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Decision Support Systems 55 (2013) 247–255

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Decision Support Systems

j ourna l homepage: www.e lsev ie r .com/ locate /dss

A multivariate intelligent decision-making model for retail sales forecasting

Z.X. Guo a,⁎, W.K. Wong b, Min Li b

a Business School, Sichuan University, Chengdu 610065, PR China b Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, China

⁎ Corresponding author. Tel.: +86 28 85417867; fax: E-mail addresses: zx.guo@alumni.polyu.edu.hk (Z.X.

tcwongca@inet.polyu.edu.hk (W.K. Wong), 11900185r@

0167-9236/$ – see front matter © 2013 Elsevier B.V. All http://dx.doi.org/10.1016/j.dss.2013.01.026

a b s t r a c t

a r t i c l e i n f o

Article history: Received 11 August 2011 Received in revised form 28 August 2012 Accepted 21 January 2013 Available online 12 February 2013

Keywords: Retail industry Early sales Sales forecasting Multivariate forecasting

A sales forecasting problem in the retail industry is addressed based on early sales. An effective multivariate in- telligent decision-making (MID)model is developed to provide effective forecasts for this problemby integrating a data preparation and preprocessing module, a harmony search-wrapper-based variable selection (HWVS) module and a multivariate intelligent forecaster (MIF) module. The HWVS module selects out the optimal input variable subset from given candidate inputs as the inputs of MIF. The MIF is established to model the rela- tionship between the selected input variables and the sales volumes of retail products, and then utilized to fore- cast the sales volumes of retail products. Extensive experiments were conducted to validate the proposed MID model in terms of extensive typical sales datasets from real-world retail industry. Experimental results show that it is statistically significant that the proposed MID model can generate much better forecasts than extreme learning machine-based model and generalized linear model do.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Retail sales forecasting is estimating the future demand of a retail product, which is essential to sound business planning [1] and is playing a more andmore prominent role in dynamic supply chain fac- ing the ever-intensifying global competition [33]. Sales forecasting is the foundation on which company plans are built [20], which is es- sential to improve a retail company's competition capacity [11]. This paper addresses a multivariate sales forecasting problem, which fore- casts the overall sales of a retail product based on its early sales volume.

1.1. Sales forecasting

The history of sales forecasting can be traced back to more than 50 years ago [1,32]. Since then a large number of sales forecasting pa- pers have been published [4,5,21,24,32,33], which involves a wide va- riety of applications in real-world industries, such as print circuit board industry [4], food industry [5] and apparel industry [14].

Some researchers investigated the sales forecasting problemby con- sidering it as univariate time series forecasting problems [23,33]. Their studies utilized input data directly from the historical sales data of time series being forecasted, which are usually based on a basic as- sumption that the underlying data-generating process of the time series is constant. This assumption is usually invalid in real world since a vari- ety of factors influencing product sales, called influencing factors, may

+86 28 85415628. Guo), connect.polyu.hk (M. Li).

rights reserved.

cause the uncertain change of data pattern, particularly in a dynamic and quick response business environment such as apparel and footwear industry. As a result, the univariate forecasting model cannot handle sudden changes caused by various influencing factors such as product attributes and economic environment.

To handle this, some researchers integrated the sales forecasting problem by using multivariate inputs including historical sales and related influencing factors [4,5]. Chang et al. [4] addressed the month- ly sales forecasting problem to help printed circuit board companies generate effective customer demand forecasts by considering indexes from 4 different domains such as macroeconomic and industry pro- duction ones. Chen and Ou [5] investigated a perishable food forecast- ing problem with the consideration of sales data of target store and neighboring stores as well as weather data. In the multivariate sales forecasting literature, a limited number of influencing factors are con- sidered due to reasons such as data unavailability, which perhaps omits important factors and thus weakens forecasting performance.

Although the multivariate forecasting model has potential and ad- vantage to effectively model the relation between sales data and var- ious influencing factors, its real-world application is constrained by some issues: (1) a large number of influencing factors can influence sales, however it is hard to identify the relationships between these factors and final sales and (2) it is usual that there are not sufficient historical data especially when lots of influencing factors are consid- ered or the sales of a new product is forecasted.

In the existing literature,most studies dealtwith sales forecasting on the basis of historical sales data of products to be forecasted. To forecast the overall sales of new retail productswithout directly available histor- ical sales data, previous studies usually considered the historical sales of their similar products [7,30,31]. Thomassey and Fiordaliso [30] also

Data preparation and preprocessing

HS-wrapper- based variable

selection

Modelling multi- variate intelligent

forecaster

Optimal input variable subset

Multivariate intelligent forecaster

Test data Final forecast of sales volume

T ra

in in

g da

ta

Fig. 1. Architecture of the MID model.

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investigated the effects of 3 variables (item price, the starting time of the sales and the life span of items) on final sales. However, it is hard to identify which past products are similar in forecasting process in in- dustrieswith large product variety and frequent product changes. These studies also cannot handle future sudden changes caused by influencing factors.

