196.344
5 72.650 66.791 78.510 179.425 72.297 68.144 76.450 178.066
6 67.011 63.319 70.704 157.736 66.660 61.446 71.873 156.384
7 48.889 33.777 64.000 88.033 46.946 35.592 58.301 80.563
8 52.582 42.362 62.801 102.237 50.822 42.796 58.848 95.470
9 47.271 37.054 57.488 81.812 46.728 39.356 54.100 79.722
10 41.880 31.784 51.976 61.078 41.129 34.171 48.087 58.190
11 38.394 29.027 47.762 47.671 38.009 31.956 44.062 46.188
12 32.894 24.065 41.723 26.517 32.253 27.130 37.376 24.051
13 32.334 24.548 40.119 24.360 31.491 27.180 35.802 21.120
14 33.142 26.277 40.006 27.467 32.683 28.977 36.388 25.703
15 34.799 28.728 40.871 33.844 34.639 31.386 37.892 33.226
16 31.497 25.948 37.045 21.141 31.071 28.480 33.662 19.504
17 29.866 24.885 34.847 14.870 29.661 27.605 31.717 14.081
18 26.236 21.980 30.492 0.907 25.993 24.695 27.291 0.028
19 25.242 24.323 26.161 2.915 25.450 21.776 29.124 2.116
20 25.538 24.814 26.262 1.777 25.719 22.458 28.980 1.080
21 25.898 25.329 26.467 0.391 26.023 23.131 28.915 0.090
22 26.454 23.878 29.030 1.746 26.329 25.885 26.774 1.266
23 26.880 24.593 29.167 3.385 26.782 26.438 27.127 3.008
24 27.224 25.216 29.232 4.709 27.158 26.902 27.414 4.454
25 26.741 25.173 28.309 2.850 26.700 26.579 26.821 2.691
26 26.676 25.500 27.852 2.599 26.639 26.602 26.677 2.459
Figure 1 The total duration forecasting result of two model (see online version for colours)

10. Hybrid artificial neural network and statistical model 411
4 Tests
From Figure 1, we could easily observe that the interval estimation of our hybrid method
is better than the classic IEACt, as to the effect of two methods are similar in the aspect of
point estimation, paired t-test is carried out on forecasting accuracy (error%) to test the
hypotheses. The aim of this test is to check whether the means of forecasting values
obtained from our hybrid method are different from those of classic IEACt. Therefore, the
following hypotheses are proposed:
H01 There is no difference between the means of the classic IEACt and the proposed
hybrid method (μ1 = μ2).
H11 There is a difference between the means of the classic IEACt method and the
proposed hybrid method (μ1 > μ2 or μ1 < μ2).
H02 The means of IEACt lower boundary and that of the proposed hybrid method are
equal (IEACt_lower = Hybrid_lower).
H12 The means of IEACt lower boundary and that of the proposed hybrid method are
not equal (IEACt_lower > Hybrid_lower or IEACt_lower < Hybrid_lower).
H03 The means of IEACt upper boundary and that of the proposed hybrid method are
equal (IEACt_upper = Hybrid_upper).
H13 The means of IEACt upper boundary and that of the proposed hybrid method are
not equal (IEACt_upper > Hybrid_upper or IEACt_upper < Hybrid_upper).
From the test results, the 2-tailed Sig (μ1 ≠ μ2) is 2.8727460171483986E-4, the
corresponding H01 single-tailed Sig (μ1 > μ2) is 1.4363730085741993E-4, under 95%
confidence level the test is significance, so we reject the null hypothesis H01.
Then, we test the interval estimation accuracy of two models, we compare the upper
and lower boundaries of two models respectively, the results are combined in Table 4.
From the test results, the 2-tailed Sig (IEACt_lower ≠ Hybrid_lower) of two models’
lower boundaries is 0.0013633818441228292, hence the corresponding H02 single-tailed
Sig (IEACt_lower < Hybrid_lower is 0.0006816909220614146, under 95% confidence
level the test is significance, so we reject the null hypothesis H02.
Similarly, the 2-tailed Sig (IEACt_upper ≠ Hybrid_upper) of two models’ upper
boundaries is 2.7602225137402837E-4, so the corresponding H03 single-tailed Sig
(IEACt_upper > Hybrid_upper) is 1.38011125687014185E-4, under 95% confidence
level the test is significance, so we reject the null hypothesis H03.
To observe the test results, it is found that our hybrid model outperforms the
traditional IEACt in both aspects of the means of point estimation and interval estimation,
especially for the interval estimation, in the former part of the project, our model could
achieve much more accurate interval estimation than IEACt does.

