ANALYSIS AND SELECTION OF A QUANTITATIVE FORECASTING MODEL FOR AN ENTERPRISE IN THE ELECTRONIC SECTOR

171 | P a g e

ANALYSIS AND SELECTION OF A QUANTITATIVE

FORECASTING MODEL FOR AN ENTERPRISE IN

THE ELECTRONIC SECTOR

Ing. Marissa González Luna

, Dr. Manuel Alonso Rodríguez Morachis

Student of the

Masters in Administrative Engineering in the Division of Graduate Studies

and Research of the Technological Institute of Ciudad Juárez.

2

Research Professor of the Division of Postgraduate Studies

and Research of the Technological Institute of Ciudad Juárez, Mexico.

ABSTRACT

In today's business environment, a company's success depends largely on good management of its supply chain.

Problems are often encountered at the beginning of the supply chain, which is the procurement of materials, due

to poor planning of customer demand and misalignment of sales forecasts into the future. In this article, the

historical data of an electronic company is analyzed, to select the best quantitative forecast model comparing the

methods of Simple and Double Exponential Smoothing and Hold-Winters Smoothing.

Keywords

:

Double Exponential Smoothing, Forecasting Methods, Hold-Winters, Inventory

Control, Simple Exponential Smoothing, Supply Chain.

I. INTRODUCTION

The manufacturing activity is encompassed in the supply chain activities, ranging from procurement of materials

to customer service and delivery. Based on this, it can be said that everything starts with a good prediction of

what is going to happen in the future, knowing that, the company assures its survival in the market by always

being ahead in the prediction of the future demands of the customers.

Many of the forecasting techniques in use today were developed in the 19th century. Before the advent of more

sophisticated forecasting techniques and computer power, the administrator's judgment was the only possible

forecasting tool [1].

García et al. (2009) analyzes that according to Hanke and Reitsch (1996) the forecasts can be classified into two

main criteria: the first criterion is time, that is, there are short and long term forecasts. The latter helps to

establish the general course of the organization over a long period of time, while the former is used to design

strategies that will have immediate use and will be implemented by middle levels in the organization. The

second type of criterion classifies forecasts in qualitative and quantitative; the first is applied when a person's

judgment is issued, while the quantitative ones refer to mechanical processes that result in mathematical data

[2].

In the company investigated, the best quantitative forecast model was analyzed with the objective of

172 | P a g e

materials. In addition, material losses due to waste, quality defect or loss, as well as sudden client orders were

taken into consideration.

Rodriguez-Coy and Rodríguez-Morachis (2010) assert that the forecast of the demand has always been

an important issue in the administration and control of operations; activities such as decision making, inventory

management, new product development, production, and supply chain planning all require a good forecast

prediction [3].

According to Chapman (2006), a basic forecasting concept would be: The formulation of forecasts (or

projection) is a technique that uses past experiences in order to predict future expectations. Some characteristics

of the demand forecasts are [4]:

 Demand forecasting typically originates in marketing [5].

 The forecastsupports the decisions that are based on it [6].

 All the forecasts will be wrong, some will exceed the demand and others will be below it, the secret for the

forecast to be successful is to choose the technique that offers the least amount of error [7].

 Quantitative methods are more accurate and convenient to use if historical data is available [8].

II. MATERIALS AND METHODS.

In this section, the historical data of an electronic company is analyzed, to select the best quantitative forecast

model comparing the methods of Simple and Double Exponential Smoothing and Hold-Winters Smoothing.

2.1 Simple Exponential Smoothing Methodology.

This is one of the techniques most used in forecasting. In the exponential smoothing method, only three pieces

of data are needed to forecast the future: the most recent forecast, the actual demand that occurred during the

forecast period and an alpha uniformity constant (α). This smoothing constant determines the level of uniformity

and rate of reaction to the differences between forecasts and real occurrences [9]:

The equation for a single forecast is:

(1)

Where:

Ft= Prognosis smoothed exponentially for period t.

Ft-1= The forecast smoothed exponentially for the previous period.

At-1= The real demand for the previous period.

α = The response rate or the smoothing constant.

This equation establishes that the new forecast is equal to the previous forecast plus a portion of the error.

For the choice of the appropriate value of alpha, exponential smoothing requires giving the smoothing constant

173 | P a g e

desired in order to provide a better track to the demand change [9].

