FORECASTING SPARE PARTS DEMAND: A CASE STUDY

AT AN INDONESIAN HEAVY EQUIPMENT COMPANY

RYAN PASCA AULIA

DEPARTMENT OF STATISTICS

FACULTY OF MATHEMATICS AND NATURAL SCIENCES

BOGOR AGRICULTURAL UNIVERSITY

BOGOR

2014

PERNYATAAN MENGENAI SKRIPSI DAN

SUMBER INFORMASI SERTA PELIMPAHAN HAK CIPTA

Dengan ini saya menyatakan bahwa skripsi berjudul Forecasting Spare

Parts Demand: A Case Study at an Indonesian Heavy Equipment Company adalah

benar karya saya dengan arahan dari komisi pembimbing dan belum diajukan

dalam bentuk apa pun kepada perguruan tinggi mana pun. Sumber informasi yang

berasal atau dikutip dari karya yang diterbitkan maupun tidak diterbitkan dari

penulis lain telah disebutkan dalam teks dan dicantumkan dalam Daftar Pustaka di

bagian akhir skripsi ini.

Dengan ini saya melimpahkan hak cipta dari karya tulis saya kepada Institut

Pertanian Bogor.

Bogor, Agustus 2014

Ryan Pasca Aulia

NIM G14100017

ABSTRACT

RYAN PASCA AULIA. Forecasting Spare Parts Demand: A Case Study at an

Indonesian Heavy Equipment Company. Advised by FARIT MOCHAMAD

AFENDI and YENNI ANGRAINI.

Forecasting spare parts demand is a common issue dealt by inventory

managers at maintenance service organization. The large number of items held in

stocks and the random demand occurrences make most of the difficulties. An

Indonesian heavy equipment company targets to advance its forecast accuracy.

Accordingly, this study has two main goals. Firstly, all Stock Keeping Units

(SKUs) are classified based on their demand patterns, utilizing their average inter-

demand interval (ADI) and squared coefficient of variation (CV2) of demand sizes

as the classifiers. After that, four simple forecasting methods are applied to each

demand class and the best forecasting method in term of its forecast errors is

chosen. Evaluation of forecast accuracy is made by means of the Mean Absolute

Scaled Error (MASE), MAD-to-Mean ratio, and Percentage Best (PBt). The

forecasting competition results show the dominance of Syntetos-Boylan

Approximation for erratic, smooth, and intermittent demand, and Simple Moving

Average for lumpy demand.

Keywords: demand categorization, demand forecasting, forecast accuracy

Scientific Paper

to complete the requirement for graduation of

Bachelor Degree in Statistics

at

Department of Statistics

FORECASTING SPARE PARTS DEMAND: A CASE STUDY

AT AN INDONESIAN HEAVY EQUIPMENT COMPANY

RYAN PASCA AULIA

DEPARTMENT OF STATISTICS

FACULTY OF MATHEMATICS AND NATURAL SCIENCES

BOGOR AGRICULTURAL UNIVERSITY

BOGOR

2014

Title : Forecasting Spare Parts Demand (A Case Study at an Indonesian

Heavy Equipment Company)

Name : Ryan Pasca Aulia

NIM : G14100017

Approved by

Dr Farit M Afendi, MSi

Advisor I

Yenni Angraini, MSi

Advisor II

Acknowledged by

Dr Anang Kurnia, MSi

Head of Department

Graduation Date:

ACKNOWLEDGEMENTS

Great thanks to God Almighty for the strength, willingness and opportunity

given to me so that I might be able to complete this paper which is entitled

Forecasting Spare Parts Demand: A Case Study at an Indonesian Heavy

Equipment Company. This study is motivated by my literature research during the

internship program held by the Department of Statistics, Bogor Agricultural

University.

I realize that this research could not happen without the support of many

people. Therefore, I would like to express my gratitude to my advisors, Dr Farit M

Afendi MSi and Yenni Angraini MSi, for their guidance and suggestion. I would

also like to thank Asep Iwan Gunawan SSi and Ali Fikri, from Parts Division at

PT United Tractors Tbk, for their help and companion. Finally, I would love to

thank my parents and brother for their prayer and affection which I cannot

possibly return.

I hope this paper would be meaningful to those who need it.