11. 412 Y. Li and L. Liu
Table 5 Paired t-test results of two model means
Paired differences
95% confidence
Std. Sig.
Std. interval of the t df
Mean error (2-tailed)
deviation difference
mean
Lower Upper
Pair 1 IEAC(t) – 1.936870 2.158306 .450038 1.003548 2.870191 4.304 22 0.000
Hybrid_forecast
Table 6 Paired t-test results of two model boundary means
Paired differences
95% confidence interval Sig.
Std. Std. error t df
Mean of the difference (2-tailed)
deviation mean
Lower Upper
Pair 1 IEAC_lo – –1.480217 1.937407 .403977 –2.318015 –.642420 –3.664 22 .001
Hybrid_lo
Pair 2 IEAC_up – 2.403217 2.667834 .556282 1.249559 3.556875 4.320 22 .000
Hybrid_up
5 Conclusions
In this paper, we propose a new hybrid model for project total duration forecasting With
the help of random number simulation and ANN non-linear fitting ability to simulate the
actual possible project performance combinations of EV, AC and ES, so as to better
forecast the performance factor SPI one step further to improve the traditional IEACt (in
which the latest SPI is regarded as PF of future unfinished part), then replace that of the
classic IEACt to forecast the total duration of the project. Forecasting results and tests
show that our hybrid method outperforms the classic IEACt in the both aspects of point
estimation and interval estimation. Of course, to make a proper T is not an easy task,
different projects due to their different changing trends of performance factor, T is
different; however, our model provides a new idea to better estimate the future
(especially the next one period) project performance index of SPI especially in the
beginning of a project when the true performance status indexes are scarce, which is also
the blind period of a project, because when the project approximates to an end, its
performance status is almost clear, and the forecasting for the total duration becomes less
significant. So our model provides a more effective SPI estimation method for the future
undone part of a project in its beginning period.
Of course our model is far from perfect, since it is build on a hypothesis that the three
main metrics: EV, AC, ES of the next one period fall in the range of normal random
numbers generated by their respective nearest T number of finished periods’ ones, if the
above three metrics change too sharply against their nearest T ones respectively, the
model may not perform well. From Figure 1, we could observe that the advantages of our
method are mainly highlighted in the former and middle part of the whole project, as to

12. Hybrid artificial neural network and statistical model 413
the final part, its prominent effect sharply decreases. This is because the normal random
numbers are a kind of simulation of possible actual combinations of performance status,
which is especially effective when the true performance indexes are scarce, with the
increase of true indexes this simulation becomes weaken; besides, when a project
approximates to its latter part, SPI tends to stabilisation, random numbers may disturb
this trend, under this circumstance, the traditional IEACt based on the average of all
history data could hit the bull’s-eye more easily.
Future work could further extend some research on the final part of the project, since
there are sufficient number of the performance indicators, we could employ a hybrid
method of time-series and EVM to have a try.
Acknowledgements
The research is supported by the National Natural Science Foundation of China under
Grant No. 90924020 and the PhD Program Foundation of Education Ministry of China
under Contract No. 200800060005.
References
Cioffi, D.F. (2006) ‘Designing project management: a scientific notation and an improved
formalism for earned value calculations’, International Journal of Project Management,
Vol. 4, No. 2, pp.289–302.
Kayacan, E., Ulutas, B. et al. (2010) ‘Grey system theory-based models in time series prediction’,
Expert System with Applications, Vol. 37, No. 2, pp.1784–1789.
Lipke, W. (2002) ‘A study of the normality of earned value management indicators’, Meas. News,
pp.1–16.
Lipke, W. et al. (2008) ‘Prediction of project outcome the prediction of statistical methods to
earned value management and earned schedule performance indexes’, International Journal of
Project Management, doi:10.1016/j.ijproman.2008.2.009.
National Institute of Standards and Technology E-handbook of Statistical Methods (2006)
‘Lognormal distribution’, available at http://www.itl.nist.gov/div898/handbook/eda/section3/
eda3669.htm.
Sallehuddin, R. et al. (2009) ‘Hybrid grey relational artificial neural network and auto regressive
integrated moving average model for forecasting time-series data’, Applied Artificial
Intelligence, Vol. 23, No. 5, pp.443–486.
Satish Kumar (2006) Neural Networks, pp.165–194, Tsinghua University Publishing Company,
Beijing, China.
Vandevoorde, S. and Vanhoucke, M. (2006) ‘A comparison of different duration forecasting
methods using earned value metrics’, International Journal of Project Management, Vol. 24,
No. 4, pp.289–302.
Yao, A.W.L., Chi, S.C. et al. (2003) ‘An improved grey-based approach for electricity demand
forecasting’, Electric Power System Research, Vol. 67, No. 3, pp.217–224.
Zou, H.F. et al. (2007) ‘An investigation and comparison of artificial neural network and time
series models for Chinese food grain price forecasting’, Neurocomputing, Vol. 70, Nos. 16–
18, pp.2913-2923.