Jéssica Arrais Martins
Instituto Federal de São Paulo, Brazil
E-mail: jessarrais@gmail.com
Jeferson Auto da Cruz
Instituto Federal de São Paulo, Brazil
E-mail: jeferson.cruz@ifsp.edu.br
Submission: 29/03/2018
Accept: 29/03/2018
ABSTRACT
The given article aims to evaluate
different quantitative demand forecast methods through a case study on a glass
tempering company. The analysis were held based on historical data series,
which allowed the use of a part of this data for method application and another
part for comparison and validation of the model`s results. The methods were
compared based on obtaining the mean absolute error. In the studied company,
the raw material request for the suppliers was made when new orders are ordered
(pulled production). This method results in longer responsiveness, mainly due
to the waiting time of raw material arrival. The application of those different
demand forecasting models were analysed over three types of products on the
tempered glass category, which represents a total volume of 65% of the
company's costs. As a result, two methods were better adapted to the real data,
providing absolute errors between 0.25 and 0.29. This given work showed that the
application of the demand forecasting methods would reduce orders delivery
time, what could lead to real gains to the analysed company.
Keywords: Demand
Forecasting; Quantitative Models; Glass Tempering
1. INTRODUCTION
Management
decisions affect competitiveness, growth, achievement of strategic objectives
and the economic outcomes of organizations. Thus, the orientation of short,
medium and long-term planning variables can aid managers to achieve better
results in key organizational issues such as: improve logistics efficiency,
faster decision-making, greater robustness over adversities and costs
reduction. When a problem or need is addressed beforehand, companies can
develop better plans to solve them, what makes demand-forecast methods a tool
of great relevance for increasing their competiveness (LEMOS, 2006).
According to Lemos (2006),
forecasting methods can be applied to several areas, such as "finance and
accounting, engineering and research, production, distribution and logistics,
human resources, marketing and sales."
The present work is based on the
sales data of products on a small glass tempering company, located in
Campinas-SP. Since 2012, the company has been distributing flat glass for
architecture, civil construction, decoration and furniture; selling mirrors,
tempered glass, laminates, common, lid tables, silicone, accessories and
ironmongery.
Currently,
the given company does not use any forecast method to plan its future demand
and manage its inventories levels. In order to verify a method that suits the
demands of this type of company, five methods of forecasting demands were
analysed and compared: last period method, global simple average method, simple
average method per period, moving average method and least squares method.
The
purpose of this study was to compare the analysed methods and to identify which
of those better suits companies’ marketing history, therefore assisting in the
decision-making regarding inventory levels and thus avoiding unnecessary costs
and reducing responsiveness over customers’ orders. For that goal, we analysed
the sales data from January 2015 to April 2017.
The
current paper is split on the following sections: first a literature review on
demand forecasting, quantitative forecast methods, an overview on the glass
industry and the case study. Afterwards, the methodology used will be presented
followed by its results, and at last, this work`s conclusion.
2. LITERATURE REVIEW
2.1.
Demand
Forecasting
Economic
and political instability as well as the development of new technologies can
make demands planning a difficult task, when becomes necessary, not only the
correct modelling, but the identification of scenario changes, which raises
uncertainties and risks; this identification usually requires the expertise of
a skilled-professional in the area. Expert predictions apply to external,
non-controllable events (LEMOS, 2006).
Lindberg
and Zackrisson (1991) list the four major problems associated with the use of
predictions:
a) The uncertainty about of the future, which is connected to forecast the
degree of precision;
b) The choice of the method used to generate the forecast;
c) The quality and reliability of the input data set in the method; and
d) The correct interpretation of the forecast, that is, how forecasts will
be used in decision-making.
Regarding
the methods of demands forecasting, there are quantitative methods, based on
historical series, and qualitative methods involving subjectivity, such as
expert opinion. Lemos (2006) points out that several studies show signs that
the integration of the two methods is the best approach to obtain better
predictions.
There
are regular and irregular demands. Lemos (2006) list five patterns of regular
demand: average demand for the period, trend (demand movement over time), seasonality
(repeating peaks and valleys), cyclical factors, and random variation
(unexplained).
Regarding
the pattern of irregular demand, this occurs in cases of high uncertainty about
the moment and level of demand. This scenario is particularly difficult to
predict, and may occur due to several factors such as large orders from some
non-frequent customer and demand derived from other products or events (BALLOU,
2001).