It is commonly accepted among retailers that the early sales of a re- tail product is an excellent indicator of its overall sales [12]. However, little attention has been paid in utilizing early sales to forecast overall sales of retail products so far. The only one work foundwas conducted by Tanaka [27], which performed long-term sales forecasting based on the early sales and the correlations between short- and long-term ac- cumulated sales within similar products groups. In his work, the fore- casting accuracy largely relied on the selection of reference group, which were determined by expert knowledge and thus subjective and probably unreliable. In addition, Tanaka's work has not consid- ered the effects of various influencing factors on overall sales, which thus could not handle sales changes caused by these factors such as production attributes and promotion strategy.

In this research, we will aim at addressing a sales forecasting prob- lem for retail products based on their early sales, called early sales- based sales forecasting problem, which forecast the overall sales vol- ume of a retail product in a selling season in terms of its early sales with the consideration of a variety of influencing factors instead of using the historical sales data of its similar products. The influencing factors include promotion strategy, product attributes (such as selling price, product type andmaterial type), early sales volumes, various eco- nomic indices, climate index, etc. The effects of economic factors can be reflected by various economic indices such as consumer confidence index (CCI), consumer price index (CPI) and gross domestic product (GDP). However, it keeps unknown if and how these factors influence the overall sales volumes of retail products. Among these influencing factors, some may be redundant or even irrelevant to the overall sales, which will detract the accuracy of forecasting model and increase its complexity and computational burden. To the best of our knowledge, it is the first paper that investigates the effects of various influencing factors on overall sales of retail products, and the relations between these factors and overall sales. This research can forecast overall sales of a retail product no matter whether the product has available histori- cal sales data of its similar products.

1.2. Techniques for sales forecasting

Techniques for time series forecasting have been widely applied to sales forecasting since most of existing sales forecasting studies were based on the concept of time series. Existing techniques for time series forecasting are generally divided into two groups: classical techniques based on mathematical and statistical models and artificial intelligence techniques. Classical techniques used include exponential smoothing [13,29], autoregressive moving average (ARIMA) methods [8,23], Kalman filter methods [17,35], and so on. Artificial intelligence tech- niques used include expert systems [21,25], fuzzy systems [24], neural network (NN)models [3–5], and hybridmodels integratingmultiple in- telligent techniques [30,33].

These classical techniques cannot be used for the modeling of non- time series. However, the sales forecasting problem investigated in this paper does not use time series of historical sales. The classical tech- niques thus cannot be used for the investigated problem. Among artifi- cial intelligence techniques, the NN model was the most commonly used one, which has been proved to be universal approximators and can effectivelymodel various time series and non-time series. A number of studies also demonstrate that the NN approach outperforms the clas- sical models due to its capacity of nonlinearity, generalization and uni- versal function approximation [2,8,28].

In recent years, a novel NN, extreme learning machine (ELM), has attracted more and more attentions from forecasting researchers

due to its feature of easy to use and fast learning speed [6,26]. The ELM can avoid many difficulties faced by traditional NN learning algo- rithms, such as the selections of stopping criteria, learning rate, and learning epochs because of its distinct learning mechanism. On the basis of ELM, Wong and Guo [33] recently developed an effective hy- brid intelligence model to provide effective and reliable forecasts for fashion sales series characterized by nonlinearity, seasonality or irreg- ularity, which utilized harmony search (HS) to improve the generali- zation and forecasting performance of the ELM, and utilized a fine- tuning process to further improve forecasting accuracy. Their model can outperform ARIMA models and an evolving NN-based forecasting model and an ELM-based model proposed by Sun et al. [26].

In this research, a multivariate intelligent decision-making (MID) model is developed to dealwith the investigated sales forecasting prob- lembased on the hybrid intelligencemodel proposed byWong andGuo [33]. To decrease the side effects of irrelevant and redundant inputs and the large computational complexity caused by too many input vari- ables, a novel variable selectionmethod, HS-wrapper-based variable se- lection, is developed in the MID model to select out an appropriate input variable subset from a large number of input variables and ex- plore the relations between overall sales of a retail product and its early sales as well as various influencing factors.

The remainder of this paper is organized as follows. In Section 2, the proposed MID model for the investigated sales forecasting prob- lem is presented. Experimental design and results are presented in Section 3. Section 4 further analyzes and discusses the experimental results and the performance and effectiveness of the proposed model. Finally, conclusions and future work are described in Section 5.

2. Multivariate intelligent decision-making model for sales forecasting

This research considers the early sales of a retail product and var- ious influencing factors as candidate input variables and assumes that there are m input variables in total and n pairs of multi-input– single-output (MISO) samples data are given. Let Xi; yið Þ denotes the ith input/output data pair (1≤ i≤n).

To forecast the overall sales of a retail product in a selling season on the basis of its early sales, this research firstly identifies the relation- ships between m input variables (xi1,xi2,⋯,xim) of Xi and the overall sales volume yi and selecting out an appropriate subset of input vari- ables from Xi as the valid inputs, and then establishes an effective model to approximate these relationships in terms of n given samples data. Lastly, the established model is utilized to forecast the sales vol- umes of other retail products on the basis of their early sales and relat- ed input variables. A multivariate intelligent decision-making (MID) model is developed to implement the said processes.

Fig. 1 shows the architecture of the proposed MID model, which is composed of 3modules, including a data preparation and preprocessing (DPP) module, a HS-wrapper-based variable selection (HWVS) module and amultivariate intelligent forecaster (MIF)module. The DPPmodule extracts sales data of past products from the point-of-sales database of retailers, and then preprocesses these data for the development and validation of theMIDmodel. The HWVSmodule selects out the optimal

Step 1.Initialize algorithm parameters

Stop

Step 2. Initialize the harmony memory

Step 7. Meet stopping criteria?

