Demand Forecasting using Artificial Neuronal Networks and Time
Series: Application to a French Furniture Manufacturer Case Study
Julie Bibaud-Alves
1,2,3
, Philippe Thomas
1,2 a
and Hind Bril El Haouzi
1,2
1
Université de Lorraine, CRAN, UMR 7039, Campus Sciences, BP 70239, 54506 Vandœuvre-lès-Nancy Cedex, France
2
CNRS, CRAN, UMR7039, France
3
Parisot Meubles, 15 Avenue Jacques Parisot, 70800 Saint-Loup-sur-Semouse, France
Keywords: Sales Forecasting, Neural Networks, Multilayer Perceptron, Seasonality, Overfitting, Time Series.
Abstract: The demand forecasting remains a big issue for the supply chain management. At the dawn of Industry 4.0,
and with the first encouraging results concerning the application of deep learning methods in the management
of the supply chain, we have chosen to study the use of neural networks in the elaboration of sales forecasts
for a French furniture manufacturing company. Two main problems have been studied for this article: the
seasonality of the data and the small amount of valuable data. After the determination of the best structure for
the neuronal network, we compare our results with the results form AZAP, the forecasting software using in
the company. Using cross-validation, early stopping, robust learning algorithm, optimal structure
determination and taking the mean of the month turns out to be in this case study a good way to get enough
close to the current forecasting system.
1 INTRODUCTION
One of the most important decision problem of supply
chain management is the demand forecasting in order
to balance inventory and service levels (Brown 1959),
(Chapman et al., 2017). (Boone et al., 2019) note that
the role and use of artificial intelligence and machine
learning methods in supply chain forecasting remains
underexplored. Besides, the important issues to the
development of supply chain forecasting are:
The processes and systems through which the
disaggregated forecasts are produced;
Methods and selection algorithms that are suitable
for supply chain data;
The impact of new data sources from both
consumer and supply chain partners;
The effects of uncertainty and forecasts errors on
the supply chain;
The effects of linking forecasting to supply chain
decisions, at both aggregate and disaggregate
levels.
Several quantitative approaches exist. For this
paper, we chose to focus our work on neural
approaches, which are more and more used in supply
chain management (Carbonneau et al., 2008). The
a
https://orcid.org/0000-0001-9426-3570
purpose of this paper is to evaluate the ability of a
neural model of time series prediction to predict sales.
As this work is being conducted as part of a
collaboration project between CRAN laboratory and
Parisot company, we apply this approach to Parisot,
which is currently using a commercial software to
establish its sales forecasts. Two main problems have
been studied for this article:
The seasonality, which will be taken into account
through two different ways as input data in the
experiments: by assigning a number to the month
in question, and by using the average, over the
period, of the recorded orders relating to the
month in question
The small amount of data available, constituting a
risk of overfitting, which will be taken into
account through the algorithm.
The paper begins by presenting a brief state of the
art regarding sales forecasts, then the neural network
methods used in this work is presented. Then we will
present the results before concluding and putting into
perspective this work.
502
Bibaud-Alves, J., Thomas, P. and El Haouzi, H.
Demand Forecasting using Artificial Neuronal Networks and Time Series: Application to a French Furniture Manufacturer Case Study.
DOI: 10.5220/0008356705020507
In Proceedings of the 11th International Joint Conference on Computational Intelligence (IJCCI 2019), pages 502-507
ISBN: 978-989-758-384-1
Copyright
c
2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
2 SALES FORECASTING
In classical forecasting techniques, it is first of all a
question of straightening the series in order to
eliminate the “accidental” variations whose origin is
known. Next, we must determine the typology of the
time series. Only after, comes the stage of the
selection of forecast techniques adapted to the
problems.
Complex time series can be broken down into
three components (Chatfield 1996), (Nelson 1973):
A trend component
A cyclical component (seasonal) which can itself
know a temporal evolution
A random component (disturbance)
Concerning forecasting techniques, (Giard 2003)
proposes the following classification, Figure 1:
Explanatory models (called exogenous): the
forecast is based on values taken by variables
other than those we are trying to predict.
