A hybrid intelligent model for medium-term sales forecasting in fashion [627454]

A hybrid intelligent model for medium-term sales forecasting in fashion
retail supply chains using extreme learning machine and harmonysearch algorithm
W.K. Wongn, Z.X. Guo
Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, PR China
article info
Article history:
Received 23 December 2009Accepted 5 July 2010
Available online 23 July 2010
Keywords:
Fashion sales forecastingHarmony searchNeural network
Extreme learning machineabstract
A hybrid intelligent (HI) model, comprising a data preprocessing component and a HI forecaster, is
developed to tackle the medium-term fashion sales forecasting problem. The HI forecaster firstly adoptsa novel learning algorithm-based neural network to generate initial sales forecasts and then uses aheuristic fine-tuning process to obtain more accurate forecasts based on the initial ones. The learning
algorithm integrates an improved harmony search algorithm and an extreme learning machine to
improve the network generalization performance. Extensive experiments based on real fashion retaildata and public benchmark datasets were conducted to evaluate the performance of the proposed
model. The experimental results demonstrate that the performance of the proposed model is much
superior to traditional ARIMA models and two recently developed neural network models for fashionsales forecasting.
&2010 Elsevier B.V. All rights reserved.
1. Introduction
Sales forecasting is the foundation for planning various phases
of a firm’s operations ( Boulden, 1958; Lancaster and Reynolds,
2002 ), which is a crucial task in supply chain management under
dynamic market demands and greatly affects retailers and other
channel members in various ways ( Xiao and Yang, 2008 ). Without
sales forecasts, operations can only respond retroactively, leading
to poor production planning, lost orders, inadequate customer
service, and poorly utilized resources ( Fildes and Hastings, 1994 ).
Recent research has shown that effective sales forecasting enables
improvements in supply chain performance ( Bayraktar et al.,
2008; Zhao et al., 2002 ). Because of ever-increasing global
competition, sales forecasting plays a more and more prominent
role in supply chain management when the profitability and the
long-term viability of a firm relies on effective and efficient sales
forecasts. This paper investigates the medium-term fashion salesforecasting problem to facilitate effective sales forecasting in
fashion retail supply chains.
1.1. Fashion sales forecasting
The fashion industry is characterized by short product life
cycles, volatile customer demands, tremendous product varieties,
and long supply processes ( Sen, 2008 ). Most fashion items’ salesare of strong seasonality. Uncertain customer demands in
frequently changing market environment and numerous expla-
natory variables that influence fashion sales cause an increase in
irregularity or randomicity of sales data. Such distinct character-
istics increase the complexity of sales forecasting in the fashion
retail supply chain. It is definitely desirable to develop forecasting
models which are flexible and robust enough to handle these
distinct characteristics of fashion sales data. Several studies have
been reported to investigate fashion sales forecasting problems
from different perspectives. Frank et al. (2004) proposed a
multivariate fuzzy logic model to forecast women’s casual sales.
Thomassey and Happiette (2007) developed a neural network
(NN)-based system to forecast sales profiles of new apparel items
by extracting and analyzing available data with a self-organizing
map NN-based clustering procedure and a probabilistic NN-based
decision tree technique. Au et al. (2008) fulfilled fashion retail
sales forecasting by developing an evolutionary NN (ENN) model,
which adopted a genetic algorithm to determine an appropriate
network structure for improving the generalization capacity of
NNs. The ENN model is effective for sales forecasting of fashion
items with features of low demand uncertainty and weak
seasonal trends. Unfortunately, most fashion items are character-ized by high demand uncertainty and strong seasonality. Sun et al.
(2008) applied an NN model with extreme learning machine for
fashion sales forecasting, and investigated the relationship
between sales amount and some significant fashion product
attributes such as color, size and price.
The studies in fashion sales forecasting mentioned above focus
on forecasting sales volumes and sales profiles of fashion items,Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/ijpeInt. J. Production Economics
0925-5273/$ – see front matter &2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.ijpe.2010.07.008nCorresponding author. Tel.: +852 27666471; fax: +852 27731432.
E-mail address: tcwongca@inet.polyu.edu.hk (W.K. Wong).Int. J. Production Economics 128 (2010) 614–624

which are usually short-term forecasting. Due to the short life
cycles and frequent replacements of fashion items, only forecast-
ing each item’s sales is not adequate in the fashion retail supply
chain. In fact, the fashion retail enterprise usually makes sourcing
budgets, on an annual, quarterly and monthly basis, by forecast-
ing total sales amounts of fashion items in one fashion item
category or in all categories of one city. Then the fashion designers
determine which items need to be purchased or produced in each
category. Each fashion item category consists of multiple items
with some common attributes. In an enterprise, the categories are
usually unchanged while the items in each category frequently
change in different selling seasons. For instance, the short sleeves
T-shirt category consists of 200 items in this season, but 150 of
them will probably be replaced by another 150 new items in the
next season. Based on soft computing techniques, Thomassey
et al. (2005) developed a forecasting support system which
involved the medium-term sales forecasting at different sales
aggregation levels. However, it is very difficult to apply the
system in practice because it uses multiple soft computing
techniques and too many parameters for such techniques need
to be set. Due to the lack of effective methodologies for fashion
sales forecasting under dynamic market demands, the medium-
term sales forecasting in today’s fashion retail supply chain
mainly depends on subjective experience or simple linear models
such as autoregressive (AR) model and moving average model.
To provide a flexible, robust, and effective methodology for
fashion sales forecasting, this paper examines the sales forecast-
ing problem based on the forecasting process in real-world
fashion retailing, which forecasts the total sales amount of each
fashion item category or each city (all categories) on a medium-
term basis (annual, quarterly and monthly).