Bogor, August 2014

Ryan Pasca Aulia

CONTENTS

LIST OF TABLES vi

LIST OF FIGURES vi

LIST OF APPENDIXES vi

INTRODUCTION 1

Background 1

Objectives 2

LITERATURE REVIEWS 2

Demand Categorization Scheme 2

Croston’s Method and Syntetos-Boylan Approximation 3

Mean Absolute Scaled Error (MASE) 3

Mean Absolute Deviation to Mean Ratio (MAD-to-Mean) 4

Percentage Best (PBt) 4

METHODOLOGY 4

Data Sources 4

Methods 5

RESULTS AND DISCUSSIONS 6

Demand Categorization Results 6

MASE and MAD-to-Mean Results 7

Percentage Best Results 9

CONCLUSIONS AND EXTENSIONS 10

Conclusions 10

Extensions 11

REFERENCES 11

APPENDIXES 12

BIOGRAPHY 16

LIST OF TABLES

1 Forecasting methods 5 2 Formulas of forecasting methods 5

3 Properties of each demand category 7 4 The Wilcoxon signed ranked test results of each demand category 9

5 The PBt results of each demand category 9 6 The best forecasting method of each demand category 10

LIST OF FIGURES

1 Syntetos et. al (2005) demand categorization scheme 3

2 The median of MASE and MAD-to-Mean acros erratic category

series 7

3 The median of MASE and MAD-to-Mean across lumpy category

series 7

4 The median of MASE and MAD-to-Mean across smooth category

series 8

5 The median of MASE and MAD-to-Mean across intermittent

category series 8

LIST OF APPENDIXES

1 The MASE and MAD-to-Mean results of erratic category 12

2 The PBt results of erratic category 12 3 The MASE and MAD-to-Mean results of lumpy category 13

4 The PBt results of lumpy category 13 5 The MASE and MAD-to-Mean results of smooth category 14

6 The PBt results of smooth category 14 7 The MASE and MAD-to-Mean results of intermittent category 15

8 The PBt results of intermittent category 15

INTRODUCTION

Background

Spare parts in automotive industry posses a wide range of characteristics.

They are highly varied in costs, service requirements, and demand patterns

(Boylan and Syntetos 2008). Many of them are slow-moving as they are only

ordered in small quantities occasionally. Thousands of these items are stored in

the warehouse and they are valuable investments for companies providing

maintenance service.

Demands of spare parts exhibit infrequent and irregular patterns, most of

which are intermittent characterized by high frequency of zero values in demand

history. This condition is sometimes accompanied by large variations of demand

sizes when they occur (erraticity), which creates lumpy demand. These make the

forecast of spare parts demand more difficult, hence a challenging task. Even so,

considerable improvements on forecast accuracy are possibly converted to

reduction of inventory costs and raised customer service levels.

Forecasts of future demands are vital input to an inventory model. They

determine how much stocks held and how much to order from vendors to meet

customer demand. Producing inaccurate forecasts can lead to unfulfilled demands

or stock-outs. Therefore, careful managerial decision must be made in order to

achieve satisfactory customer service at minimum inventory costs.

Many forecasting techniques have been proposed in literature. However, it

is difficult to decide the most superior one and generalize it to a particular case.

This is due to the type of data and how forecast errors are measured. Different

accuracy metrics can pick different forecasting methods as the most accurate one

for the same data. Moreover, optimal parameter value for a certain method may

vary from one condition to another.

The heavy equipment company which provided the data exercised in this

study aims to improve their forecast accuracy. The company applies both

deterministic and stochastic model to generate forecasts. As for the statistical

model, which becomes the focus of this study, they use Simple Moving Average

(SMA) of the previous twelve monthly demands. The forecasts made by those

models act as direct input to determine the maximum inventory level on a max-

min system.

Trying to provide some alternatives, simple forecasting methods usually

found in practice are Single Exponential Smoothing (SES), Croston’s method, and

Syntetos-Boylan Approximation (SBA). These methods are easy to apply in the

software package used by the company and have been reported to produce

reasonable results in previous studies. Their performances are going to be

compared with SMA, which is treated as the benchmark method.