Step 3. Calculate the objective function value of each harmony

in terms of cross-validation

Yes

Step 4. Improvise a new harmony

Step 5. Calculate the objective function value of the new harmony

in terms of cross-validation

Step 6. Update the harmony memory

Obtain the best harmony as the optimal input variable subset

No

Fig. 2. Flowchart of the HWVS module.

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input variable subset from given candidate input variables for pruning redundant and irrelevant ones and providing a better understanding on the inherent characteristic of sales data. The selected input variable subset is then used to establish the MIF for modeling the relationship between the selected input variables and the sales volumes of retail products. Lastly, the established MIF is utilized to forecast the overall sales volumes of retail products.

2.1. Data preparation and preprocessing

A large variety of influencing factors can affect the overall sales vol- ume of a retail product in a selling season. The following influencing fac- tors are considered as candidate input variables for further extracting the optimal input variable subset.

1) Original selling price: It represents the original selling price of the retail product.

2) Style type: It indicates the type of styles of retail products, such as trouser, T-shirt and coat.

3) Material type: It indicates the type ofmaterials for retail products, such as leather, nylon and polyester.

4) Promotion strategy: Different promotion strategies have effects on sales volumes of retail products. This research classifies these strategies into A, B, and C categories, which represent the very high, high, and medium degrees respectively at which the strate- gies can improve sales volumes.

5) Shop quantity: It indicates the number of retail shops that sell the forecasted product.

6) Release date: It indicates which date a retail product starts to be sold in the market. Its value indicates which day it is in a year.

7) Life span: It indicates howmany days a retail product is sold in the market.

8) Early sales volumes: It is unclear that how the early sales volume affects the overall sales so far. This research regards the accumu- lated sales volumes within the first 3, 7, 10 and 14 days as 4 can- didate input variables.

9) Climate index: It indicates the average temperature of the coming next selling season counting from the release date. Retail prod- ucts with different release dates have different climate indices.

10) Economic indices: Various available indices reflecting economic performances, including CCI, CPI, GDP, producer price index (PPI), total retail sales index and price index for ‘clothing and footwear’, are considered as candidate input variables. The value of each eco- nomic index takes the average of the index values from its latest 6 months.

To forecast the sales volume of a retail product in a whole selling season, the training samples used need to satisfy the conditions: (1) the life span of each selected retail product should be around a whole selling season; and (2) the average selling prices of retail products could not be much lower than their original selling prices.

Among the candidate input variables described above, some are qualitative ones, including style type, material type and promotion strategy, which need to be changed firstly to numeric variables for the development of forecasting model. This research uses numeric values to replace the values of each qualitative variable. For example, we use 0, 1 and 2 to replace the 3 categories of promotion strategies, A, B and C.

Data preprocessing has significant effects on the performance of supervised learning models [19] because unreliable training samples probably lead to wrongmodel parameters. Incomplete data is an inev- itable 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. The missing observation is filled in by using the mean of its latest two neighboring data in its time series. In addition, data normalization can speed up the training time of NNs by starting the training process for each feature within the same scale. The

z-score normalization method [19] is adopted to normalize the input and output variables. The preprocessed data are used as training and test samples of variable selection and MIF modules.

2.2. HS-Wrapper-based variable selection

It is crucial to find out the optimal variable subset from all candidate input variables because redundant or even irrelevant input variables probably decrease the accuracy of forecasting model and increase its complexity and computational burden. A variety of variable selection approaches have been developed [15], mainly including filter approach, embedded approach and wrapper approach. The wrapper approach [18] is employed to develop the HWVSmodule for selecting out the op- timal input variable subset because the wrapper approach utilizes learning machine as a black box to score different variable subsets according to their modeling performance, which is regardless of the chosen learningmachine. To implement thewrapper approach, 3 issues need to be defined, including (1) how to search the space of all possible variable subsets; (2) how to evaluate the forecasting performance of a learning machine (forecaster) and (3) which forecaster to be used. TheHWVSmodule utilizes HS to search the space of all possible variable subsets. The K-fold cross-validation method is utilized to perform per- formance evaluation. An NN-based forecaster, called MIF that will be described in detail in Section 2.3, is developed to model the mathemat- ical relationships between selected input variables and sales volumes of retail products.

Fig. 2 shows the workflow of the HWVSmodule. The steps involved are the same as the corresponding ones of the improved HS algorithm proposed byMahdavi et al. [22], except for steps 2 and 3, which are de- tailed as follows.

Step 2: Initialize the harmony memory. The HM is generated randomly, in which each HM member (called a harmony, an solution individual), s, represents a fea- sible input variable subset. s is denoted by a binary string, s ¼ s1; s2;…; sC½ �. si is a binary value, which indicates that the ith input variable is selected if si=1; otherwise it is not.

Step 3: Calculate objective function value of each harmony in terms of cross-validation. Minimizing the forecasting error is the most important objec- tive of forecasting. The objective function valueOF of a harmony is represented by a function of forecasting error. Based on the K-fold cross-validation method, the objective function value OF is calculated by evaluating the forecasting performance

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generated by the corresponding input variable subset. The de- tailed procedures to obtain OF are described below:

(1) The normalized training samples, generated in Section 2.1, are randomly partitioned into K sample subsets, numbered 1 to K. Set i=1.