In
the literature it is noted that the Box Jenkins model, also known as ARIMA
(Auto Regressive Integrated Moving Averages), has been widely used for
predictions. This model aims to capture autocorrelation between the values of a
time series and make future predictions (Werner and Ribeiro, 2003). Despite its
good results, a survey conducted in Brazilian food companies indicates that
this method is one of the least used because of the difficulty in understanding
it (CECATTO; BELFIORE, 2015).
Some
studies have pointed to better results with the use of the ARIMA method such as
Werner (2003), who uses this model to forecast demand in the computer technical
assistance area, and Arthus et al. (2016), which compares forecasting methods
for soybean crop in west of Pará State in Brazil.
Another
method found in the literature is the Hierarchical Analytical Process, which
uses comparisons in pairs of variables that affect product`s demand, the weight
given to each variable are defined by specialists. Silva and Werner (2016) use
this method to predict demand in the animal food sector.
There
are also applications of neural networks for demands forecasting, this is the
case of demands forecasting to industrial production of different segments made
by Fávero and Zoucas (2016).
2.2.
Last
period method
In
this method the future demand, month n+1, is calculate based on the previous
month real demand, month n; in other words month by month the last period real
demand is repeated.
2.3.
Simple
Average method (global e per period)
In
this method the future demand is calculated using the average of previous
periods demands. For the global simple average all previous months are
considered; to calculate the demand from period n+1 the demands of months from
1 to n are used. For the simple average per period a period is choosen, for
exemple if the quarter period is choosen the calculated demand for January,
February and March is equal to the three first months real demands average.
Since all values, distant and recent, have
the same weight, the method does not have a rapid response to the last period
data changes (WANKE ; JULIANELLI apud CAMBI; JACUBAVICIUS, 2016).
2.4.
Moving
Average method
The
moving average method is largely used for ease of execution and need of very
few historical data. In it the number of observations (n) considered for the
calculation of the average is kept constant and then the arithmetic or weighted
average of n observations is calculated, eliminating the most distant
observation and including the most recent one.
For
n equal to three, for example, the demand for the month of April would be the
average of the demands from January to March and the one of May would be the
average of the months from February to April. As this method disregard more
distant data it may not be suitable for series with trend and seasonality
(MAKRIDAKIS; WHEELWRIGHT; HYNDMAN apud LEMOS, 2006).
2.5.
Least
Square Averages method
This
method consists of fitting two parameters, a and b, of the equation of a line
(y = ax + b), where y is the prediction for period x, in order to minimize the
sum of the quadratic differences between the line and the predicted points
divided by square of the standard deviation (FILHO et al., 2011).
2.6.
The
glass industry
There
are a numerous utilities and features of the glass such as: brittle material
with much greater compressive than flexural strength, transparent material,
high resistance to chemical attack, thermal insulation efficiency and capacity
of maintenance a vacuum. Nowadays glass manufacturing technologies and methods
have been evolving thus widening its application for a variety of uses, in an
estimated 800 glass types (SHREVE; BRINK JR., 2008).
Physically,
glass can be defined as a rigid sub-cooled liquid with an indefinite melting
point and high viscosity that prevent crystallization (SHREVE; BRINK JR.,
2008); chemically is the result of the union of non-volatile inorganic oxides,
sands and other substances that form a random atomic structure. Even with
numerous new formulations for glass, lime, silica and soda still make up
approximately 90% of the glass in the world, however the small changes introduced
can have effects with great impact in future (SHREVE; BRINK JR., 2008).
Among
the numerous glass classes there are special glasses, which include coloured,
opaline, translucent, safety glasses, including laminated glass and tempered
glass, photosensitive and special for chemical and industrial use (SHREVE;
BRINK JR., 2008).
On
the manufacturing of these products, processes used aim not only at the form
and precision required, but also at the properties that their use requires. The
properties are the result not only of the chemical composition, but also of its
microstructure, which depends, among other factors, on the thermal exposure
suffered by the product during its processing. The properties, in turn, will
determine the performance of the product (KIMINAMI; CASTRO; OLIVEIRA, 2013).
The
heat treatment consists of controlled succession of heating and cooling that
aims to alter the microstructure of the material giving it the desired
characteristics. The controlled thermal annealing, which causes the non-uniform
stresses to be replaced by controlled, uniform and low-intensity voltages,
characterizes tempered glass manufacturing (SHREVE; BRINK JR., 2008). These
techniques are used to obtain various types of glass, such as tempered glass
that is a strong and tough type, which has high internal stresses that shatters
the glass when it is broken.
2.7.
Study
case
According to Gil (2002), a study
case is a deep and exhaustive study of some object, allowing its ample and
detailed knowledge. Yin (2001) cites that for long the study case has been
viewed as a method with insufficient rigor, not providing basis for
generalizations.