To examine forecast accuracy, the company utilizes the Mean Absolute

Percentage Error (MAPE). Unfortunately, this measure is very problematic in

situation where demands are highly intermittent as it causes degeneracy and

asymmetry issues. For that reason, this study employs different accuracy

measures: the Mean Absolute Scaled Error (MASE), MAD-to-Mean ratio, and

2

Percentage Best (PBt). Each accuracy measure provides its own unique

information.

A comparative study by Syntetos and Boylan in 2005 is used as the primary

reference of this paper. They compared the performance of SMA, SES, Croston’s

method and their new estimator (SBA) on demand series from automotive

industry. The results suggested the superiority of SBA. Moreover, Syntetos and

Boylan made some comments about the behavior of the error measures adopted in

their study.

Due to the large number of Stock Keeping Units (products kept in stock) or

SKUs, and their wide range of characteristics, a classification scheme ought to be

built. To serve this purpose, Syntetos et al. (2005) provided a demand

categorization scheme to select the most appropriate forecasting procedure. They

compared the theoretical Mean Squared Error (MSE) of SES, Croston’s method,

and SBA, and established regions of superior performance of each method. As the

scheme borders, Syntetos et al. constructed the cut-off values of the average inter-

demand interval (ADI) and squared coefficient of variation (CV2) of non-zero

demand to four discrete demand categories (erratic, lumpy, smooth, and

intermittent).

Objectives

The objective of this study is to categorize every spare parts demand history

into four demand patterns and the best forecasting method on each demand

category is decided. Hopefully, this study could offer some recommendations

about the most appropriate forecasting approach to those four demand categories.

LITERATURE REVIEWS

Demand Categorization Scheme

Johnston and Boylan (1996) conducted a simulation study to determine the

condition under which Croston’s method should be used instead of SES. They

discovered that Croston’s method was superior to SES when the average inter-

demand interval (ADI) was greater than 1.25 forecast review periods. The main

contribution of this study was the identification of ADI as a classification

parameter to define intermittency.

Syntetos et al. (2005) continued their work and compared three forecasting

methods (SES, Croston’s method, and SBA) based on their theoretical MSE to

identify the regions of their lesser MSE. They took into account two parameters to

produce their classification scheme (the left side of Figure 1), namely the demand

interval (ADI) and demand size variability (CV2). ADI measured the average

number of time periods between two consecutive demands and CV represented

the standard deviation of demand sizes divided by the average demand sizes when

they occur.

As the result (the right side of Figure 1), they classified demand patterns

into the following categories: erratic (but not very intermittent), lumpy, smooth,

3

and intermittent (but not very erratic). They concluded that SBA was theoretically

expected to perform better than SES and Croston’s method when ADI>1.32

and/or CV2>0.49. For ADI≤1.32 and CV

2≤0.49, Croston’s method was supposed

to perform better than the other two methods. This condition was prevailed when

all points in time were considered. Boylan et. al (2008) later demonstrated by

empirical study that the approximate ADI range 1.18-1.86 is insensitive to issue

points forecast accuracy.

Figure 1 Syntetos et. al demand categorization scheme (Boylan et. al (2008))

Croston’s Method and Syntetos-Boylan Approximation

Croston (1972) observed the inadequacy of SES to forecast items with

intermittent demand, which resulted in excessive stock levels. To handle this

problem, he suggested separate estimates of demand size and frequency.

Furthermore, he modified the basic stock replenishment rules to incorporate his

estimator.

In modeling process, Croston assumed that both demand sizes and intervals

have constant means and variances (stationary) and are mutually independent.

Demand was assumed to occur as a Bernoulli process, thus inter-demand intervals

were assumed to be geometrically distributed. Furthermore, the demand sizes

were assumed to follow the normal distribution (Boylan and Syntetos 2008).

Croston’s method works as follows. When demand occurs, SES estimates of

the average demand size and the average inter-demand interval are updated.

Otherwise, the estimates are the same as the previous ones. If demand occurs in

every period, Croston’s forecasts are identical to those of SES (Boylan and

Syntetos 2008).

In spite of its theoretical superiority, empirical evidence revealed modest

improvements of Croston’s method over simpler forecasting techniques. Syntetos

and Boylan (2001) tried to identify the cause of this discrepancy and found a

mistake on mathematical derivation of Croston’s formulas. They then proposed a

bias-adjusted estimator and compared the performance of the two estimators

through simulation. The outcomes encouraged revision of Croston’s original

estimate to overcome its inherent positive bias.