Autoprojective models (called endogenous): the
future is simply deduced from the past. We can
refer to (Kendall 1976), (Kendall and Stuart
1976).
Figure 1: Forecasting techniques classification.
The choice of the technique must minimize the
cost of forecasting for a given level of precision,
taking into account the type of time series, and the
purpose, depending on whether the forecast will be
used in the short or long term.
As part of Industry 4.0, the 4
th
Industrial
Revolution centred on the data valorisation,
researchers are turning to approaches based on
artificial intelligence and new technologies
increasingly accessible to businesses (Liu et al.,
2013). These new approaches seem to offer overall
better results than traditional methods (Jurczyk et al.,
2016).
3 MULTILAYER PERCEPTRON
3.1 Structure
The traditional multilayer neural network consists of
only one hidden layer (using a sigmoidal activation
function) and one output layer. It is commonly
referred to as a multilayer perceptron (MLP) and has
been proven to be a universal approximator (Cybenko
1989), (Funahashi 1989). Its structure is given by:
2 1 1
11
ˆ
..
oi
nn
o h h hi i h
hi
y g w g w x b b









(1)
where
i
x
are the n
i
inputs,
1
hi
w
are connecting
weights between input and hidden layers,
1
h
b
are the
hidden neurons biases, g
h
(.) is the activation function
of the hidden neurons (hyperbolic tangent),
2
h
w
are
connecting weights between hidden and output
layers, b is the bias of the output neuron, g
o
(.) is the
activation function of the output neuron, and
ˆ
y
is the
network output. The considered problem is a
regression one. The g
o
(.) is a linear activation
function.
Learning of a MLP is performed by using a local
minimum search. Therefore, the model accuracy
depends of the choice of the initial parameter set. The
one used here is a modification of the Nguyen and
Widrow (NW) algorithm (Nguyen and Widrow
1990). It allows a random initialization of weights and
biases, combined with an optimal placement in the
input space (Demuth and Beale 1994)
This type of MLP has been extensively used in a
broad range of problems including classification,
function approximation, regression, or times-series
forecasting.
The considered problem here is a sales forecasting
problem which can be viewed as a special case of
times-series forecasting including consideration of
seasonality.
Moreover, this problem must be solved by using
small datasets which can lead to overfitting problem.
3.2 The Seasonality Problem
Seasonality is an aspect of the data that makes the
prediction task difficult. (Zhang and Qi 2005) studie
the effectiveness of seasonal series pre-treatments on
the performance of multilayer perceptron. They
Demand Forecasting using Artificial Neuronal Networks and Time Series: Application to a French Furniture Manufacturer Case Study
503
conclude that even with pre-processing, their
performance remains limited.
To take into account the phenomenon of
seasonality, we propose to test and compare two
approaches using the dataset of the company (here
AZAP FORECAST and HISTORICAL ORDERS,
used in the columns CDES 1 to 3 in the following
paper):
We replace the month with a number, Table 1,
which is varied (as example, in a first approach,
January is assigned the value 1, February 2…, in
a second step, January is assigned the value 12,
February 1…), Table 2 ;
We add the average value of sales for the chosen
month considering the whole dataset (for January
is 34586, for February is 33154, etc.), Table 3.
Table 1: Construction of the input file considering the
number of the month.
HISTORICAL
ORDERS
CDES-
1
CDES-
2
CDES-
3
MONTH
MONTH
NUMBER
46 592
0
0
0
January
1
29 820
46 592
0
0
February
2
37 487
29 820
46 592
0
March
3
35 861
37 487
29 820
46 592
April
4
18 772
35 861
37 487
29 820
Ami
5
43 712
18 772
35 861
37 487
June
6
33 106
43 712
18 772
35 861
July
7
24 074
33 106
43 712
18 772
August
8
25 832
24 074
33 106
43 712
September
9
31 578
25 832
24 074
33 106
October
10
22 093
31 578
25 832
24 074
November
11
41 048
22 093
31 578
25 832
December
12
31 821
41 048
22 093
31 578
January
1
38 660
31 821
41 048
22 093
February
2
Table 2: Principle of shift of the number of the month.