Thus Yin (2001) brings the
characteristics of all phases of research that distinguish this method from
others, guiding the researchers who are using it to confer rigor to their work.
For Yin (2001), this strategy of research conducting aims to respond how or why
something happens, there is no control over behavioural events and there is
focus on real events.
The study case research deals with a
unique situation in which there are more variables of interest than data
points; is based on various sources of evidence and uses for its benefit the
prior development of theories.
3. METHODOLOGY
The study evaluated how the
company’s demand behaves based on its real historical sales, and, from the
application of these data, it was analysed the results of the five forecast
methods, what explains the case study strategy chosen.
3.1.
Data
collect and minning
In
order to obtain the data and understand the current status of the demands
planning of the analysed company, interviews were conducted with the company's
production manager, from whom the historical sales were obtained. The received
data are the monthly reports, in PDF format and separated by product category,
of all products sold in the period from January 2015 to April 2017.
For delimitation of the scope,
necessary for the beginning of the analyses, the category that represents the
highest total sales value was chosen. For the products of this category, all
the data were prepared and, through the elaboration of ABC curves of the
quantity of material (m²) and cost price, the three most representative
products were identified in terms of cost and, consequently, inventory. The
validation and data mining were done through interviews and discussions with
the company's production manager.
3.2.
Demand
forescast methods application
The
use of methods with time series analysis is based on the assumption that there
is constancy in the data patterns used in the forecasting process, the model is
adjusted to past data.
After
the choice of products to be analysed, five forecasting methods were applied.
The following methods were used: last period method, global simple average
method, simple average method per period, quarterly period, moving average
method (with previous number considered equal to three) and method of the least
squares average.
The
data obtained from the company comprise a period of twenty-eight months,
between January 2015 and April 2017. From those, the period until March 2017
were used as a basis for the application of the five methods, while the data
from January 2016 onwards were used to compare the actual demands against the
calculated demand by the applied models, and verify which model best suits the
real curve.
3.3.
Prevision
and real forecast comparison
After
the application of the forecasting methods, the obtained models were used to
predict the sales of the last 16 months (from January 2016 to April 2017) and
then the results of the five forecasts methods were compared with the real
demands through the absolute average errors of the sample (SANTOS; RODRIGUES,
2006). After this comparison, the method that best suited with the actual data
(lowest error) was chosen for the three products analysed.
The following equation was used to
calculate the absolute mean error:
(1)
Where, “Rk” is the real
demand for period “k”, “Pk” is the expected demand in period k and
“n” is the total of periods considered.
4. RESULTS
In
the analysed company, the usual period for manufacturing orders, which works
from Monday to Friday, is two days, and the delivery period to customers is
seven calendar days. At the time these study were held, when a new purchase
order is placed, an inventory report is issued and analysed to verify the
requirements for production.
In
case of stock scarcity of the necessary raw material, the suppliers are
contacted for procurement. The usual raw material delivery lead time is three
to five days, but there may be delays, especially in the periods when the
suppliers` furnaces are under maintenance. Thus, when there is no raw material
available there may be delays on the delivery deadline agreed with customers.
The
twenty-eight reports obtained have data of more than thirty products, separated
in the following categories: common glass, mirror, laminated glass, labour,
scrap and tempered glass. For each of those products, the reports contain the
following data: quantity of parts sold, weight, area (m²), cost price and sales
value.
Among
the categories, the Temperate Glass was chosen for analysis, since it is the
category that represents the majority of total raw material costs and company
revenues. As for costs, temperate glass represented 93% in 2015, 73% in 2016
and 73% in the first four months of 2017, with an average of 83% for the 28
months analysed. Regarding billing, it represented 84% in 2015, 65% in 2016 and
59% in the first four months of 2017, with an average of 73% for the 28 months analysed.
In
order to delimit the products of the chosen category that would be analysed, an
ABC curve of the cumulative percentage of total cost price of the 28 months per
product was elaborated, according to Figure 1 below.
Figure 1: ABC curve of accumulated percentage
from total cost per product.
Source:
Elaborated by the authors.
Note from this curve that 14% of the
products (first three) represent 78% of the procurement costs and, hence, of
this category`s inventory. Therefore, were chosen for analysis the three more
representative: uncoloured temperate-glass 8mm, uncoloured temperate-glass 10mm
and uncoloured temperate-glass 6mm. As for the whole company`s purchasing cost
for raw materials, these products correspond to 65%, while only 57% of the net
revenue.
Once the samples were defined, the
analysis begun from sales history with focus on area (m²) sold from each
product. See Figure 2 (below) for their data.