(2) The ith sample subset is used as validation data for testing the forecaster, and the remaining K−1 subsample sets are used as training data to train and establish the forecast- er (Section 2.3 will describe how the forecaster is implemented in detail). The mean squared error of fore- casting outputs of these validation data is denoted by Mi.

(3) i= i+1. Go to (4) if i>K, otherwise go to (2).

(4) OF ¼ XK i¼1

Mi

! =K .

The less the objective function value, the better solution the harmony represents.

2.3. Multivariate intelligent forecaster

The output of the MIF is the final forecast of overall sales volume of a retail product. The input variable subset, generated by the HWVS module, is adopted as the input variables of the MIF. The hybrid intel- ligent forecaster, developed byWong and Guo [33], is modified to im- plement the MIF module. Fig. 3 shows the flowchart of the MIF.

The MIF generates the final forecast on the basis of the forecasting outputs generated by an HS-ELM-based NN. The NN is run repeatedly Nmax hl times so as to decrease the randomicity of NN outputs. In each run, the NN has a specified number (i) of hidden neurons, which increases successively from 1 to Nmax hl. The NN is used to approximate the relationship between the selected input variables and the sales volumes of retail products. The output of the NN needs to be de-normalized to get the initial forecasts of sales volumes because the input and output of the HS-ELM-based NN are normalized values. These initial forecasts, generated by HS-ELM-based NNs with different number of hidden neurons, can be unreasonable because NNs may be overfitted. They are thus input into the heuristic fine-tuning process for generating the final forecast of sales volume.

The heuristic fine-tuning process is firstly utilized to identify and eliminate unreasonable initial forecasts generated by overfitted NNs. Themean of remaining reasonable initial forecasts is thefinal sales fore- cast. The processes to identify unreasonable forecasts are described as

i=i+1

Initialization: Set i=1, Nmaxhl

i> Nmaxhl

HS-ELM-based NN

forecasting process

Denormalization

Heuristic fine-tuning process

Final forecast of sales

volume

Yes

No

Initial forecasts

Fig. 3. Flowchart of the MIF.

follows. Let outNN denote the denormalized NN output. MinOutS and MaxOutS denote the minimal and maximal values of actual outputs of training samples. The initial forecast is considered as unreasonable if one of the following conditions is met:

(1) outNN>k1 ⋅MaxOutS, (2) outNNbMinOutS/k2

where k1, k2 are pre-given constants greater than 1 and less than 2. The greater the standard deviation of the training samples' outputs is, the greater the values of k1 and k2 are. We set both k1 and k2 are equal to 2. The remaining forecasts except unreasonable ones are then averaged as the final sales forecasts.

3. Numerical experiments

Extensive experiments were conducted to evaluate the forecasting performance of the proposed MID model in terms of real-world sales data of apparel products, which forecasted the overall sales volumes of various retail products based on their early sales. This section presents how these experiments were conducted and the results of 4 experi- ments using typical sample data. To validate the general forecasting performance of the MID model, these experiments investigate sales forecasting tasks in different regions with a large number of retail shops and products. Each of the first 3 experiments considers different influencing factors and candidate input variables, inwhich 10 sets of dif- ferent datasets are utilized respectively to evaluate and compare the forecasting performances generated by the proposedmodel and several comparedmodels. Each dataset consists of a specified number of sample pairs, in which the last 3 input–output sample pairs are utilized for out-of-sample test whereas the others are training samples. In experi- ment 4, 3 sets of datasets with more sample pairs are investigated, which are formedby combining thedatasets in experiments 1–3 respec- tively. In each of the 3 datasets, the last 10 input–output samples are utilized for out-of-sample test. The 33 sets of datasets used in the 4 ex- periments contain a large amount of samples. Due to page limit, these datasets are placed on Internet (http://myweb.polyu.edu.hk/~tcguozx/ datasets/).

3.1. Experimental design

Real sales data were collected from one of the largest fashion retail companies in Hong Kong and Mainland China, which include sales data of fashion products from different retail shops and cities from 01/2007 through 12/2009. The life span of each selected retail prod- uct is greater than 160 days and less than 200 days. Data of available economic indices of each city can be collected from the Municipal Sta- tistics Bureau of this city. The average selling prices of selected prod- uct is greater than 80% of its original price. Experiments have not considered the effects of 3 influencing factors, including style type, material type and promotion strategy due to their data unavailability and incompleteness.

3.1.1. Forecasting models used for comparison This research conducted experiments from two aspects: (1) the fore-

casting performance of the proposed model was compared with 2 mul- tivariate models, including the improved ELM (IELM) model and the generalized linear model [10]; (2) to observe the benefits brought by the HWVS module, this research also compared the performances of the 3 models using all candidate input variables as the inputs of the MIF module and using only the selected input variables, generated by the HWVS module, as inputs.

The IELM model is developed based on the ELME model proposed by Sun et al. [26]. Wong and Guo [33] have demonstrated that the forecasting performance of the ELME model is inferior to that of the HS-ELM-based model. It is one of the main reasons that the ELME model lacks of effective mechanism to determine appropriate input

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Experiment 1: test sample 1

GLM1 GLM2

IELM1

IELM2

MID1

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Fig. 4. Output comparison of the 1st test sample in each dataset.