1.2. Techniques for sales forecasting
Various time series forecasting models have been widely applied
in sales forecasting, such as exponential smoothing models
(Gardner, 2006; Geurts and Kelly, 1986; Harrison, 1967; Taylor,
2007 ), ARIMA models ( Dalrymple, 1978; Goh and Law, 2002; Tang
et al., 1991 ), expert systems ( Lo, 1994; Smith et al., 1996 ), fuzzy
systems ( Chang et al., 2008; Chen and Wang, 1999; Frank et al.,
2004 )a n dN Nm o d e l s( Ansuj et al., 1996; Chu and Zhang, 2003; Sun
et al., 2008; Thiesing and Vornberger, 1997; Zhang and Qi, 2005 ).
The exponential smoothing and the ARIMA models are categor-
ized as linear methods which employ a linear functional form for
time-series modeling ( De Gooijer and Hyndman, 2006 ). As such
linear methods cannot capture features that commonly occur in
many actual time-series data, such as nonlinear patterns, occasional
outlying observations and asymmetric cycles ( Makridakis et al.,
1998 ), they are not suitable for fashion sales series characterized by
strong nonlinearity. Expert systems, fuzzy systems and NN models
belong to heuristic methods, among which NNs are the most
attractive alternatives for both fo recasting researchers and practi-
tioners since a large number of re search papers reported successful
experiments and practical tests, and showed that NNs exhibit better
forecasting performances than some traditional approaches ( Ansuj
et al., 1996; Chu and Zhang, 2003; Tang et al., 1991 ).
Ansuj et al. (1996) presented the use of back-propagation (BP)
NN model in analyzing the behavior of sales in a medium size
enterprise and reported that the BP model generated moreaccurate forecasts than ARIMA models with interventions did.
Thiesing and Vornberger (1997) developed an NN-based forecast-
ing system to predict the weekly product demand in a German
supermarket company. Alon et al. (2001) compared the perfor-
mance of NN models with the Levenberg–Marquardt learning
algorithm and traditional statistical methods in forecasting USaggregate retail sales, and concluded that the NN model was able
to effectively capture the dynamic nonlinear trend and seasonal
patterns, as well as the interactions between them. Chu and
Zhang (2003) compared the performance of NN models and
various linear models for forecasting aggregate retail sales
and reported that the overall best model is the NN model built
on deseasonalized time series data. Chang et al. (2005) proposed
an evolving NN forecasting model by integrating genetic algo-
rithms and BP NN to generate more accurate forecasts than
traditional statistical models and BP networks.
The previous studies usually adopted NNs with gradient
learning algorithm such as BP which is known to have slowconvergence speed caused by the problem of local minima. In
recent years, a new learning algorithm called extreme learning
machine (ELM) has been proposed ( Huang et al., 2004 ) which
tends to provide a better generalization performance and much
faster learning speed than gradient learning algorithms. The ELM
can also avoid many difficulties faced by gradient learning
algorithms, such as the selections of stopping criteria, learning
rate and learning epochs due to its distinct learning mechanism.
Sun et al. (2008) ’s research in fashion sales forecasting demon-
strated that the ELM-based NN had a much shorter training time
and higher forecast accuracy than BP NNs. However, ELM
determines randomly the input weights and hidden biases, which
may lead to a higher number of hidden neurons and adversely
affect the generalization performance of the network. Further-
more, the available historical sales data (training samples) for
medium-term fashion sales forecasting are usually limited, and
therefore the NN forecasting model is more apt to be over-
parameterized and overfitted. Zhu et al. (2005) developed an
evolutionary ELM by combining a modified differential evolution
and an ELM, and concluded that higher generalization perfor-
mance can be obtained by using an optimization technique todetermine the optimal input weights and hidden biases.
To overcome the drawbacks of existing NN forecasting models, in
this paper, a hybrid intellige nt (HI) model comprising a data
preprocessing component and a HI f orecaster is developed to tackle
the sales forecasting problems in t he fashion retail supply chain. In
the HI forecaster, it will be the first time that a novel meta-heuristic
optimization technique, harmony search (HS) algorithm ( Mahdavi
et al., 2007 ), is integrated with ELM to construct a novel learning
algorithm to obtain optimal NN weights and achieve better NN
generalization performance. A heuristic fine-tuning process will also
be presented and used in the HI forecaster to further improve the
forecasting performance. The HI m odel will be able to effectively
handle the nonlinearity and irregularity of medium-term fashion
sales caused by various realistic factors in the dynamic fashion retail
supply chain, such as short product life cycles, volatile customer
demands and tremendous product varieties.
The rest of this paper is organized as follows. In Section 2, the
proposed HI model for medium-term fashion sales forecasting
is presented. Experimental design is presented in Section 3
concerning how numerical experiments are conducted to com-
pare the forecasting performances of the proposed model and
existing models. Section 4 presents and analyzes the experimental
results. Section 5 further discusses the forecasting performance of
the proposed model and its components based on extensive
experimental results. Finally, conclusions and future work are
described in Section 6.
2. Hybrid intelligent model for medium-term fashion sales
forecasting
The HI model is composed of a data preprocessing component
and a HI forecaster. Fig. 1 shows the framework of the HI model.W.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 615

The data preprocessing component involves three processes,
including detecting and removing outliers, interpolating missing
data and data normalization. The preprocessed historical sale data
are used as training samples of the HI forecaster generating the
final sales forecast. The details of the HI model are given in the
following sub-sections.
2.1. Data preprocessing
Data preprocessing has a significant impact on the perfor-
mance of supervised learning models ( Kotsiantis et al., 2006 )
because unreliable samples probably lead to wrong outputs.
