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Classification for forecasting and stock control: A case study
Article in Journal of the Operational Research Society · April 2008
DOI: 10.1057/palgrave.jors.2602312 · Source: OAI
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Journal of the Operational Research Society (2008) 59, 473 --481

2008 Operational Research Society Ltd. All rights reserved. 0160-5682/08 $30.00
www.palgrave-journals.com/jors
Classification for forecasting and stock control:
a case study
JE Boylan1∗ , AA Syntetos2 and GC Karakostas3
1 Buckinghamshire
and
3 Eurometal
Chilterns University College, Buckinghamshire, UK; 2 University of Salford, Salford, UK;
SA, Greece
Different stock keeping units (SKUs) are associated with different underlying demand structures, which in
turn require different methods for forecasting and stock control. Consequently, there is a need to categorize
SKUs and apply the most appropriate methods in each category. The way this task is performed has significant
implications in terms of stock and customer satisfaction. Therefore, categorization rules constitute a vital
element of intelligent inventory management systems. Very little work has been conducted in this area and,
from the limited research to date, it is not clear how managers should classify demand patterns for forecasting
and inventory management. A previous research project was concerned with the development of a theoretically
coherent demand categorization scheme for forecasting only. In this paper, the stock control implications of
such an approach are assessed by experimentation on an inventory system developed by a UK-based software
manufacturer. The experimental database consists of the individual demand histories of almost 16 000 SKUs.
The empirical results from this study demonstrate considerable scope for improving real-world systems.
Journal of the Operational Research Society (2008) 59, 473 – 481. doi:10.1057/palgrave.jors.2602312
Published online 18 October 2006
Keywords: categorization; forecasting; inventory; intermittent demand; case study
Introduction
Inventory management is a very complex problem area and
it is this complexity that has necessitated the development
of intelligent systems to assist decision making. Ultimately,
ordering decisions must be made at the level of the individual
item or product. Thus, operational rules for the classification of stock keeping units (SKUs) are essential components
of inventory systems. They allow the appropriate amount
of managerial attention and the right forecasting and stock
control methods to be used on the right products. The classification of SKUs has significant implications for stock-holdings
and customer service levels (CSLs).
Demand categorization has attracted very limited academic
interest. There has been a considerable amount of research
on classifying inventory and forecasting methods, but not on
distinguishing between different demand patterns to guide
forecasting and stock control. Notable exceptions are the
papers by Williams (1984) and Eaves and Kingsman (2004).
Although some work has been done on the implications of
forecasting on stock control (eg, Watson, 1987; Gardner,
1990; Strijbosch et al, 2000), more theoretical and empirical
research is much needed in this area.
∗ Correspondence: JE Boylan, Buckinghamshire Business School,
Buckinghamshire Chilterns University College, Chalfont St Giles,
Buckinghamshire, HP8 4AD, UK.
E-mail: john.boylan@bcuc.ac.uk
The selection of forecasting and stock-control methods is
generally based on the values of parameters that define the
current state of the SKU. The parameters most commonly
applied for this purpose relate to the underlying demand
patterns. Other relevant parameters, not considered in this
research, include discount break-points and foreign exchange
rates (see eg, Kobbacy and Liang, 1999).
This paper offers some empirical evidence on demand categorization based on underlying demand patterns. The forecasting and stock-control classification system employed by a
UK-based software manufacturer is examined. The company
sought to improve the classification capability of its software
by (i) considering alternative classification parameters and
(ii) removing hard-coded classification parameter values and
enabling users to select their own values from appropriate
menus. It is the standard practice of the manufacturer to test
all new approaches extensively, prior to adoption, to establish
‘proof of concept’. The empirical database supplied by the
company for this purpose consisted of the individual demand
histories of approximately 16 000 SKUs from the automotive,
aerospace and chemical industries.
The remainder of the paper is structured as follows. Firstly,
a categorization framework is presented. Secondly, the
company’s old method of classification is summarized. A literature review follows. The objectives of the empirical investigation are stated. These are informed both by the company’s
old classification method and recent theoretical developments.