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Fig. 5. Output comparison of the 2nd test sample in each dataset.

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weights of NNs and the number of appropriate hidden neurons. It is well-known that the number of hidden neurons has large effects on NN performances [36]. To decrease the randomicity of NN outputs generated by the ELMEmodel with a specified number of hidden neu- rons, in the IELM model, we firstly obtain Nmax hl forecasting outputs by repeatedly running the ELME models with different number of hidden neurons from 1 to Nmax hl; these forecasting outputs are then input into the heuristic fine-tuning process for generating the final forecasting output of the IELM model.

The generalized linear model (GLM) was developed by Nelder and Wedderburn [10], which is a flexible generalization of various least squares regressionmodels, including linear regression, logistic regres- sion and Poisson regression. To use generalized linear models, we as- sume that the observations (sales volumes of retail products) obey a normal distribution.

3.1.2. Accuracy measures No accuracymeasure is generally applicable to all forecasting tasks

due to various forecasting objectives as well as data scales and pat- terns [9,16]. To reduce possible bias generated by one single accuracy measure, this research utilized three measures of forecast accuracy, including root mean square error (RMSE), mean absolute percentage error (MAPE) and mean absolute error (MAE), to evaluate the perfor- mance of each forecasting result generated by the MIF.

Let Yt denote the observation at time t and Ft denote the forecast of Yt. Then define the forecast error et=Yt−Ft. The three accuracy mea- sures are formulated as follows:

(1) RMSE ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mean e2ð Þ

p (2) MAPE ¼ mean jet=Yt

j � �

� 100% (3) MAE=mean(|e|).

3.2. Experiment 1

In this experiment, each dataset consists of 41 sample pairs. The output of each sample is the actual overall sales volume of a fashion product in all retail shops of the investigated company in city A. Each sample has 14 candidate inputs, including original selling price, shop quantity, release date, life span, 4 early sales volumes, climate index and 5 economic indexes. The economic indexes include CPI, GDP, PPI, total retail sales index and price index for ‘clothing and foot- wear’. On the basis of available training samples, the subset of input variables, generated by the HWVS module, comprises 3 variables, in- cluding shop quantity, accumulated sales volume in the first 10 days and climate index.

The comparisons of actual and forecasted outputs are shown in Figs. 4–6, each of which shows the forecasting outputs, generated by different models, of a test sample in each dataset. The solid line plots the actual sales volumes of different fashion products in all retail shops of the investigated company. The forecasts generated by differ- ent models are represented by different signs. The signs ‘∗’, ‘x’, ‘□’, ‘+’, ‘○’ and ‘·’ represent, respectively, the forecasts generated by the GLM with all candidate inputs (GLM1), the GLM with selected inputs (GLM2), the IELM model with all candidate inputs (IELM1), the IELM model with selected inputs (IELM2), the MIF with all candidate inputs (MID1) and theMIF with selected inputs (MIDmodel, MID2). It can be clearly found from Figs. 4 to 6 that the proposedMIDmodel generates forecasts of sales volumes closer to the actual values.

On the basis of the forecasting outputs shown in Figs. 4–6, we fur- ther evaluate the performance change generated by the selected input variable subset and compare the forecasting results generated by the GLM, the IELM model and the MID model. Fig. 7 shows the summary comparison result, in which subfigures (a)–(c) represent the results respectively under accuracy measures MAE, MAPE and RMSE. Each subfigure contains 6 bars named B1–B6. The upper and lower parts of the first 5 bars, B1–B5, show the number of datasets getting better

forecasting performances, generated respectively by GLM2 and GLM1, IELM2 and IELM1, MID2 and MID1, MID1 and IELM1, MID2 and IELM2. The 6th bar shows the results generated by MID2, IELM2 and GLM2, which shows, from top to bottom, the number of datasets for which the 3 models generate best performances respectively. For identification purpose, we use a very small part in a bar to indicate 0.

It can be clearly found from bars B1–B3 that the three models with the selected variable inputs (GLM2, IELM2 andMID2) can generate su- perior performances to their corresponding models with all candidate inputs whichever accuracy measures are used. For example, if MAE is used as the accuracymeasure, GLM2, IELM2 andMID2 generate better forecasting performances for 6, 9 and 8 datasets whereas GLM1, IELM1 and MID1 generate better forecasting performances for 4, 1 and 2 datasets. Bars B4 and B5 indicate that the MID1 and MID2 generate better forecasts than IELM and IELM2. The results of B6 indicate that MID2 usually generates better forecasting results than IELM2 and GLM2 whichever accuracy measure is used except for generating an inferior MAPE result for one dataset to IELM2, which shows that the proposed MID model (MID2) exhibits much superior performance to IELM2 and GLM2 in this experiment.

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Fig. 6. Output comparison of the 3rd test sample in each dataset.

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3.3. Experiment 2

Each dataset consists of 35 sample pairs in this experiment. The output of each sample is the actual sales volume of a fashion product in a retail shop of the investigated company in city A. Each sample in- cludes 13 candidate input variables, which are the same to variables in experiment 1 except for excluding the input ‘shop quantity’. The HWVS module generates the subset of 7 input variables from these 13 candidate variables, which include life span, sales volumes in the first 3, 7 and 10 days, climate index, total retail sales index and price index for ‘clothing and footwear’.