Mean Absolute Scaled Error (MASE)

Hyndman (2009) proposed an accuracy measure based on scaled errors. It

scales the absolute error based on the in-sample Mean Absolute Error (MAE)

from a benchmark forecasting method, such as the naive method. A scaled error is

4

independent of the scale of the data and is finite except when all historical data are

equal. It is less than one if it is generated by a more accurate forecast than the

average one-step naive forecast computed in-sample and vice versa. The MASE is

simply the average of the absolute scaled error.

Mean Absolute Deviation to Mean Ratio (MAD-to-Mean)

Hoover (2006) recommended the use of MAD-to-Mean as an appropriate

measure to asses forecast accuracy because it is scale independent and intuitively

understandable to both managers and forecasters. This measure is always finite

unless all historical data happen to be zero. Hyndman (2006) argued that MAD-to-

Mean assumes the mean is stable over time, which is often the case with

intermittent data.

Percentage Best (PBt)

Percentage best is defined as the percentage of times that one method

performs better than all other methods. This non-parametric measure requires one

or more descriptive accuracy measures, such as the MASE and MAD-to-Mean, to

provide comparisons on the relative performance of every method in each one of

the series. However, this measure gives no indication on how much one method

outperforms the other methods (Syntetos and Boylan 2005).

METHODOLOGY

Data Sources

The data exercised in this study was queried from a branch office of a heavy

equipment company in Indonesia. They were in forms of sales transaction record

from January 2010 to June 2013. At first, they were pivoted for each parts number

to obtain monthly order quantity (demand). All SKUs that were ordered at least

once during 2012 were further considered. They consisted of bolt, cartridge, filter,

piston, ring, valve, etc.

The demand series were divided into in-sample and out-of-sample set,

where demands in 2013 were reserved for data validation process. To allow for

fair comparisons with SMA which only made use of the latest twelve months data,

the fitting process for all other methods started at January 2012. At the end of

December 2012, one to six months ahead forecasts were made. Each forecasting

method would generate flat forecasts for all horizons.

5

Methods

The procedures involved in this study are:

1. Demand Categorization

Compute for all SKUs the ADI = (ti−ti−1Ni=1 )

Nand CV2 =

X i2N

i=1 −( X i)Ni=1

2N /N

[ X iNi=1 N]

2 where N denote the number of periods with non-zero

demands, t and X refer to time period and demand size when they occur.

Subsequently, each SKU is categorized based on the cut-off values

suggested by Syntetos et al. (2005).

2. Demand Forecasting

Apply the four forecasting methods described in Table 1 to every

demand series. The formulas of those methods are given in Table 2.

Table 1 Forecasting methods

Forecasting Methods Smoothing Constants (α)

Simple Moving Average 12-months span Single Exponential Smoothing 0.05, 0.10, 0.15, 0.20

Croston’s Method 0.05, 0.10, 0.15, 0.20

Syntetos-Boylan Approximation 0.05, 0.10, 0.15, 0.20

Table 2 Formulas of forecasting methods

Forecasting

Methods Formulas

SMA (12) 𝑋 𝑡+1 =1

12 𝑋𝑡−𝑘

11

𝑘=0

SES 𝑋 𝑡+1 = 𝛼𝑋𝑡 + (1 − 𝛼)𝑋 𝑡

Croston

If 𝑋𝑡 = 0, then 𝑋 𝑡+1 = 𝑋 𝑡 , 𝑇 𝑡+1 = 𝑇 𝑡

If 𝑋𝑡 ≠ 0, then 𝑋 𝑡+1 = 𝛼𝑋𝑡 + (1 − 𝛼)𝑋 𝑡 , 𝑇 𝑡+1 = 𝛼𝑇𝑡 + (1 − 𝛼)𝑇 𝑡

𝑑 𝑡+1 =𝑋 𝑡+1

𝑇 𝑡+1

SBA

If 𝑋𝑡 = 0, then 𝑋 𝑡+1 = 𝑋 𝑡 , 𝑇 𝑡+1 = 𝑇 𝑡

If 𝑋𝑡 ≠ 0, then 𝑋 𝑡+1 = 𝛼𝑋𝑡 + (1 − 𝛼)𝑋 𝑡 , 𝑇 𝑡+1 = 𝛼𝑇𝑡 + (1 − 𝛼)𝑇 𝑡

𝑑 𝑡+1 = (1−𝛼

2)𝑋 𝑡+1

𝑇 𝑡+1

The notations of the above formulas (Table 2) are elaborated next.