2.2 Double Exponential Smoothing Methodology.

If a trend model were to be predicted using simple exponential smoothing, the forecast would have a delayed

growth reaction. The forecast would then tend to underestimate the real demand. To correct this, one can

estimate the slope and multiply the estimate by the number of future periods to be forecast. Dual exponential

smoothing incorporates the influence of trend and seasonality when specific values for these components can be

identified. The calculation of double exponential smoothing is similar to that of the basic smoothing model,

except that there are three components and three smoothing constants to represent the components: basic, trend,

and seasonal[10].

The system of equations is as follows [1]:

The series smoothed exponentially or estimated current level.

(2)

The estimate of the trend.

(3)

The forecast for the pperiods of the future.

(4)

Where:

Lt= New smoothed value (current level estimate).

α = smoothing constant for the level (0 <α <1)

Yt= New observation or actual value of the series in period t.

β = Smoothing constant for the trend estimate (0 <α <1).

Tt = Trend estimate.

P = Periods to be forecast in the future.

Forecast for period p in the future

.

2.3 Hold-Winters Smoothing Methodology.

The Winters method is a useful procedure when there is tendency and seasonality, and these two components

are additive or multiplicative. The Winters Method calculates dynamic estimates for three components: level,

174 | P a g e

values for the seasonal component are obtained from a regression of indicator variables using data without trend

[11].

There are two models of the Winters formulas, the multiplicative and the additive. The multiplicative model is

used when the magnitude of the seasonal pattern increases as the data values increase and/or decreases as the

data values decrease. The additive model is used when the magnitude of the station pattern does not change

when the series goes up or down. If the pattern in the data is not very obvious and there is trouble choosing

between additive and multiplicative procedures, both procedures can be used and the one with the smallest

accuracy measurements can be chosen. The following equations are the smoothing equations of the

Hold-Winters method [11]:

Smoothing equation for the additive model:

(5)

(6)

(7)

(8)

Smoothing equation for the multiplicative model:

(9)

(10)

(11)

(12)

Where:

Lt = Level at time t.

α = The weighting for the level.

Tt = Trend estimate at time t.

 = Weighting for the trend.

St = The seasonal component at time t.

 = The weighting for the seasonal component.

P = The seasonal period.

Yt = Value of the data at time t.

Forecast in a period ahead in time t.

2.4 Forecast Error.

According to Ballou (2004). The forecast error is defined as [12]:

(13)

Where:

175 | P a g e

Models.

Forecast Demand vs. Real Demand Calculations Choose of the Best Forecast Model for Each Part number Forecast and Demand Error Calculations Forecast and Demand Error Calculations Forecast and Demand Error Calculations Simple ExponentialSmoot hing DoubleExponential Smoothing Hold- Winters Smoothing Forecasting Methods to be Tested

Data Analysis Recollection of Historical Data DR= Actual demand.

Dp= Forecast demand.

For this investigation, the historical data of 55 periods were collected. A period includes the use plus the waste

of material, each period represent a week. Samples were taken from two part numbers, 300-05798 key product

for the customer and high value part; N10-2222LF high volume and common use in 53% of the products

manufactured by the company.

The software used for the research is Minitab 17 Statistical Software®, this application provided several options

of forecast models, with which it was possible to define the trend of the data and to provide an adequate forecast

for data collected.

Figure 1 shows in general the steps to follow in the methodology for this research, after the

identification of the problem what follows is the collection of the data and the analysis of the same, analysis

shows that both numbers obey horizontal patterns and / or seasonal, it is for this reason that the following

methods that estimate these types of patterns will be tested: Simple Exponential Smoothing, Double Exponential

Smoothing, and Hold- Winters Smoothing.

176 | P a g e

Table 1.Calculated Quantity of Use Plus the Delay in Sales (300-05798).

Table 2. Calculated Quantity of Use Plus the Delay in Sales (N10-2222LF).

After observing the patterns of the data, a normality test was applied, which indicates that the data has a normal

trend and parametric tests of averages comparison and tests of variances can be used, in order to demonstrate the

hypothesis that the real data is statistically equivalent to those predicted for each of the selected models.