Due to the page limit, this paper does not present the comparison results of actual and forecasted outputs in experiments 2–4. Similar to Fig. 7, Fig. 8 shows the further summary result of this experiment by further comparing the forecasting results generated by different models. The results from bars B1–B3 show that GLM2 and IELM2 can generate slightly better forecasting performances than GLM1 and IELM1 while MID2 generates much better performance than MID does since MID2 generates superior forecasting results for 8, 8 and 9 datasets, respectively, in terms of 3 different accuracy measures. The results from bars B4–B6 show that (1)MID1 generates better forecast- ing results than IELM for at least 7 datasets in terms of different accu- racy measures; (2) MID2 always generates better forecasting results than IELM2 and GLM2 for all 10 datasets whichever accuracy measure is used. These results show that the proposed MID model exhibits much better forecasting performance than other models do in this experiment.

Fig. 7. Comparison of forecasti

3.4. Experiment 3

Each dataset consists of 32 sample pairs in this experiment. The output of each sample is the actual sales volume of a fashion product in a retail shop of the investigated company in city B. Each sample in- cludes 9 candidate input variables, including original selling price, re- lease date, life span, 4 early sales volumes in a retail shop, climate index and total retail sales index. In experiments 1–2, 5 economic in- dexes were included. However, this experiment used another factor because the values of the 5 factors could not be obtained effectively due to incomplete information released by relevant government de- partment and organization. On the basis of available training samples, the subset of input variables, generated by the HWVS module, con- tains original selling price, life span, sales volume in the first 14 days and total retail sales index.

Fig. 9 shows the summary result of this experiment. The results from bars B1–B3 demonstrate that GLM2, IELM2 and MID2 can gener- ate obviously better forecasting performance than their correspond- ing models with all candidate inputs. For instance, GLM2 and IELM2 generate superior forecasting results for 8 and 9 datasets respectively whichever accuracy measure is used. Bars B4 indicate that the MID1 generate better forecasting results than IELM1 for 9 datasets. In addi- tion, bars B5 and B6 indicate that MID2 generate superior forecasting results to IELM2 and GLM2 for at least 9 datasets whichever accuracy measure is used. These results also show that the proposedMIDmodel exhibits much superior forecasting performance to other models in this experiment.

3.5. Experiment 4

3 sets of datasets with more observations are utilized to evaluate the forecasting performances of different models. The 3 datasets con- sists of 76, 65 and 60 observations respectively. The last 10 observa- tions of each dataset are used for out-of-sample test. Table 1 shows the forecasting results for the 3 datasets in terms of different accuracy measures. It is clear that, in this experiment, MID2 generates the best forecasting performances (out-of-sample test) and the second best fitting performances (in-sample test, only inferior to MID1).

The experimental results above were obtained based on the fol- lowing setting: the values of parameters of HS algorithms were shown in Table 2, in which PARmin and PARmax denote the minimum and the maximum of PAR, and bwmin and bwmax denote the minimum and the maximum of bw. In addition, the maximum number Nmax hl of hidden neurons is equal to 5. The activation function g(x) of NN is the sigmoidal function, i.e., g xð Þ ¼ 1

1þe−x. 10-fold cross-validation method was used in the HS-wrapper module.

ng results (Experiment 1).

Fig. 8. Comparison of forecasting results (Experiment 2).

253Z.X. Guo et al. / Decision Support Systems 55 (2013) 247–255

4. Discussion

This section presents an in-depth discussion on the forecasting per- formance of the proposed MID model. Further analysis is firstly conducted to validate the superiority of the proposed model over other models based on the experimental results presented in Section 3. The performance of HWVS model and its effects on final forecasting results are then discussed.

4.1. Further performance comparison and analysis

Extensive experiments were presented to validate the forecasting performance of the proposed MIDmodel in Section 3, in which 33 dif- ferent datasets were investigated. These datasets involve different cit- ies and a large variety of retail shops and retail products, and can reflect typical sales patterns in retailing.

On the basis of the experimental results described in Section 3, Table 3 shows a summary comparison between the proposed MID model (MID2) and 5 other comparedmodels. In this table, the first col- umn shows the number of datasets for which MID2 generates best forecasting performance compared with other 5 models, and the sec- ond to fifth columns show the comparison results betweenMID2with MID1, IELM2, IELM1, GLM2 and GLM1 respectively. In this table, the first value of each cell represents the results of out-of-sample test while the value in the bracket represents the result of in-sample test. Taking MAE as an example, MID2 generates best forecasts in all 6 models for 20 datasets in terms of out-of-sample test, and for 15 datasets in terms of in-sample test. It can be found from this table, MID2 generates much higher training accuracies than IELM2, IELM1, GLM2 and GLM1. However, it can only outperform MID1 for 13

Fig. 9. Comparison of forecastin

datasets in terms of in-sample test. It is becauseMID1 hasmore inputs and more complicated network connections, which can bring higher fitting (training) accuracy although they are prone to overfitting and generating poor forecasts.