Although fashion sales data are usually noisy and influenced by
various unpredictable external factors, previous studies in fashion
sales forecasting did not consider data preprocessing of sales data.
Effective data preprocessing methods are applied to avoid the
effects of noisy and unreliable data in this study.
In fashion retail market, time series of most item categories’
sales are of strong seasonality, such as knit short sleeves dress
(spring/summer) and coats (fall/winter). In this study, the same-
period time series are also used to observe the change trend of
fashion sales, which comprises the sales data only from the same
period of past years. Let si,jdenote the sales amount in jth month
ofith year. The following sequence represents the original
monthly time series Sfrom the first month of ith year to the
12th month of i+kth year,
si,1,si,2,… ,si,12 ,siț1,1,siț1,2,… ,siț1,12 ,:::,sițk,1,sițk,2,… ,sițk,12:
The time series Sinvolves 12 monthly same-period time
series. Let Sjdenote the same-period time series in jth month
ðj¼1,2,… ,12Ț.Sjcan be represented as follows:
si,j,siț1,j,… ,sițk,j:
2.1.1. Detecting and removing outliers
An outlier is an observation that deviates much from the rest
of observations so as to arouse suspicion that the outlier was
generated by a different mechanism. On the basis of extensive
analyses on historical sales data of different fashion item
categories, this study considers the observation si,jin the same-
period time series Sjof an item category as an outlier if it satisfies
the following condition:
absðsi,j/C0mean ðSjȚȚ4nUstdðSjȚ,
where mean (U) denotes the mean function, std(U) denotes the
standard deviation function and abs(U) denotes the absolute value
function. In this research, nis set to 3.
The outlier needs to be removed and then be handled as a
missing observation.2.1.2. Interpolating missing data
Incomplete data are an inevitable problem in handling most
real-world data sources. The missing data need to be interpolated
to keep the completeness and the change trend of time series. In
this study, the missing observation is filled in by using the mean
of its latest two neighboring data in its same-period time series.
2.1.3. Normalization and de-normalization
Data normalization can speed up training time of NNs by
starting the training process for each feature within the same
scale. The z-score normalization method ( Kotsiantis et al., 2006 )i s
adopted to normalize the input and output variables in this
research. Taking the same-period time series Sjas an example, its
normalized series S0
jis
Suj¼Sj/C0mean ðSjȚ
stdðSjȚ:
The de-normalization process is described as follows:
Sj¼mean ðSjȚțSujUstdðSjȚ:
2.2. Hybrid intelligent forecaster
After the sales time series are preprocessed, a HI forecaster is
applied to generate medium-term sales forecasts. The essential of
the HI forecaster is a novel learning algorithm-based NN
forecasting. The HS–ELM learning algorithm is developed to
improve NN generalization ability by integrating a HS algorithm
with ELM. In addition, it is known that the number of hidden
neurons has large effects on NN performances ( Zhang and Qi,
2005 ). To decrease the randomicity of NN outputs, the HI
forecaster considers the forecasting outputs of multiple NNs
with different number of hidden neurons. In the HI forecaster, the
HS–ELM-based NN firstly generate multiple forecasting outputs
by repeatedly running the network with different number of
hidden neurons from 1 to Nmax hl /C1Nmax hl denotes the maximum
number of hidden neurons. After the outputs of the proposed NNs
are de-normalized, a heuristic fine-tuning process is then used to
analyze these outputs and generate the final sales forecast. The
flow chart of the HI forecaster is shown in Fig. 2 , and its details are
described in the following sub-sections.
2.2.1. Extreme learning machine
The ELM is a novel learning algorithm for single-hidden-layer
feedforward NNs (SLFNs). Assume that SLFNs with Lhidden
neurons and activation function g(x) are trained to approximate N
Fig. 1. Framework of the hybrid intelligent model.
Fig. 2. Flow chart of the hybrid intelligent forecaster.W.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 616

distinct samples ( ui,yi) with zero error means, where uiis the
input of samples and ui¼½ui1,ui2,… ,uin/C138TARn;yiis the output of
samples and yi¼½yi1,yi2,… ,yim/C138TARm. In ELM-based NNs, the
input weights and hidden biases are generated randomly. The
nonlinear SLFNs can thus be converted into the following
relationship:
Hb¼T, ð1Ț
where H¼{hij}(i¼1,y,Nand j¼1,y,L) denotes the hidden-layer
output matrix, hij¼g(wjUui+bj) is the output of jth hidden neuron
with respect to ui;wj¼[wj1,wj2,y,wjn]Tis the weight vector
connecting jth hidden neuron and input neurons, and bjdenotes
the bias of jth hidden neuron; wjUuidenotes the inner product of
wjandui;b¼[b1,y,bj,y,bL]T(j¼1,y,L) is the matrix of output
weights and bj¼[bj1,bj2,y,bjm]Tdenotes the weight vector
connecting the jth hidden neuron and output neurons; Y¼[y1,
y2,y,yN]Tis the matrix of targets (desired outputs).
The determination of the output weights between the hidden
layer and the output layer is to find the least-square solution to
the given linear system. The minimum norm least-square (LS)
solution to the linear system (1) is
^b¼HyY,
where Hyis the Moore–Penrose generalized inverse of matrix H.
The minimum norm least-square solution is unique and has the
smallest norm among all the least-square solutions.