Figure 2: Sales history in m² /product per month
Source:
Elaborated by the authors.
The last period, global simple mean,
simple average per period, moving
average and least square method where applied to the available data-series.
Figures 3, 4 and 5 show the comparison from actual demand, withdrawn from the
sales reports (January 2016 to April 2017), and the results of forecasting
methods calculated from previous data to match report period.
Figure 3: Uncoloured Temperate Glass 8mm -
actual and demand forecast (m²) per month
Source: Elaborated
by the authors.
Figure 4: Uncoloured Temperate Glass 10mm -
actual and demand forecast (m²) per month
Source:
Elaborated by the authors.
Figure 5: Uncoloured Temperate Glass 6mm -
actual and demand forecast (m²) per month
Source:
Elaborated by the authors.
For
the 8mm uncoloured tempered glass, the model with the lowest mean absolute
error was the Moving Average method, with an error of 0.24 followed by the
least squares (0.25), last period (0.27), global simple mean (0.36) and simple
average per period (0.68).
For the uncoloured 10mm glass, the model
with the lowest mean absolute error was the least squares model, with an error
of 0.27, followed by the moving average method (0.33), global simple mean (0,
33), last period (0.34) and simple average per period (0.53).
For
the uncoloured 6mm glass, the method with the lowest mean absolute error was
the moving average method, with error of 0.29, followed by the last period
(0.32), simple average per period (0.33 ), the least squares (0.34) and global
simple mean (0.35).
Figures
6, 7 and 8 below show the comparison of the actual demands with the demands
foreseen by the method that best suited each product per month.
Figure 6: Uncoloured Temperate Glass 8mm (m²)
Source:
Elaborated by the authors.
Figure 7: Uncoloured Temperate Glass 10mm (m²)
Source:
Elaborated by the authors.
Figure 8: Uncoloured Temperate Glass 6mm (m²)
Source:
Elaborated by the authors.
The
demands obtained by the forecasting methods chosen for each product differ from
the actual demands of the analysed periods with absolute mean errors of 0.25 to
0.29, where there were periods with larger and lower forecasts than those
presented in the real data.
By
applying the chosen methods there would be no need to order during the months when
the forecasts were higher than the actual demands, and there are no delays in
delivery times to customers due to lack of raw material, however over the
months where forecasts were lower than actual demand, there would be a need to
purchase raw materials, but with fewer occurrences than those without
forecasting (current situation), since new orders would be needed only for the
difference between the forecasts and the actual demands.
In
both cases, the application of the chosen forecasting methods could increase
company`s responsiveness on deliveries to customers by reducing production
delays due to lack of raw material. The method also reduces bottlenecks in
production, reduces idle labour, and increases the company's competitiveness
over to competitors.
5. CONCLUSIONS
Among the forecast methods avaluated
in this work, the methods that presented the best results (smallest mean
absolute errors) were the moving average methods, with an error of 0.24 for
uncoloured temperate glass of 8mm and of 0.29 for the uncoloured temperate
glass of 6mm, and the method of the average of the least squares average, with
error of 0.27 for the uncoloured temperete glass of 10mm.
With the application of forecasting
methods, it is expected to reduce delays in delivery to customers generated by
lack of raw material to start production. In addition to the reduction of
deadlines, the application of forecasting methods tends to reduce bottlenecks
in production and idle labor caused by lack of raw material and increase
competitiveness compared to competitors due to the reduction in the delivery
time of orders to customers.
The three analyzed products
represent a total of 78% of the stock value of the analyzed category, tempered
glass, and 65% of the total value of the company's stock; as to billing, they
account for 73% of the value of the analyzed category and 57% of the total of
the company and serve as the basis for structuring the best analysis model.
After structuring the model, the application to the other items can be done directly
with the existing historical data. This result is effective when compared to no
application of any method (as performed by the company).
It is worth noting that the wide
range of products (finishings) whose choices are exclusive (the customer who
chooses a green tempered glass will not opt for colorless glass, for example)
makes forecasting difficult and statistical models even more relevant.
The applied methods are
quantitative, considering only historical data, not counting with the opinion
of a specialist. For better results it is indicated that the prevision of na
specialist (qualitative method) is incorporated into the quantitative
forecasting methods. Modeling serves as support for decision making. By adding
the modeling to the forecasts of external events, a more assertive future
demand perspective can be obtained. Thus, it is expected that the sum of the
methods proposed with the analysis of the managers contributes to the correct
acquisition of material, reducing unnecessary stocks and delays in deliveries
to the customers.
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