HISTORICAL
ORDERS
CDES-
1
CDES-
2
CDES-
3
MONTH
NUMBER
January1
MONTH
NUMBER
January2
MONTH
NUMBER
January3
46 592
0
0
0
1
2
3
29 820
46 592
0
0
2
3
4
37 487
29 820
46 592
0
3
4
5
35 861
37 487
29 820
46 592
4
5
6
18 772
35 861
37 487
29 820
5
6
7
43 712
18 772
35 861
37 487
6
7
8
33 106
43 712
18 772
35 861
7
8
9
24 074
33 106
43 712
18 772
8
9
10
25 832
24 074
33 106
43 712
9
10
11
31 578
25 832
24 074
33 106
10
11
12
22 093
31 578
25 832
24 074
11
12
1
41 048
22 093
31 578
25 832
12
1
2
31 821
41 048
22 093
31 578
1
2
3
38 660
31 821
41 048
22 093
2
3
4
3.3 The Overfitting Problem
One of the main risks encountered in the use of
machine learning is the overfitting problem. This
problem is related to the fact that the dataset used to
learn is generally noisy and generally corrupted by
outliers. If the model used includes too many
parameters (degrees of freedom), the learning step
can lead to learning noise at the expense of learning
the underlying system. To avoid this, different
approaches may be used individually or in
combination.
A classical approach is to perform a cross
validation. Different approaches may be used. The
considered here is the holdout method consisting by
dividing the dataset into learning and validation
dataset. This approach allows to detect and avoid this
phenomenon by conjunction with the second
approach: the early stopping. Early stopping consists
to stop the learning when the performance of the
model begins to deteriorate on the validation dataset.
The early stopping may be automatized by
monitoring some parameters of the learning
algorithm used. As example, in the Levenberg-
Marquardt algorithm, it is possible to monitor the
evolution of the gradient value and/or of the evolution
of the parameter chosen to ensure the inversion of
the Hessian matrix (Levenberg 1944), (Marquardt
1963). The learning algorithm used here is derived
from the one proposed by (Norgaard 1995) which
includes such mechanisms.
Table 3: Construction of the input file considering the
average of the month.
AZAP
FORECASTS
HISTORICAL
ORDERS
CDES-
1
CDES-
2
CDES-
3
MONTH
MONTH
MEAN
55 805
46 592
0
0
0
January
34586
45 573
29 820
46 592
0
0
February
33154
41 987
37 487
29 820
46 592
0
March
31819
46950
35861
37 487
29 820
46 592
April
31688
39270
18772
35 861
37 487
29 820
Ami
24800
51663
43712
18 772
35 861
37 487
June
33862
47088
33106
43 712
18 772
35 861
July
31975
33124
24074
33 106
43 712
18 772
August
28447
27542
25832
24 074
33 106
43 712
September
30370
30520
31578
25 832
24 074
33 106
October
39067
23529
22093
31 578
25 832
24 074
November
29261
47602
41048
22 093
31 578
25 832
December
37296
45186
31821
41 048
22 093
31 578
January
34586
45572
38660
31 821
41 048
22 093
February
33154
The overfitting is directly related to the inclusion
of useless parameters in the model. Another approach
to avoid this problem is to determine the optimal
structure of the model. This may be done by using
constructive approach (Kwok and Yeung 1997) or
NCTA 2019 - 11th International Conference on Neural Computation Theory and Applications
504
pruning procedure (Thomas and Suhner 2015).
Another approach is to use trial and error approach to
determine the optimal structure of this model. This is
this last approach which is used here because it is the
simplest.
The last approach to limit the overfitting problem
is to include a regularization effect in the learning
algorithm. This effect may be obtained by adding a
weight decay term to the criterion to minimize in the
learning algorithm (Norgaard 1995). Another
approach is to use a robust criterion to minimize in
the learning algorithm (Thomas et al., 1999). This is
this second approach which is used here.
So, to conclude, to avoid the overfitting risk, the
optimal structure is obtained by using trial and error
approach. A cross-validation is performed, and an
automatic early stopping is performed. Last, a robust
criterion is included in the learning algorithm.