Xt and X t represent demand and demand forecast in period t while Tt and

T t represent inter-demand interval between the latest and previous demand

and forecasted inter-demand interval in period t. At last, d t symbolizes

forecast of the demand rate in period t.

The smoothing constants exercised are identical to those in Syntetos

and Boylan (2005). It should be noted that the same smoothing constant is

applied to update demand sizes and intervals for the last two methods. In

regard to the initial value of SES, the average demand over the first 24

months is used. Similarly, the average of demand size and inter-demand

6

interval over the first 24 months are taken to be the initial SES estimates of

demand size and inter-demand interval.

3. Forecasts Evaluation

Calculate the forecast errors (MASE, MAD-to-Mean, and PBt) of all

demand series and asses the performance of the four forecasting methods.

The descriptive measures, MASE and MAD-to Mean, are aggregated

across series and the method that generates the lowest median is

considered as the best. To determine the PBt across series, the minimum

MASE and MAD-to-Mean of every forecasting method on each demand

series are first calculated and then ranked. When ties occur on a series, all

methods with minimum MASE or MAD-to-Mean value are tallied. The

method that produces the highest PBt is regarded as the best method.

Finally, the best forecasting method on each category is compared

with SMA. Two-sided Wilcoxon signed rank tests are conducted to test the

median of pair-wise MAD-to-Mean difference between the best

forecasting method and SMA across series. The null hypothesis is the

median of differences between the two corresponding methods is equal to

zero.

The test statistic (W) is obtained the following way. Initially, the

signed differences on each series are calculated and their absolute values

are ranked from smallest to largest across series. Afterward, the sign of the

differences is assigned to the resulting rank associated with them and the

sum of the ranks with positive and negative signs is computed. The

smaller of the two sums is the test statistic. For large number of series (n),

W∗ =W−n(n+1)/4

n n+1 (2n+1)/24 approximately follow standard normal distribution

(Daniel 1990).

RESULTS AND DISCUSSIONS

Demand Categorization Results

A total of 9,308 SKUs have been forecasted, 7,432 of them fall into the

intermittent category. The other 1,320 items are categorized as lumpy demand,

while the remaining 279 and 277 items fall into the erratic and smooth category.

Overall, the ADI ranges from 1 to 35 months with median 8.75 months and the

CV2 ranges from 0 to 6.8 with median 0.12. The average demand per unit time

ranges from 0.03 to 21,380.33 units per month.

The properties of SKUs on each demand category are shown in Table 3.

SKUs on intermittent category are highly varied in inter-order interval, some are

only ordered once in a year while the other are ordered more frequently. They,

together with those on lumpy category, are very slow-moving and yet make the

majority of items held in stocks. Meanwhile, SKUs on smooth and erratic

category are ordered almost every month although they are ordered with very

variable quantities.

7

Table 3 Properties of each demand category

Demand Categories

Average Demand

per Period (unit

per month)

Squared

Coefficient of

Variation of

Demand Sizes

Average Inter-

demand Interval

(month)

Median IQR Median IQR Median IQR

Erratic 8.083 14.236 0.744 0.466 1.129 0.177

Lumpy 1.278 2.090 0.750 0.464 2.917 3.056

Smooth 11.500 26.722 0.353 0.141 1.029 0.167

Intermittent 0.139 0.333 0.080 0.210 11.667 12.500

MASE and MAD-to-Mean Results

The MASE results generally confirm those of the MAD-to-Mean. For

erratic and smooth category they pick SBA (α=0.20) as the best method, while for

the lumpy category SMA is considered as the best. Slight disagreement is

observed on intermittent category. The MASE of SBA (α=0.05) is the lowest

across series, while SES (α=0.05) results in the lowest MAD-to-Mean followed by

SBA (α=0.05).