To present results and select the best forecast model, after having obtained the calculations for the three selected

models, comparing the forecast demand vs. the real demand, in addition to reviewing the forecast error where

the error is smaller and the forecast is closer to the real demand would be the most appropriate method.

177 | P a g e

Figure 3. Simple Exponential Smoothing with Values of 0.6 (N10-2222LF).

III. RESULTS.

After nine weeks of follow-up to the selected models for each part number, the conclusion is that the models

continue to give a good fit to the actual data in Tables 3 and 4.The tables show the results week to week of

178 | P a g e

implemented by the company.

Table 3.Follow-up to Number 300-05798.

179 | P a g e

than the forecasts currently being handled by the company. If the change in the wayof forecasting data is

implemented, only in these two part numbers taken from the sample it will generate a reduction in the cost of

maintaining inventory of $408,658.43 American dollars in just 9 weeks.

IV. DISCUSSION.

At the beginning of this investigation it was found that the company did not have a method to calculate demand

forecasts in a reliable way, since the same department of marketing is aware that the demand they present to the

purchasing department has an accuracy of the 46%, leading the company to have over inventory of materials

that does not require up to fourteen million dollars, with a sales delay of sixteen million dollars.

It is thus decided to analyze the historical data collected for 55 weeks and to calculate a better forecast

by means of quantitative methods, and after testing several methods, it is concluded that for the part number

300-05791 reliable demands can be obtained using the Double Exponential Smoothing method and for the

N10-2222LF good results are obtained using the Simple Exponential Smoothing method.

The methodology described in the research is not exclusive to only those two part numbers, since it has

mathematical validity, it is recommended to extend this analysis to the rest of the products that represent a

problem in the company, since these numbers model the greater part of the behaviors of the finished products

that the company produces. Greater benefits can be obtained in the planning of its raw materials as well as

reduction of costs by maintenance of inventory.

In addition, considering that the models investigated are of universal validity, their application in other

products of different branches in the manufacturing industry is recommended, since as has been seen in other

investigations carried out in other companies of the manufacturing sector of the region, quantitative forecasting

methods have solved the problem of calculating demand forecasts in each of the case studies.

REFERENCES

[1] Hanke J. y Wichern D (2010). Pronósticos en los negocios. 9na. Ed. Pearson Educación. Naucalpan de

Juárez, Estado de México, México.

[2] García S. A., Vázquez C. D., Reyes O. H., Sáenz S. A., Limón L. A. (2009). Investigación en el ámbito

empresarial “Pronósticos, supervisión e indicadores financieros” (Estudios de casos) Edición electrónica

Texto completo en www.eumed.net/

[3] Rodríguez-Coy. M. y Rodríguez-Morachis. M. (2010). Aplicación de Métodos de Pronósticos en Productos

con Demandas Inciertas. 3er. Congreso Internacional de Investigación CIPITECH, (3), 8, 618-624.

[4] Chapman S. (2006). Planificación y control de la producción. México: Pearson. Naucalpan de Juárez,

Estado de México, México.

[5] Krajewski L., Ritzman L. y Manhotra M. (2008). Administración de Operaciones: Procesos y Cadena de

Valor. 8va Ed. Pearson Educación Naucalpan de Juárez, Estado de México, México.

[6] Chopra, S. y Meindl, P. (2008). Administración de la Cadena de Suministro. Estrategia, Planeación y

180 | P a g e

Ed. Cengage Learning. Pennsylvania, EE.UU.

[8] Nahmias S. (2007). Análisis de la producción y las operaciones. 6ta. Ed. McGraw-Hill México, D.F.

México.

[9] Chase R., Jacobs R. y Aquilano N. (2009) Administración de operaciones: Producción y cadena de

suministros. 12ma Ed. McGraw-Hill. México D.F. México.

[10] Bowersox D, Closs D y Cooper M. (2007).Administración y logística en la cadena de suministros. 2da

Ed.McGraw-Hill. México D.F. México.

[11] Minitab Inc., “Métodos para analizar series de tiempo”. (Documento Web Copyright © 2016).

http://support.minitab.com/es-mx/minitab/17/topic-library/modeling-statistics/time-series/basics/methods-for-analyzing-time-series/ September 25th 2016.

[12] Ballou R. (2004). Logística: Administración de la cadena de suministro. 5ta Ed.Pearson Educación.