4 APPLICATION AND
EXPERIMENTAL RESULTS
4.1 Industrial Context
This paper is a case study, based on the data from
Parisot – Saint Loup’s Unit. It’s an octogenarian
French furniture industry. It sells furniture kits made
of particle board in France and around the world. The
catalog consists of furniture for bedroom, living
room, kitchen, bathroom, in single package or multi
package.
This company has had to face in recent years
many changes. Sudden adaptations have not
necessarily been optimal and have led to bad long-
term practices. These bad practices now prevent the
company from remaining competitive.
Today, the forecasts are made using AZAP
1
.
AZAP is a publisher of a software suite that assists
with optimum Supply Chain management. It covers
the management functions of sales forecasting and
demand management, industrial planning and
inventory level optimization of companies looking to
significantly cut costs, optimise stock management
and improve customer service promptly.
The need of the company is to improve the sales
forecasting function without the need of encapsulated
business logic. Thus, the ML (Machine Learning)
could be a good candidate.
1
http://www.azap.net/en/
4.2 Dataset
We used the summary file of final forecasts and
orders recorded by large groups of customers. The
data are monthly recorded from 2012 to 2018,
constituting 81 values (named HISTORICAL
ORDERS in the next tables), which is a small dataset.
We chose to separate the series into two datasets, one
for learning and one for validation. The chosen
method is that of 80/20 randomly. So, the learning
dataset includes 62 patterns when the validation one
includes 16 patterns. The dataset is normalized before
to perform the learning:
min
max min
x
norm
xx
x
x
(2)
where min
x
is the minimum and max
x
is the
maximum of the variable x.
In order to compare the results between them, we
use the root mean square error value (RMSE):
2
1
1
ˆ
( ) ( )
N
n
RMSE y n y n
N

(3)
Where N is the size of the dataset, y(n) is the n
th
target, and
ˆ
()yn
its estimation.
4.3 Structure Determination using a
Trial / Error Approach
The first step in this study was to determine the
structure of the neural network.
In times-series forecasting, the prediction of the
output (here HISTORICAL ORDERS) is performed
by using past data of orders. The first step is to
determine the time window. To do that, we varied the
number of inputs considering the data about the
orders, as shown by Table 4. This amounts to varying
the number of delayed data to be taken into account
in relation to the value considered (here CDES 1,
CDES 2 and CDES 3).
Table 4: Construction of delayed data to be taken into
account as inputs.
AZAP
FORECASTS
HISTORICAL
ORDERS
CDES-1
CDES-2
CDES-3
55 805
46 592
0
0
0
45 573
29 820
46 592
0
0
41 987
37 487
29 820
46 592
0
46 950
35 861
37 487
29 820
46 592
39 270
18 772
35 861
37 487
29 820
51 663
43 712
18 772
35 861
37 487
Demand Forecasting using Artificial Neuronal Networks and Time Series: Application to a French Furniture Manufacturer Case Study
505
We varied the frame size from 3 to 6, and, to avoid
the problem of local minimum search, this task is
performed hundred times and the best result is kept.
The number of hidden neurons is tuned to 4. Table 5
presents the best RMSE obtained on the validation
data set in function of the number of delayed inputs.
This RMSE is calculated with normalized dataset.
These results show that using a time window of size
3 is enough to learn the problem. Including more
delayed inputs tends to degrade the accuracy of the
model on the validation dataset (overfitting). So, in
the sequel, the time window is tuned to 3.
Table 5: Results of the determination of the time window.
The number of delayed data
3
4
5
6
RMSE
0.0365
0.0511
0.0412
0.0585
In a second step, the optimal number of hidden
neurons is expected, we varied its number from 3 to
6. As for the determination of the number of delayed
inputs to use, to avoid the local search minimum
problem, ten learning has been performed on ten
different initial sets of parameters and the best result
is kept. Table 6 presents the RMSE obtained on the
validation dataset (normalized) when the number of
hidden nodes varies. These results show that the
variation of this number has no significant impact on
the accuracy of the model. So, the number of hidden
neurons is set to 3.