474
Journal of the Operational Research Society Vol. 59, No. 4
The next sections explain the empirical findings, from forecasting and stock-control perspectives. Unresolved issues are
discussed as part of a ‘research agenda’ for demand categorization. Conclusions are summarized at the end of the paper.
Categorization framework
Infrequent demand occurrences or irregular demand sizes,
when demand occurs, do not allow lead time demand to be
represented by the normal distribution. In these cases, demand
will be called non-normal. By using this nomenclature, it is
not meant that all regular, non-sporadic, non-lumpy demands
are necessarily normally distributed. A different distribution
may be more appropriate, although the normality assumption
should reasonably represent many real-world cases (see eg,
Silver et al, 1998).
A rather modest part of the operational research literature
has been devoted to exploring non-normal demand patterns.
Nevertheless, there are inconsistencies in definitions of nonnormal demand patterns. For example, Williams (1984) argues
that the variances of the number of orders, order sizes and
lead-times should be taken into account, whereas Gelders and
Van Looy (1978) define non-normal patterns by the magnitude
of demand over a calendar year.
A categorization framework has been developed (see
Figure 1), to link definitions of non-normal demand patterns
with factors that have been proposed in the literature. The
first column contains three of these factors. Of course, the
framework can be extended to take other factors into account,
such as the variance of lead-time. The second column defines
‘intermittent’ and ‘erratic’ demand, according to the factors
proposed in the forecasting-categorization of Syntetos et
al (2005). In the final column, ‘lumpy’ demand is defined
according to Syntetos et al (2005), while the ‘clumped’
category contains more regular demand patterns, including
fixed clump-sizes (Ritchie and Kingsman, 1985). The ‘slow’
category is defined according to demand volume. This allows
the ‘slow’ category to be the ‘C’ class in an A–B–C classification by volume. However, in the remainder of the paper,
the company’s usage is followed, where the ‘slow’ category
is restricted to intermittent demand patterns.
In summary, according to this framework:
• An intermittent demand item is an item with infrequent
demand occurrences.
• A slow moving item is an item whose average demand
per period is low. This may be due to infrequent demand
occurrences, low average demand sizes or both.
• An erratic demand item is an item whose demand size is
highly variable.
• A lumpy demand item is an intermittent item for which
demand, when it occurs, is highly variable.
• A clumped demand item is an intermittent item for which
demand, when it occurs, is constant (or almost constant).
The framework is conceptual, rather than operational, since
‘high’ and ‘low’ are not quantified. The conceptual framework was used to guide discussions with the company and
experimentation with their software.
Case study: old method of classification
The empirical investigation presented here is based on the
categorization scheme employed by the forecasting and
stock control software manufacturer, as shown pictorially in
Figure 2. (The nomenclature differs slightly from Figure 1
since an item must be non-intermittent to be ‘erratic’, and
intermittent to be ‘slow’.) The criteria used in this categorization scheme reflect, according to the manufacturer, an
approach that is not untypical within this specialized software
sector.
In the old system, the number of zero demand time
periods (r ), during the last n time periods (n = 13), is
High
Intermittent
Mean inter demand interval
Non-intermittent
Low
Mean demand size
Low
AND/OR
Slow
High
Erratic
Lumpy
AND
Coefficient of variation
of demand sizes
Non-erratic
Low
Figure 1
Clumped
AND
Categorization of non-normal demand patterns.
JE Boylan et al—Classification for forecasting and stock control
Forecasting
475
Stock control
Average demand
Low
Slow
Lumpy
Fast
Erratic
Intermittent
Order frequency
Non-intermittent
High
Low
High
Variability of demand
Figure 2
A software package categorization scheme.
compared against a corresponding break-point to determine
intermittence. (A break-point of 7 has been used traditionally.
If r 7, then demand is classified as intermittent; if r < 7, then
demand is non-intermittent.) In this paper, the term ‘breakpoint’ will be used to denote a critical value of any parameter
that determines the category of an SKU.
The average demand per unit time period (over the last
13 periods) is used as a criterion for further distinguishing
between lumpy and slow-moving SKUs in the intermittent
demand category. (The average demand break-point is set to
0.5.) If demand has been classified as non-intermittent, the
variability of the demand per period is compared against a
specified break-point to further distinguish between fast and
erratic SKUs.