On erratic category (Figure 2), SMA is better than smoothing methods for

lower smoothing constants (α=0.05, 0.10) but worse for higher ones (α=0.10,

0.15). It can be seen from Figure 2 that SBA continually performs better than the

rest smoothing methods, with one exception for its MASE at α=0.05 where SES is

better. On lumpy category where SMA is the best, SES constantly performs as the

second best followed by SBA and Croston as shown in Figure 3.

Figure 2 The median of MASE and MAD-to-Mean across erratic category series

Figure 3 The median of MASE and MAD-to-Mean across lumpy category series

8

SBA once again performs better than the remaining forecasting methods on

smooth category apart from its MASE at α=0.05 (Figure 4). This is also the case

with intermittent category excluding its MAD-to-Mean at α=0.05 (Figure 5). It

should be noticed from Figure 5 below that SES performance on intermittent

category deteriorates greatly for alphas higher than 0.05.

Figure 4 The median of MASE and MAD-to-Mean across smooth category series

Figure 5 The median of MASE and MAD-to-Mean across intermittent category

series

Higher smoothing constant is preferred for erratic, lumpy, and smooth

category, where α=0.20 generally produces the best result. In contrast, lower

smoothing constant (α=0.05) is found to be optimal for intermittent category. This

study also finds that, for the same alpha values, SBA performs better than Croston

in all cases. These outcomes can be verified from the line plots shown above.

On the whole, the MAD-to-Mean of lumpy category is the highest among

other demand categories which makes this category hardest to forecast. As

expected, the MAD-to-Mean of smooth category is found to be the lowest.

Regarding the MASE results, intermittent category produces MASE across series

which is considerably below the other three demand categories. This means that

on this category the performance of all corresponding methods is the finest when

compared to the naive forecasts.

Talking about the variation of MASE and MAD-to-Mean across series, the

inter-quartile range (IQR) of MASE and MAD-to-Mean on lumpy and

intermittent category is much higher than those of erratic and smooth category.

This can be interpreted as SKUs on these categories are forecasted with various

levels of accuracy. Perhaps this is contributed by the large number of items which

fall in these categories.

As mentioned earlier, the performance of the best forecasting method on

each category is going to be compared with SMA which is viewed as the standard

9

method. Since SMA is the best on lumpy category, it is going to be compared

with the second best method (SES with α=0.20). Exception is made on

intermittent category, where SES (α=0.20) generates the lowest MAD-to-Mean. In

its place, SBA (α=0.20) is going to be matched with SMA because of its more

stable forecast errors across alpha values.

The two-sided Wilcoxon signed rank test results are reported in Table 4.

All methods with exemption on lumpy category show significant improvement

over SMA at 1% significance level. In addition, there is not enough evidence that

SMA is better than SES (α=0.20) on lumpy category. Nevertheless, SMA is the

one recommended here owing to its simple calculation.

Table 4 The Wilcoxon signed rank test results of each demand category

Demand Categories Wilcoxon Signed Ranked Tests 𝑊∗ Statistic P-value

Erratic SBA (α=0.20) vs. SMA 4.702 0.000

Lumpy SES (α=0.20) vs. SMA 0.338 0.735

Smooth SBA (α=0.20) vs. SMA 3.748 0.000

Intermittent SBA (α=0.05) vs. SMA 32.337 0.000

Percentage Best Results

The Percentage Best results based on MASE and MAD-to-Mean are alike,

so they are averaged and rounded to the nearest half percentages in Table 5. This

is in line with Syntetos and Boylan (2005) finding that PBt seems to be insensitive

to the descriptive measure chosen. Additionally, the accuracy differences on

MASE and MAD-to-Mean across series are not necessarily reflected on PBt,

which only counts the number of series for which one method performs better

than all other methods based on their MASE or MAD-to-Mean values.

Table 5 The PBt results of each demand category

Forecasting Methods Demand Categories

Erratic Lumpy Smooth Intermittent

SMA 18.0% 24.5% 16.0% 13.5%

SES 25.5% 31.0% 24.5% 34.5%

CRO 19.0% 16.5% 21.0% 8.0%

SBA 37.5% 28.0% 38.5% 44.0%

Table 5 suggests the superiority of SBA, with the exception for lumpy

category where SES performance is slightly better than SBA. This indicates that

SBA is suitable for majority of the SKUs though different smoothing constant

should be implemented depending on their demand characteristics.