We further used p-values tomeasure the forecasting results gener- ated by different models. This research uses A≡(or≻)B to represent that A generates better forecasting accuracies for p% (or more than p%, p≥50) of datasets than B does. For example, MID2≡OtherModels represents that MID2 generates higher forecasting accuracies for p% of datasets than other comparedmodels do. To further analyze the su- periority of MID2 over other models, we define four null hypotheses (HA0, HB0, HC0 and HD0) and their corresponding alternative hypoth- eses below:

HA0: MID2≡OtherModels; HA1: MID2≻OtherModels; p=55. HB0: MID2≡MID1; HB1: MID2≻MID1; p=65. HC0: MID2≡ IELM1; HC1: MID2≻ IELM1; p=80. HD0: MID2≡GLM2; HD1: MID2≻GLM2; p=90.

To validate if the proposed model is significantly superior to other models whichever accuracy measure is employed, we calculate the p-value of each hypothesis by using the minimal number of datasets shown in the corresponding column of Table 3. That is, we take num- bers 23, 26, 31 and 33 to calculate the p-values of the four null hypoth- eses respectively. The four p-values are 0.045, 0.048, 0.023 and 0.028 respectively, which are all less than 0.05.We thus reject these hypoth- eses at the 5% significance level. Take null hypotheses HA0 as an exam- ple. There is a 95% chance of accepting the alternative hypothesis HA1. That is, formore than 55% of datasets,MID2 generate the best forecast- ing accuracies among 6 compared models at the 5% significance level. In addition, the results of rejecting hypotheses HB0–HD0 show that, for

g results (Experiment 3).

Table 1 Performance comparison of different models for larger-size samples.

MID2 MID1 IELM2 IELM1 GLM2 GLM1

In sample

Out of sample

In sample

Out of sample

In sample

Out of sample

In sample

Out of sample

In sample

Out of sample

In sample

Out of sample

Data of Exp. 1 MAE 304.2 782.4 231.7 889.1 730.7 825.0 909.8 529.0 1158.8 1421.7 809.8 365.3 MAPE 23.8% 24.3% 27.3% 33.6% 69.4% 30.4% 98.4% 42.4% 39.3% 333.7% 27.5% 85.8% RMSE 637.8 1372.3 325.8 1512.3 1318.3 1300.7 1623.3 691.8 1981.7 2019.3 1316.5 566.1

Data of Exp. 2 MAE 39.8 35.1 44.0 60.4 49.9 126.3 127.6 70.3 126.9 119.3 101.0 145.2 MAPE 18.3% 14.0% 21.3% 27.8% 19.5% 46.0% 45.8% 28.8% 80.8% 75.0% 64.4% 91.3% RMSE 53.7 46.5 56.6 73.3 70.3 214.6 226.2 77.7 178.7 143.9 145.4 228.5

Data of Exp. 3 MAE 39.1 64.8 56.1 67.6 238.1 117.8 278.4 120.1 155.7 207.3 222.0 215.0 MAPE 16.8% 27.5% 22.2% 30.2% 85.2% 56.1% 96.3% 54.5% 142.8% 97.8% 203.7% 101.4% RMSE 57.6 88.9 105.1 89.8 363.1 160.9 435.1 161.7 248.9 390.3 279.1 292.9

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more than 65%, 80% and 90% of datasets, MID2 generate higher fore- casting accuracies than MID1, IELM1 (IELM2), and GLM1 (GLM2) models at the 5% significance level. The results of statistical tests indi- cate that it is statistically significant that the proposed MID model (MID2) can generate much better forecasting performances than IELM models and GLMs do in terms of three accuracy measures (MAE, MAPE and RMSE).

4.2. Performance and effects of HWVS module

We further compare the forecasting results generated by different forecastingmodels with/without the usage of HWVSmodule, including GLM2/GLM1, IELM2/IELM1, and MID2/MID1. Take the forecasting re- sults in terms of accuracy criterion MAE as an example. GLM2 can gen- erate superior forecasts to GLM1 for 22 datasets while IELM2 (MID2) can generate superior forecasts to IELM1 (MID1) for 26 (25) datasets. p-Values are utilized to further measure these forecasting results in terms of MAE. We define three null hypotheses (HE0, HF0, and HG0) and their corresponding alternative hypotheses below:

HE0: GLM2≡GLM1; HA1: GLM2≻GLM1; p=50. HF0: IELM2≡ IELM1; HB1: IELM2≻ IELM1; p=60. HG0: MID2≡MID1; HC1: MID2≻MID1; p=60.

The p-values under these hypotheses are 0.028, 0.014, and 0.032 respectively, which are all less than 0.05.We thus reject these hypoth- eses at the 5% significance level. That is, for more than 50% of datasets, GLM2 generates higher forecasting accuracies than GLM1 does at the 5% significance level. For more than 60% of datasets, IELM2 and MID2 generate higher forecasting accuracies than IELM1 and GLM1, respec- tively, at the 5% significance level. These indicate that it is statistically significant that the models with the HWVS module can generate bet- ter forecasts than corresponding models without the HWVS module. The same conclusion could be drawn when other accuracy criteria were used. It shows that the HWVS module is effective to improve the forecasting accuracy.