Intermittent demand requirements are estimated using a
13-period simple moving average (SMA (13)). Nonintermittent demand is estimated using various forms of
exponential smoothing, depending on the trend and seasonal
characteristics of the demand series. In the next stage, stock
control applications are selected based on a sub-categorization
scheme. For slow demand, the Poisson distribution is used
to calculate the order quantity. For lumpy demand, a proprietary empirical method is used instead. For non-intermittent
demand, continuous order level or periodic order-up-to-level
methods are used depending on the client’s requirements (with
demand standard deviation adjustments for the erratic SKUs).
Literature review
Williams (1984) analysed the demand data of a public utility
and proposed a method of demand pattern categorization
based on an idea called variance partition. According to
this method, the variance of the demand during lead time is
split into its constituent parts: variance of the order sizes,
transaction variability and variance of the lead times. The
categorization scheme meets various theoretical and practical
requirements that were proposed in Williams’ work.
Nevertheless, the break-points were chosen arbitrarily, so
that they make sense only for the particular situation that was
analysed in the 1984 paper. This raises some doubts about the
potential applicability of the proposed categorization scheme
in other contexts. Eaves and Kingsman (2004) analysed
demand data from the Royal Air Force and concluded that
Williams’ classification scheme did not adequately describe
the observed demand structure. Consequently, a revised classification scheme was proposed (for more details, see Eaves,
2002). The break-point values assigned to the categorization
parameters were chosen subjectively, based on management decisions, thereby restricting the generalization of their
results. Of course, the production of universally applicable
rules was not the objective of either academic paper. In both
papers, a case-study-based solution was developed.
In both categorization schemes discussed above, forecasting methods and stock control models are selected once
the demand patterns have been categorized. This is also true
for the software solution summarized in the previous section.
Johnston and Boylan (1996) re-conceptualized the term
‘intermittence’ by considering the mean inter-demand intervals for which Croston’s (1972) method, specifically designed
for intermittence, outperformed single exponential smoothing
(SES). The authors recommended a rule that if the mean interdemand interval ( p) is greater than 1.25 forecast revision
periods, then Croston’s method should be used, rather than
SES (based on the simulated mean squared error (MSE)). This
form of rule is based on the premise that it is preferable to
identify conditions for superior forecasting performance, and
then to categorize demand based on these results, rather than
the other way round. The essence of the re-conceptualization
lies in this approach and the identification of the mean interdemand interval as a categorization parameter, rather than the
specification of an exact break-point value. Indeed, it seems
more logical to work in the following way: (i) compare
alternative estimation procedures, (ii) identify the regions of
superior performance for each one of them and (iii) define
Journal of the Operational Research Society Vol. 59, No. 4
476
Low
p = 1.32(cut-off value)
High
High
Erratic
(Syntetos & Boylan)
Lumpy
(Syntetos & Boylan)
CV = 0.49
2
(cut-off value)
‘Smooth’
(Croston)
Intermittent
(Syntetos & Boylan)
Low
Figure 3 Demand-based categorization for forecasting (after
Syntetos et al, 2005).
the demand patterns based on the methods’ comparative
performance, rather than arbitrarily defining demand patterns
and then testing which estimation procedure performs best
on each particular demand category.
Johnston and Boylan (1996) compared SES and Croston’s
method, but did not question the validity of Croston’s method
itself. Croston’s (1972) method works in the following way:
estimates of mean demand sizes and intervals are updated
using SES, after a demand occurrence, and the ratio of the size
to interval estimates is used as an estimate of the mean demand
per unit time period. Croston’s estimator was found by
Syntetos and Boylan (2001) to be biased. The Syntetos–
Boylan approximation (SBA) (Syntetos and Boylan, 2005,
2006a) adjusts the biased estimates by applying a multiplicative factor of (1 − /2) to the Croston estimate, where is
the smoothing constant used to update estimates of the mean
inter-demand interval.