2.2.2. HS–ELM learning algorithm
In this study, the HS–ELM learning algorithm is developed to
train NNs, in which the improved HS algorithm ( Mahdavi et al.,
2007 ) is adopted to search for optimal input weights and hidden
biases of ELM instead of generating these weights and biases
randomly. HS algorithm is a newly developed meta-heuristic
technique, which generates a new vector (individual) by con-
sidering all existing vectors, whereas the traditional evolutionary
algorithm such as genetic algorithm (GA) only considers two
parental vectors. This distinct feature of HS algorithm increases
the algorithm’s flexibility so that the algorithm can generate
better solutions than conventional mathematical methods or GA-
based approaches do ( Lee and Geem, 2004; Mahdavi et al., 2007 ).
The following steps describe how the HS–ELM algorithm is
implemented.
Step 1: Initialize algorithm parameters.
The parameters related to the problem and HS algorithm need
to be specified in this step, which include the possible ranges
of values for all decision variables (input weights and hidden
biases), the number of decision variables ( P), the harmony
memory size ( HMS ), harmony memory consideration rate
(HMCR ), pitch adjustment rate ( PAR) and the number of
improvisations ( NI). The harmony memory (HM) and the
HMS are similar to the genetic pool and the population size in
the genetic algorithm, respectively. HMCR usually ranges
between 0.6 and 0.9 and PAR ranges between 0.1 and 0.5.
Step 2: Initialize the harmony memory.
The HM is generated randomly, in which each HM member
(solution vector), v, represents a distinct feasible solution of all
decision variables. That is, v¼[v1,v2,y,vP]. The decision
variables are composed of all input weights and hidden biases.
Step 3: Calculate output weights and fitness of each individual.
For each individual in the HM, the corresponding output
weights of the HS–ELM-based NN are analytically computedby Moore–Penrose generalized inverse ( Huang et al., 2004 ).
Based on the individual and its output weights, the fitness of
the individual is evaluated by comparing the sample output
and the NN output according to a specified error criterion(accuracy measure) such as root mean square error and mean
absolute percentage error.
Step 4: Improvise a new harmony.
After the fitness of all individuals in the population is
calculated, two HS procedures are used to improvise a new
harmony (generate a new solution vector). Generating a
new harmony is called improvisation. A new harmony,
v
0¼[v01,v02,y,v0P], is generated based on the following two
procedures:
(1)Memory consideration : The new variable value v0iis selected
from memory with probability HMCR or selected randomly
from the allowed value range with probability (1 /C0HMCR ):
vui’vuiAfv1
i,v2
i,… ,vHMS
igwith probability HMCR ,
vuiAVi with probability ð1/C0HMCR Ț:(
(2)Pitch adjustment : The decision variable obtained by the
memory consideration should be pitch-adjusted with prob-
ability PAR:
vui’vui¼vu17randbw with probability PAR ,
vui¼vu1 with probability ð1/C0PAR Ț,(
where bwis an arbitrary distance bandwidth and rand is a
random function generating a random number between 0
and 1. In this paper, the values of PAR and bware set
according to the methods presented by Mahdavi et al.
(2007) .
Step 5: For the solution vector newly generated, its corre-
sponding output weights and fitness are calculated by using
the methods described in Step 3.
Step 6: Update the harmony memory.
If the new solution vector is better than the worst vector in the
HM in terms of the objective function value (fitness), the new
vector is included in the HM and the existing worst harmony is
excluded from the HM. The HM is then sorted by the objective
function value.
Step 7: Check termination criterion.
The HS in this study is controlled by a specified number of
improvisations and a diversity measure. The diversity measure
is satisfied if a specified percentage PerHM of HM members is
the same in current generation. If either of the two termination
criteria is satisfied, the HS process is terminated. Otherwise,
repeat Steps 4–6.
The input of NNs usually use several latest sales in the existing
literature ( Au et al., 2008; Sun et al., 2008 ). The strong
nonlinearity and seasonality of sales data series increase the
complexity of fashion sales forecasting. Due to the seasonal
characteristic of fashion sales, this study attempts to investigate
fashion sales series from a new perspective. By analyzingextensively the change trends of monthly sales data, it can be
found that the patterns in its same-period time series are much
simpler than its original pattern if the original monthly time
series are of strong seasonality. In this research, for the monthly
time series with strong seasonality, we use their same-period
time series to forecast the next month’s sales amount. Further-
more, the output of the NN needs to be de-normalized since its
training samples are normalized data. The de-normalized output
is the initial sales forecast.
2.2.3. Heuristic fine-tuning process
The initial sales forecasts from the HS–ELM-based NNs with
different number of hidden neurons are transferred to the
heuristic fine-tuning process. The initial forecasts can be un-
reasonable because the NN may be overfitted. Let PN denote theW.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 617

set of percent changes of two neighboring values in a same-period
sales data series Sjand pfdenote the percent change of the
forecast of the series Sjto its latest same-period observation.
The initial forecast is considered as unreasonable if one of the
following conditions is met:
pf4max ðPNȚatpf40 and max ðPNȚ40,
pf4absðmin ðPNȚȚatpf40 and max ðPNȚo0,
absðpfȚ4max ðPNȚatpfo0 and min ðPNȚ40,
pfomin ðPNȚatpfo0 and min ðPNȚo0,
where max( U), min( U) and abs(U) are maximum, minimum and
absolute value functions, respectively. Lastly, all the reasonable
initial forecasts are averaged as the final sales forecast.
3. Experimental design
To evaluate the performance of the proposed forecasting
model, extensive experiments were conducted in terms of real
fashion sales data, which forecast the total sales amounts of
various item categories and cities on a monthly, quarterly or
annual basis.
3.1. Fashion sales data
Real sales data were collected from one of the largest fashion
retail companies selling medium-priced fashion products in
Mainland China, which include monthly sales data of different
cities and different item categories of each city from 01/1999 to
12/2006. The data from last 2 years are out-of-sample data used
to compare and evaluate the accuracy of forecasting models. For
each out-of-sample observation, its previous sales data are used
as training samples to set the forecasting model for making one-
step-ahead forecast.