10

The forecast errors of all methods are still considerably high, which is

probably attributable to the long forecast horizon. The benefits obtained from the

above-discussed methods seem lost when forecasting is done for more than one

period ahead. This is related to the ability of those methods which can only

produce flat forecasts no matter how long the forecast horizon is. The best

forecasting method for each demand category based on three error measures is

recapped in Table 6.

Table 6 The best forecasting method of each demand category

Demand Categories Forecast Accuracy Measures

MASE MAD-to-Mean PBt

Erratic SBA (α=0.20) SBA (α=0.20) SBA

Lumpy SMA SMA SES

Smooth SBA (α=0.20) SBA (α=0.20) SBA

Intermittent SBA (α=0.05) SES (α=0.05) SBA

Based on this table, SBA (α=0.20) is recommended for both erratic and

smooth category. Meanwhile, SBA (α=0.05) is advised for intermittent category

considering SES deteriorating performance on higher alpha values. As for lumpy

category, the hardest category to forecast, SMA is preferred than SES (α=0.20) on

account of its simplicity. This is of course a rather surprising finding, which calls

for more investigation. It should be pointed out that these outcomes may only be

applicable to the current data set.

CONCLUSIONS AND EXTENSIONS

Conclusions

This study attempts to provide alternative forecasting strategy for an

Indonesian heavy equipment company. To help achieving this goal, SKUs are

classified into four demand categories, making use of their average inter-demand

interval and squared coefficient of variation of demand sizes as the classification

parameters with the cut-off values suggested from literature. The forecasting

results imply that Syntetos-Boylan Approximation is the most appropriate

forecasting method for erratic, smooth, and intermittent demand. On the other

hand, Simple Moving Average should be maintained as the standard forecasting

method for items with lumpy demand. Nonetheless, the search for a more

powerful forecasting method which is straightforward to apply on the company

software package is not over yet.

11

Extensions

Several extensions can be made for future studies. The optimization of the

smoothing constants used to update forecasts has not been taken into

consideration. Also, the effect of forecast lead time on forecast accuracy

necessitates further assessment. More importantly, the forecasting implication of

employing the recommended method on the company inventory system needs to

be evaluated. To practitioners, what matters the most are stock control

performance metrics such as inventory turnover and customer service level.

REFERENCES

Boylan JE, Syntetos AA. 2008. Forecasting for Inventory Management of Service

Parts. In: Kobbacy KAH, Murthy DNP, editors. Complex System Maintenance

Handbook. London (GB): Springer-Verlag. pp 479-508.

Boylan JE, Syntetos AA, Karakostas GC. 2008. Classification for Forecasting and

Stock Control: A Case Study. J Opl Res Soc. 59: 473-481.

Croston JD. 1972. Forecasting and Stock Control for Intermittent Demands. Opl

Res Q. 23: 289-304.

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Appendix 1 The MASE and MAD-to-Mean results of erratic category