Table 6: Results of the determination of the number of the
hidden neurons.
The number of hidden neurons
3
4
5
6
RMSE
0.0365
0.0366
0.0377
0.0369
For all following experiments, the structure of the
MLP includes:
The small amount of data available, which
constitutes a risk of over-learning
4 inputs: the time window of 3 historical values
and an input related to the month: the number or
the mean of orders to the month considered.
3 hidden neurons.
4.5 Comparison
In a first step, the seasonality is considered by
associating each month to a real value (Table 2 ). This
approach presents the drawback to introduce an
important gap between two consecutive months. As
example, by associating 1 to January, 2 to
February…, the transition from December to January
induces a jump from 12 to 1. To evaluate the impact
of this jump on the accuracy of the model, a
permutation of these association is performed (in a
first experiment, January is associated to 1, in a
second it is associated to 2…). As for the
determination of the structure, 10 learning has been
performed with 10 initial set of parameters for each
experiment in order to avoid the local minimum
search problem.
Table 7 presents the RMSE obtained on the validation
dataset for these 12 experiments. In order to compare
these results with those obtained with AZAP, this
RMSE is calculated on non-normalized dataset.
These results show that the position of the jump in
the year has an important impact on the results. As
example, when it is situated between January and
February (line NN FORECASTS January12) the
accuracy is 27% worse than that it is situated between
May and June (line NN FORECASTS January8).
We can see that NN forecasts with some
sequences (January3, January 4 and January 8) are
slightly better than the AZAP forecasts.
Table 7: Results considering the variation of the month
number.
CONSIDERED EXPERIMENT
RMSE
AZAP FORECASTS
5882
NN FORECASTS January1
7071
NN FORECASTS January2
6189
NN FORECASTS January3
5814
NN FORECASTS January 4
5882
NN FORECASTS January5
6332
NN FORECASTS January6
6870
NN FORECASTS January7
6678
NN FORECASTS January8
5753
NN FORECASTS January9
6140
NN FORECASTS January10
6050
NN FORECASTS January11
6213
NN FORECASTS January12
7287
The second approach to consider the seasonality,
is to associate to each month the average sales for the
considered month (Table 3). Table 8 presents the
RMSE obtained on the validation dataset with this
strategy and compares the obtained results with those
obtained with AZAP and with the best model using
the preceding strategy. These results show that the
using of the average sales for the considered month
improves the accuracy of the model comparatively to
the two others. The improvement is of 5.5%
comparatively to the preceding approach and up to
8% comparatively to AZAP. This can be explained by
the fact that this approach gives a richer information.
NCTA 2019 - 11th International Conference on Neural Computation Theory and Applications
506
Table 8: Results considering the input of the month mean.
CONSIDERED EXPERIMENT
RMSE
AZAP FORECASTS
5882
NN FORECASTS January8
5753
NN FORECASTS mean of the month
5450
5 CONCLUSIONS
This paper presents an initial work of a Ph.D study in
collaboration with a French furniture manufacturer.
Its goal is to propose a machine learning approach to
perform sales forecasting.
A classical neural network model (multilayer
perceptron) is used. The main difficulty is related to
the small size of the dataset which can lead to the
overfitting problem. To avoid it, a combination of
different strategies is used (cross-validation, early
stopping, robust learning algorithm, optimal structure
determination).
The second difficulty is related to the taking into
account of the seasonality. Two approaches have
been proposed and compared. This study has shown
that taking the mean of the month into account as an
input is significant to solve the problem of
seasonality.
We have to take in account that our result consists
of the basic forecasts in the AZAP process, and we
compare our results with the final forecasts obtained
after the forecaster job. In future works, we must add
the information of the commercial and marketing
forecasts taking into account the effect of publicity
and events. We can also test the impact of
agglomerating or disaggregating customer hierarchy
data. Last, the cross-validation approach used here is
the holdout method which is simple but maybe not the
more efficient when the dataset is small. Other cross-
validation approaches must be tested and compared in
the future such as k-fold or leave one out as example.
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