3.2. Parameter setting for proposed model
Table 1 shows the parameters of the proposed model for
experiments presented in this paper, in which Ninlay denotes the
number of input neurons and Nmax hl denotes the maximum
number of hidden neurons; PAR min and PAR max denote the
minimum and the maximum of PAR, and bwmin and bwmax
denote the minimum and the maximum of bw. Columns 2 and 3
show the parameters for monthly forecasting of one or all
categories of a city, respectively, while columns 3 and 4 showthe parameters for quarterly and annual forecasting, respectively.
The activation function g(x) of NN is the sigmoidal function, i.e.,
g(x)¼1/1+ e/C0x. In this paper, the monthly forecasting of each
fashion item category is fulfilled by using its same-period time
series, whereas others are fulfilled by using their original time
series directly.
3.3. Forecasting models used for comparison and their parameters
The forecasting performance of the proposed model is
compared with that of 6 different models, including the ELME
model proposed by Sun et al. (2008) , ENN model proposed by Au
et al. (2008) , ARIMA( p,d,q) model, AR( p) model, and AR2 model.
The AR2 model is the same as the AR( p) model except using
different time series forms. The first four models use original time
series while the last one uses the same-period series. The
parameters of these models for different medium-term forecast-
ing problems are shown in Table 2 . For annual forecasting, the AR
model is the same as the AR2 model, and the ARIMA model is not
applicable because the available sample data are insufficient toestimate this model. The other parameters of the first two NN
models are the same as the corresponding parameter setting in
Sun et al. (2008) and Au et al. (2008) .
3.4. Accuracy measures
No accuracy measure is generally applicable to all forecasting
problems due to various forecasting objectives and data scales ( De
Gooijer and Hyndman, 2006; Hyndman and Koehler, 2006 ). Let Y
t
denote the observation at time tand Ftdenote the forecast of Yt.
Then define the forecast error et¼Yt/C0Ft. In this paper, the
following three measures of forecast accuracy are adopted to
calculate the fitness of each solution vector of the HI forecaster:
(1) Root mean square error ( RMSE ):RMSE is popular and often
chosen by practitioners because of its ease of use and its
theoretical relevance in statistical modeling. RMSE is ex-
pressed as follows:
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
mean ðe2Țq
:
(2) Mean absolute percentage error ( MAPE ): This criterion is less
sensitive to large errors than RMSE and can be expressed as
MAPE ¼mean100et
Yt/C18/C19
:
(3) Mean absolute scaled error ( MASE ): To overcome the draw-
backs of existing measures, Hyndman and Koehler (2006)
proposed MASE as the standard measure for comparing
forecast accuracy across multiple time series after comparing
various accuracy measures for univariate time seriesTable 1
Parameters of hybrid intelligent models used in experiments.
Medium-term forecasting
Monthly Quarterly Annual
One category One citya
Ninlay 21 2 4 2
Nmax hl 10 50 15 10
HMCR 0.95 0.95 0.95 0.95
PAR min 0.45 0.45 0.45 0.45
PAR max 0.99 0.99 0.99 0.99
HMS 30 100 50 30bw
min 1e-6 1e-6 1e-6 1e-6
bwmax 44 4 4
NI 1000 10,000 5000 1000
PerHM (%) 90 90 90 90
aOne city means all item categories of a city.Table 2
Parameters of different models used in experiments.
Medium-term forecasting
Monthly Quarterly Annual
ELME model Ninlay 12 4 2
Nmax hl 50 15 10
ENN model Ninlay 12 4 2
ARIMA ( p,d,q) (12, 0, 12) (4, 0, 4) –
AR p 12 4 3
AR2 p 33 –W.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 618

forecasting. MASE is expressed as follows:
MASE ¼meanet
ð1=n/C01ȚPn
i¼29Yi/C0Yi/C019/C12/C12/C12/C12/C12/C12/C12/C12/C12/C12 !
:
MASE is less than one if it arises from a better forecast than the
average one-step Naı ¨veforecast computed in-sample. The Naı ¨ve
model uses directly the last observation of the time series as the
forecast. Conversely, it is greater than one if the forecast is worse
than the average one-step Naı ¨ve forecast computed in-sample.
4. Experimental results and analysis
This section presents experimental results of 3 experiments,
which make monthly, quarterly and annual forecasting, respec-
tively. In each experiment, the sales amounts of the same 4 cities
and 4 fashion item categories are forecasted, respectively. The
cities selected are the most important 4 ones for the company’s
business. The 4 categories are skirts (spring/summer), jackets(spring/summer), coats (fall/winter) and pants (fall/winter). Their
sales are from a same city, which are of strong seasonality and
have more significant influences on the company’s business than
other categories do.
4.1. Experiment 1: monthly forecasting
The monthly time series of category 1 and city 1’s sales are
shown in Figs. 3 and 4, respectively, in which the last 24
observations from the last 2 years are out-of-sample data for
model comparison. It is clear that the time series of category 1 has
stronger seasonality and less randomicity than city 1’s. The
comparison of actual sales and out-of-sample forecasts of
category 1 and city 1, generated by the proposed model, are
shown in Figs. 5 and 6. Due to space limitations, this paper does
not present the figures of actual sales and forecasting results of
other categories and cities.
The comparison of forecasting results of the proposed model
and 5 other models is shown in Tables 3–5. Taking category 1 as
an example, the proposed model produces smaller RMSE ,MAPE
Fig. 3. Monthly time series of category 1’s sales (01/1999–12/2006).