In the experiments described in Section 3, different candidate inputs were used due to different data availabilities in cities involved. In each experiment, we searched for the optimal input variable subsets sepa- rately because each experiment used different candidate input variables and different sales patterns. The input variable subsets, generated by the HWVS module, contain 3, 7, and 4 variables in experiments 1–3, which are selected out from 15, 13 and 9 candidate variables respectively. Dif- ferent optimal input variable subsets were then obtained. That is

Table 2 Parameters of HS algorithms used in experiments.

HMS NI HMCR PARmin PARmax bwmax bwmax PerHM

HS-wrapper 50 100 0.95 0.45 0.99 1.E−06 4 90% HS-ELM 100 200 0.95 0.45 0.99 1.E−06 4 90%

because different intrinsic relations exist between input data (influenc- ing factors) and output data (overall sales) in different cases investigat- ed in corresponding experiments. Actually, it depends on sample data whether an influencing factor needs to be used as a final input variable and incorporated into the forecasting model. According to the variable selection results, the factors, included in the optimal input variable sub- set, need to be incorporated. It can be found from experimental results that the forecasting performance was not deteriorated by the exclusion of several variables. It indicates that the available influencing factors are enough to reflect the corresponding input/output relations in each ex- periment. It also indicates that the proposed model, including the HWVSmodule and theMIF module, is effective to approximate the cor- responding input/output relations and generate reliable forecasts in these cases.

In addition, the proposed HWVS module effectively reduced the number of input variables whichever candidate input variables were utilized, which resulted in less model parameters and was helpful to decrease the complexity of forecaster so as to improve the generaliza- tion performance of the forecaster.

5. Conclusions

This paper addresses the early sales-based retail forecasting prob- lem in the retail industry, which is helpful for related retail enterprises to make scientific and reliable replenishment forecasting and thus im- prove the performance and efficiency of their retail supply chains.

An effective MIDmodel was developed to handle the problem inves- tigated, in which a DPP module, a HWVS module and a MIF were inte- grated. The DPP module is responsible for capturing and preprocessing sales data of past products and values of related candidate input variables for the development and validation of the MID model. The HWVS mod- ule selects out the optimal input variable subset from given candidate in- puts. Using the selected input variables as the inputs of MIF, the MIF is then established to model the relationship between the selected input variables and the sales volumes of retail products. Lastly, the established MIF is utilized to forecast the sales volumes of retail products.

Extensive experiments were conducted to evaluate the proposed MID model in terms of a large variety of typical datasets from real- world retail data. The experimental results indicated that the MID model can tackle the investigated multivariate sales forecasting prob- lem effectively and it is statistically significant that the proposed model could provide much superior performance over the IELM model and the generalized linear model. Experimental results also

Table 3 Number of datasets for which MID2 generates better forecasting (training) results.

5 other models MID1 IELM2 IELM1 GLM2 GLM1

MAE 23 (17) 26 (17) 32 (33) 32 (33) 33 (33) 33 (33) MAPE 26 (15) 28 (16) 32 (33) 32 (33) 33 (29) 33 (30) RMSE 24 (15) 28 (15) 31 (33) 31 (33) 33 (33) 33 (33)

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showed that the HWVS module can effectively find the appropriate variable input by eliminating reluctant and irrelevant inputs which- ever candidate input variables are used, which results in less model parameters and higher forecasting accuracy. These results show that the proposed model is effective and widely applicable to multivariate sales forecasting problems. In addition, the proposed MID model does not rely on the time series of historical sales data of products to be forecasted, which can thus provide overall sales forecasts for both old and new retail products.

Future research will focus on utilizing the proposed MID model to handle other multivariate forecasting problems, such as multivariate time series forecasting problem, and compare the performance of pro- posed model with multivariate time series forecasting model such as autoregressive moving average model with exogenous inputs. In addi- tion, it is also a worthwhile research direction to compare the effects of different variable selection methods on the forecasting performance of MID model, and further improve the generalization performance and the computational efficiency of MID model by utilizing partially connected NNs [34] to replace the HS-ELM-based NN.

Acknowledgement

The authors acknowledge the supports from Sichuan University, the Fundamental Research Funds for the Central Universities (Grant No. SKYB201301) and the National Natural Science Foundation of China (Grant Nos 71020107027, 71172197).

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Z.X. Guo received his Ph.D. degree from The Hong Kong Polytechnic University. Currently, he is an associate pro- fessor at Business School of Sichuan University. His recent research interests include production planning and con- trol, sales forecasting, intelligent decision making and op- timization. He has published more than 10 research papers in refereed journals, such as Information Sciences, International Journal of Production Economics, and IEEE Transactions.

W.K. Wong received his Ph.D. degree from The Hong Kong Polytechnic University. Currently, he is the associate pro- fessor in this university. He has published more than fifty scientific articles in refereed journals, including Interna- tional Journal of Production Economics, Expert Systems with Applications, European Journal of Operational Re- search, International Journal of Production Research, Com- puters in Industry, The IEEE Transactions on Systems, Man, and Cybernetics, among others. His recent research inter- ests include modeling of supply chain management, manufacturing planning and scheduling, data mining and knowledge discovery, and time series forecasting.

Min Li received her Bachelor degree in Electronics and Infor- mation Engineering from the Donghua University, China. She is currently an MPhil student at Institute of Textiles and Clothing of The Hong Kong Polytechninc University, Hong Kong, China. Her recent interest include fashion retail fore- casting and supply chain management.