Forecasting Methods MASE MAD-to-Mean

Median IQR Median IQR

SMA 0.795 0.531 0.640 0.364

SES (α=0.05) 0.882 0.688 0.688 0.517

SES (α=0.10) 0.826 0.551 0.640 0.425

SES (α=0.15) 0.778 0.539 0.615 0.385

SES (α=0.20) 0.765 0.559 0.607 0.381

CRO (α=0.05) 0.908 0.701 0.699 0.541

CRO (α=0.10) 0.840 0.600 0.650 0.487

CRO (α=0.15) 0.805 0.553 0.638 0.414

CRO (α=0.20) 0.778 0.566 0.618 0.406

SBA (α=0.05) 0.892 0.722 0.678 0.529

SBA (α=0.10) 0.815 0.547 0.635 0.475

SBA (α=0.15) 0.757 0.569 0.613 0.419

SBA (α=0.20) 0.736 0.572 0.585 0.427

Appendix 2 The PBt results of erratic category

Forecasting Methods PBt

MASE MAD-to-Mean

SMA 17.80% 17.97%

SES 25.64% 25.37%

CRO 19.28% 19.24%

SBA 37.29% 37.42%

13

Appendix 3 The MASE and MAD-to-Mean results of lumpy category

Forecasting Methods MASE MAD-to-Mean

Median IQR Median IQR

SMA 0.723 0.722 1.000 0.636

SES (α=0.05) 0.880 1.071 1.245 1.650

SES (α=0.10) 0.817 0.866 1.200 1.259

SES (α=0.15) 0.789 0.789 1.166 0.984

SES (α=0.20) 0.764 0.779 1.117 1.000

CRO (α=0.05) 1.021 1.519 1.368 2.204

CRO (α=0.10) 0.987 1.372 1.326 2.078

CRO (α=0.15) 0.959 1.286 1.288 1.960

CRO (α=0.20) 0.931 1.235 1.292 1.884

SBA (α=0.05) 1.019 1.490 1.347 2.145

SBA (α=0.10) 0.971 1.311 1.307 2.057

SBA (α=0.15) 0.927 1.271 1.271 1.912

SBA (α=0.20) 0.902 1.184 1.254 1.828

Appendix 4 The PBt results of lumpy category

Forecasting Methods PBt

MASE MAD-to-Mean

SMA 24.47% 24.51%

SES 30.94% 30.92%

CRO 16.40% 16.56%

SBA 28.18% 28.01%

14

Appendix 5 The MASE and MAD-to-Mean results of smooth category

Forecasting Methods MASE MAD-to-Mean

Median IQR Median IQR

SMA 0.863 0.570 0.504 0.337

SES (α=0.05) 0.911 0.603 0.499 0.386

SES (α=0.10) 0.863 0.553 0.500 0.348

SES (α=0.15) 0.863 0.543 0.500 0.324

SES (α=0.20) 0.882 0.533 0.487 0.331

CRO (α=0.05) 0.911 0.630 0.498 0.395

CRO (α=0.10) 0.891 0.548 0.492 0.344

CRO (α=0.15) 0.878 0.521 0.502 0.352

CRO (α=0.20) 0.890 0.528 0.511 0.349

SBA (α=0.05) 0.894 0.612 0.490 0.393

SBA (α=0.10) 0.863 0.535 0.486 0.346

SBA (α=0.15) 0.838 0.524 0.478 0.330

SBA (α=0.20) 0.818 0.546 0.464 0.341

Appendix 6 The PBt results of smooth category

Forecasting Methods PBt

MASE MAD-to-Mean

SMA 16.14% 16.31%

SES 24.41% 24.36%

CRO 21.06% 21.02%

SBA 38.39% 38.31%

15

Appendix 7 The MASE and MAD-to-Mean results of intermittent category

Forecasting Methods MASE MAD-to-Mean

Median IQR Median IQR

SMA 0.688 0.733 1.000 0.667

SES (α=0.05) 0.550 0.866 0.831 1.271

SES (α=0.10) 0.620 0.756 1.037 1.017

SES (α=0.15) 0.688 0.884 1.161 1.047

SES (α=0.20) 0.707 0.938 1.229 1.465

CRO (α=0.05) 0.541 1.001 0.892 1.618

CRO (α=0.10) 0.552 0.986 0.921 1.587

CRO (α=0.15) 0.563 0.975 0.948 1.532

CRO (α=0.20) 0.591 0.964 0.979 1.495

SBA (α=0.05) 0.533 0.994 0.887 1.593

SBA (α=0.10) 0.543 0.982 0.899 1.540

SBA (α=0.15) 0.550 0.971 0.915 1.480

SBA (α=0.20) 0.555 0.951 0.925 1.473

Appendix 8 The PBt results of intermittent category

Forecasting Methods PBt

MASE MAD-to-Mean

SMA 13.58% 13.63%

SES 34.61% 34.56%

CRO 8.03% 8.09%

SBA 43.78% 43.73%

16

BIOGRAPHY

Ryan Pasca Aulia was born in Padang as the eldest son of Ahmad Fauzan

and Yasmurti Pertamasari on September 16 1993. He completed high school

education from SMAN 10 Padang and MTsN Model Padang before pursuing his

Bachelor of Statistics degree at Bogor Agricultural University in 2010. During his

sophomore and junior years, he took some basic courses in Financial and

Actuarial Mathematics.

He was a member of Beta Club, the English club of statistics undergraduate

student. He contributed to the 8th Statistika Ria and Kompetisi Statistika Junior

2013 as the competition staff. He was also a semifinalist to the national statistics

competition at the 9th Statistika Ria and Seminar Nasional & Olimpiade Nasional

Statistika 2013.