Fig. 4. Monthly time series of city 1’s sales (01/1999–12/2006).W.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 619

and MASE , which shows that the proposed model generates better
results whichever accuracy measure is used. For other categories
and cities, the RMSE ,MAPE and MASE generated by the proposed
model are usually the minimum value or very close to theminimum value. It is clear that the proposed model exhibits much
better monthly forecasting performance than other models
whichever accuracy measure is used.
4.2. Experiment 2: quarterly forecasting
Figs. 7 and 8 show the quarterly time series of category 1 and
city 1’s sales and their forecasting results generated by the
proposed model. The change trends of forecasts generated by the
proposed model and the real data are consistent as shown in Fig. 7
but quite different as seen in Fig. 8 . This is because the quarterly
time series of category 1 are regular and strongly periodic whilethe time series of city 1 is irregular and almost random. For
instance, the 25 and 26 observations in Fig. 8 deviate markedly
from their historical data. Their forecasts do not match the real
data very well because no univariate time series forecasting
model can foresee these abnormal sudden changes.
The comparison of quarterly forecasting results of the
proposed model and 5 other models is shown in Tables 6–8. For
all forecasting cases except category 2, the RMSE ,MAPE and MASE
generated by the proposed model are the minimum value or very
close to the minimum value. For category 2, the forecasts
generated by the proposed model are superior to two NN
models and ARIMA model but inferior to two AR models. On the
whole, similar to the monthly forecasting results, the proposed
model provides more accurate quarterly forecasting than other
models do.
4.3. Experiment 3: annual forecasting
The annual time series are strongly nonlinear and much
irregular due to various uncertainties in fashion retailing. Fig. 9
shows the annual sales series of category 1 and city 1 and their
forecasting results generated by the proposed model.
It is very difficult to predict these irregular annual time series,
especially when the sample data are insufficient. The comparison
of annual forecasting results generated by the proposed model
and 3 other models is shown in Tables 9–11. It can be easily found
from Tables 9–11 that, on the whole, the proposed model also
exhibits superior performance over other models although the
superiority is not as prominent as that in experiments 1 and 2. In
this experiment, the AR model and the ENN model provide better
forecasting results in several cases. That is because NN models are
prone to being over-parameterized when training samples are
insufficient and the limited samples are not enough to model the
strong nonlinearity of annual sales series.
5. Discussion
This section presents an in-dept h discussion on the forecasting
performance of the proposed HI model. The forecasting performance
Fig. 5. Monthly forecasting result generated by the proposed model (category 1).
Fig. 6. Monthly forecasting result generated by the proposed model (city 1).
Table 3
Comparison of monthly forecasting results (category 1 and city 1).
Category 1 City 1
RMSE MAPE (%) MASE RMSE MAPE (%) MASE
Proposed model 2.6E+06 19.3 0.30 3.9E+06 14.6 0.58
ELME model 3.5E+06 79.2 0.39 3.9E+06 15.3 0.58ENN model 2.8E+06 57.6 0.32 5.4E+06 24.8 0.91ARIMA 3.2E+06 31.8 0.35 7.4E+06 27.5 1.07AR 2.6E+06 36.9 0.31 4.9E+06 17.2 0.67AR2 3.4E+06 26.2 0.37 5.8E+06 22.6 0.91
Table 4
Comparison of monthly forecasting results (categories 2–4).
Category 2 Category 3 Category4
RMSE MAPE (%) MASE RMSE MAPE (%) MASE RMSE MAPE (%) MASE
Proposed model 2.8E+06 25.6 0.50 1.7E+06 37.0 0.58 1.5E+06 58.1 0.46
ELME model 2.4E+06 78.0 0.46 2.4E+06 86.3 0.81 2.6E+06 5209.9 1.15ENN model 2.5E+06 48.6 0.48 2.1E+06 55.4 0.71 2.9E+06 3464.8 1.14ARIMA 2.2E+06 38.1 0.39 1.9E+06 35.5 0.54 2.7E+06 6665.4 0.92
AR 2.2E+06 32.7 0.41 1.9E+06 41.3 0.56 1.6E+06 582.9 0.49
AR2 3.0E+06 31.5 0.53 2.7E+06 53.4 0.79 2.1E+06 84.0 0.64W.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 620

of the proposed HI model is analyzed firstly based on the
experimental results presented in Section 4. Further analysis is then
conducted to validate the superiority of the proposed model over
other models based on public benchmark datasets. The effectiveness
of the model’s components, including heuristic fine-tuning process,
data preprocessing component and HI forecaster, are also analyzed
in this section.
5.1. Performance comparison and analysis
Based on the above three experiments presented in Section 4,
Fig. 10 further shows the comparison of forecasting performances
generated by different models, in which each bar indicates the
number of best forecasts generated by its corresponding model in
terms of a specified accuracy measure. For instance, the proposed
HI model generates the best forecasting performance for 14
forecasting cases when RMSE is used as the accuracy measure. It
is proved that the proposed model is able to provide much superior
forecasting performances to other models. Its superiority would be
more obvious if we did not consider the results of Experiment 3 in
which insufficient sample data probably weaken its performance.
The proposed model uses a heuristic fine-tuning process to
eliminate unreasonable forecasts, and the experimental results
indicate that this is helpful to improve forecasting performance.
Actually, for some forecasting cases in the experiments (e.g., the
monthly forecasting of 4 categories), the MAPE s generated by
ELME and ENN models are much greater than the MAPE s
generated by traditional models. These abnormally large MAPE s
are caused by unreasonable forecasts. The experimental results
also revealed that different accuracy measures have effects on
forecasting performance. For instance, for the monthly forecasting
of category 2, the proposed model generates minimal MAPE but
almost maximal RMSE and MASE . Therefore, it is important to
select appropriate accuracy measures in practice.
5.2. Further analysis on forecasting performance of proposed model
It can be found from the experimental results of Section 4 that
for the proposed HI model, the ENN model and the AR model are
two major competitive ones especially when annual forecasting
was conducted. To further compare the annual forecasting
performance of the HI model and the two models, we made
comprehensive simulation studies using public benchmark
datasets with sufficient sample data. This paper presents the
forecasting results of 7 set of irregular annual time series from the
well-known forecasting competition ( Makridakis and Hibon,
2000 ). These time series included 4 industry datasets with 33
observations (series N188–N191) and 3 finance datasets with 28
observations (series N359–N361), which were all irregular ones
without seasonality. Each time series contained one or more
outliers. The last 6 observations of each time series were used as
out-of-sample data to compare the forecasting models.Table 5
Comparison of monthly forecasting results (cities 2–4).
City 2 City 3 City 4
RMSE MAPE (%) MASE RMSE MAPE (%) MASE RMSE MAPE (%) MASE
Proposed model 1.8E+07 17.7 0.93 6.8E+06 15.2 1.12 5.3E+06 15.5 0.54
ELME model 1.8E+07 17.2 0.88 8.0E+06 19.9 1.39 6.1E+06 17.7 0.63ENN model 2.2E+07 17.6 0.97 7.6E+06 16.5 1.27 6.6E+06 21.4 0.73
ARIMA 2.1E+07 25.1 1.11 7.6E+06 19.5 1.37 7.4E+06 24.0 0.85
AR 2.0E+07 19.0 0.95 7.0E+06 15.4 1.14 6.2E+06 16.5 0.60AR2 2.1E+07 20.5 1.03 1.0E+07 26.1 1.88 7.6E+06 19.6 0.74
Fig. 7. Quarterly forecasting result generated by the proposed model (category 1).
Fig. 8. Quarterly forecasting result generated by the proposed model (city 1).
Table 6
Comparison of quarterly forecasting results (category 1 and city 1).
Category 1 City 1
RMSE MAPE (%) MASE RMSE MAPE (%) MASE
Proposed system 4.4E+06 11.9 0.07 7.7E+06 11.0 0.62
ELME model 6.0E+06 14.8 0.09 1.0E+07 15.1 0.85ENN model 5.1E+06 14.3 0.09 9.0E+06 12.1 0.67ARIMA 1.0E+07 15.3 0.16 1.1E+07 15.5 0.93
AR 5.4E+06 8.7 0.08 7.8E+06 11.2 0.65
AR2 5.2E+06 15.9 0.09 8.2E+06 11.7 0.69W.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 621

Table 12 shows the annual forecasting results of the 7 datasets
based on the proposed HI model, the HI forecaster, the ENN model
and the AR model. The HI forecaster is same as the HI modelexcept that it does not contain the data preprocessing component.
The parameter settings of these models were the same with
those described in Section 3. It can be easily found from Table 12Table 7
Comparison of quarterly forecasting results (categories 2–4).
Category 2 Category 3 Category 4
RMSE MAPE (%) MASE RMSE MAPE (%) MASE RMSE MAPE (%) MASE
Proposed model 5.5E+06 17.2 0.15 3.1E+06 15.1 0.13 1.9E+06 16.2 0.13
ELME model 7.3E+06 20.9 0.20 3.6E+06 23.3 0.23 9.0E+06 140.7 0.38ENN model 6.8E+06 20.3 0.19 2.2E+06 14.4 0.16 6.0E+06 232.1 0.32
ARIMA 5.8E+08 27.2 0.16 3.9E+06 20.2 0.25 4.2E+06 40.5 0.24
AR 4.4E+06 9.9 0.10 3.2E+06 25.2 0.23 4.1E+06 18.0 0.19AR2 5.2E+06 10.2 0.12 4.0E+06 34.1 0.28 5.5E+06 34.6 0.22
Table 8Comparison of quarterly forecasting results (cities 2–4).
City 2 City 3 City 4
RMSE MAPE (%) MASE RMSE MAPE (%) MASE RMSE MAPE (%) MASE
Proposed model 2.8E+07 9.4 0.66 1.1E+07 10.7 1.07 8.3E+06 9.4 0.45
ELME model 3.6E+07 13.5 0.94 1.5E+07 14.0 1.54 1.4E+07 12.1 0.62ENN model 3.3E+07 11.1 0.79 1.1E+07 10.6 1.16 8.5E+06 9.0 0.41ARIMA 2.1E+07 7.6 0.51 1.3E+07 13.9 1.45 1.0E+07 10.2 0.53AR 3.0E+07 10.4 0.74 1.2E+07 11.5 1.28 7.0E+06 8.0 0.38AR2 3.9E+07 14.7 1.03 1.3E+07 11.0 1.21 1.2E+07 13.8 0.64
Fig. 9. Annual forecasting result generated by the proposed model (category 1 and city 1).
Table 9
Comparison of annual forecasting results (category 1 and city 1).
Category 1 City 1
RMSE MAPE (%) MASE RMSE MAPE (%) MASE
Proposed model 1.2E+07 6.5 0.65 2.8E+07 10.4 1.53
ELME model 4.5E+07 21.4 2.27 8.1E+07 23.8 3.65ENN model 5.0E+06 2.3 0.25 3.8E+07 15.9 2.39AR 1.2E+07 6.2 0.66 3.2E+07 10.6 1.57W.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 622

that, for each time series, the HI model generate much better
forecasts than ENN and AR models do. This indicates that, for the
annual time series with sufficient samples, the HI model can
demonstrate much better performance. The HI forecaster also
yields much superior performance over the ENN and AR
models on the whole, which means that the proposed HS–ELM
learning algorithm is capable of obtaining good generalization
performance. Moreover, the performance generated by the HI
model is much superior to that generated by the HI forecaster. It
implies that the data preprocessing component in the HI model is
helpful to improve the forecasting performance since the HI
forecaster can be considered as a HI model without data
preprocessing component. That is, the data preprocessing
component is able to tackle outliers and missing data well so
that the forecasting performance generated by the HI model can
be improved.
According to the forecasting results based on real fashion retail
data and benchmark data from M3 competition, it can be
concluded that the proposed model is widely applicable since
it is capable of generating accurate forecasts for a variety of
time series with irregular patterns as well as strong seasonal
patterns.6. Conclusions
This paper investigates the medium-term sales forecasting
problem based on the real forecasting process in fashion retailing,
which is helpful for fashion retail enterprises to facilitate
medium-term sales forecasting and thus improve the perfor-
mance and efficiency of fashion retail supply chain.
An effective HI model was developed to deal with the
investigated problem, in which a data preprocessing component
and a HI forecaster were presented. The data preprocessing
component is used to detect and remove outliers, interpolate
missing data and normalize sample data. The HI forecaster firstly
generates multiple initial forecasts by HS–ELM learning algo-
rithm-based NNs integrating an improved HS algorithm with an
ELM algorithm, and then uses a heuristic fine-tuning process to
generate the final sales forecasts based on the initial forecasts. The
data preprocessing component, the HS–ELM learning algorithm
and the heuristic fine-tuning process introduced in this paper are
helpful to improve forecasting performance from different
perspectives. The data preprocessing component conduces to
bring more reliable training samples. The HS–ELM learning
algorithm can conduce to the improvement of NN generalization
ability while the fine-tuning process can further improve forecast
accuracy by eliminating unreasonable initial forecasts and
averaging multiple NN forecasts.
Extensive experiments were conducted to validate the pro-
posed HI model in terms of real fashion retail data. The
experimental results have shown that the HI model can tacklethe medium-term sales forecasting problem effectively, which
also demonstrates that the proposed model can provide much
superior performance over traditional ARIMA models and two
recently developed sales forecasting NN models. Further experi-
ment was presented based on 7 irregular annual datasets from M3
competition, which further validates the effectiveness of the
proposed HI model and shows that the HI model is more powerful
to tackle the time series with sufficient sample data. Furthermore,
since the time series tackled in this paper involves various
patterns such as irregularity and seasonality, the proposed model
is widely applicable and can be easily extended to solve other
forecasting problems with similar time series patterns.
The proposed model provides forecasts only based on
historical sales data, which cannot reflect the effects of exogenousTable 10
Comparison of annual forecasting results (categories 2–4).
Category 2 Category 3 Category 4
RMSE MAPE (%) MASE RMSE MAPE (%) MASE RMSE MAPE (%) MASE
Proposed model 1.7E+07 11.1 1.21 4.1E+06 7.0 0.57 1.4E+07 24.9 3.03
ELME model 3.3E+07 22.2 2.42 1.8E+07 31.4 2.54 3.5E+07 61.2 7.44ENN model 2.1E+07 14.0 1.53 2.5E+06 4.3 0.35 1.6E+07 28.1 3.41
AR 1.2E+07 7.7 0.84 4.5E+06 7.7 0.62 1.5E+07 26.9 3.27
Table 11
Comparison of annual forecasting results (cities 2–4).
City 2 City 3 City 4
RMSE MAPE (%) MASE RMSE MAPE (%) MASE RMSE MAPE (%) MASE
Proposed model 1.4E+08 13.5 1.87 4.4E+07 12.7 1.58 2.1E+07 4.8 0.60
ELME model 1.7E+08 16.3 2.26 6.7E+07 18.0 3.43 4.1E+08 101.0 17.13ENN model 1.4E+08 13.9 1.93 9.5E+07 27.1 5.46 3.7E+07 10.9 1.86AR 1.2E+08 13.7 1.84 3.6E+07 10.6 1.31 4.5E+07 13.9 1.76
Fig. 10. Comparison of forecasting performance of different models.W.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 623

factors, such as weather and economic indexes, on fashion sales.
Future research will focus on investigating multivariate HI
forecasting models considering the effects of various exogenous
changes on fashion sales. Moreover, it is also a worthwhile
research direction to explore effective intelligent model for short-
term sales forecasting on the basis of the findings in this research.
Acknowledgement
The authors would like to thank The Hong Kong Polytechnic
University for the financial support in this research project
(Project no. A-PA9R).
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Comparison of annual forecasting results (benchmark datasets).
Time series Proposed model HI forecaster ENN AR
RMSE MAPE MASE RMSE MAPE MASE RMSE MAPE MASE RMSE MAPE MASE
N188 1182 0.16 6.55 1499 0.20 8.88 1876 0.26 11.14 1147 0.16 6.88
N189 1514 0.12 3.65 1551 0.12 3.69 2534 0.17 5.33 1952 0.13 4.21
N190 606 0.06 1.97 727 0.09 2.70 760 0.09 2.87 772 0.11 3.37
N191 1553 0.13 3.24 1773 0.16 3.86 1674 0.15 3.84 1847 0.14 3.37
N359 3485 0.30 2.88 3491 0.33 2.98 3626 0.33 2.94 3973 0.42 3.66
N360 3643 0.59 5.73 3925 0.67 6.02 4626 0.60 6.74 3701 0.73 6.16
N361 2240 0.41 2.99 2280 0.50 3.26 2409 0.54 3.38 3071 0.78 5.02W.K. Wong, Z.X. Guo / Int. J. Production Economics 128 (2010) 614–624 624