Syntetos et al (2005) used the three-stage approach
discussed above to develop a theoretically coherent demand
categorization scheme based on the mean inter-demand
interval ( p) and the squared coefficient of variation of
demand sizes (CV2 ). The definition of the alternative demand
patterns resulted from a direct comparison between the theoretical MSE performances of Croston’s method, SES and the
SBA. Both the parameters and their break-point values were
the outcome of this formal comparison, and the validity of
the scheme was empirically tested and confirmed on 3000
SKUs from the automotive industry. The contribution of this
work lies in the identification of the CV2 as an additional
categorization parameter for demand forecasting purposes.
Nevertheless, inventory control issues were not addressed.
The scheme is presented pictorially in Figure 3.
Purpose of empirical investigation
The old classification scheme used by the software manufacturer was found to have some limitations, in the light of the
theoretical considerations summarized in the previous section.
The categorization of ‘intermittent’ and ‘non-intermittent’
demand was based on the number of zero demand time periods
(r ), during the last n time periods (n = 13). This is a sound
approach, being equivalent to the mean inter-demand interval
recommended in the literature. However, the break-point of
r = 7 was determined subjectively. Therefore, the first objective of the empirical analysis is to compare the forecasting and
stock-control implications of different choices of the breakpoint for the number of zeroes in the last 13 periods. To
conduct this analysis, the following estimators are considered:
SES and SMA (13) for ‘non-intermittent’ demand; Croston’s
method and the SBA for ‘intermittent demand’.
The inclusion of CV2 as a further parameter to distinguish
intermittent demand was discussed with the company. They
were interested in its inclusion at a later stage of development
but did not wish to change too many aspects of their system
at the first stage. Consequently, the CV2 parameter was not
included as a forecasting classification parameter in this study.
In the old system, the categorization of ‘slow’ and ‘lumpy’
demand was based on the average demand. This does not
appear to capture the essence of ‘lumpiness’, as described in
the conceptual framework of Figure 1. This argument was
accepted by the company, since it was known that, in the
old system, low-volume high-variation items had insufficient
stock and high-volume low-variation items had excess stock.
Two categorization variables were discussed, namely the ratio
of variance to mean of demand and the squared coefficient
of variation of demand size (CV2 ). The first measure is an
index of dispersion for the Poisson distribution. The second
measure was preferred by the company, since it is dimensionless and would allow the same variable to be used in distinguishing ‘intermittent’ from ‘non-intermittent’ and ‘slow’ and
‘lumpy’, if CV2 is included in the former categorization at a
later stage of development. Therefore, the second objective of
the empirical analysis is to assess the stock-control implications for slow and lumpy demand, if new forecasting methods
are used and the company replaces average demand by CV2
as the categorization parameter.
In the following sections, the forecasting implications of the
‘intermittent’/‘non-intermittent’ categorization and the stockcontrol implications of the ‘slow’/‘lumpy’ categorization are
summarized, in accordance with the design of the software
package (see Figure 2).
Empirical investigation: forecasting
Summary characteristics of the demand data sets used in this
research are presented in the following table.
The demand data series have been divided into three
blocks: (i) initialization, (ii) calibration and (iii) performance
measurement. The lengths of these blocks are shown in the
final column of Table 1. The ‘initialization block’ is used
to initialize values required for methods based on recursive formulae (such as the mean inter-demand interval for
Croston’s method). In the ‘calibration block’, the optimal
JE Boylan et al—Classification for forecasting and stock control
Table 1
477
Empirical demand data sets
SKUs
Periods
Time bucket
Period breakdown
Motor spare parts
Aerospace spare parts
Chemical products
12 881
3025
53
26
52
60
Monthly
Bi-monthly
Monthly
13/7/6
18/18/16
24/24/12
smoothing constants are identified, based on MSE. Finally,
the optimal smoothing constants are used to update forecasts
in the ‘performance block’, in which performance statistics
are calculated.
The three data sets do not contain items categorized by the
company as ‘obsolete’, ‘dying’ or ‘new’. The data sets contain
only those SKUs with greater than or equal to two zeroes and
less than or equal to eleven zeroes in the last thirteen periods,
excluding the performance block. Also, the data sets do not
include SKUs with strictly less than seven zeroes in the last 13
(excluding the performance period) that were found to have
a 13-period global trend that was statistically significant (5%
level, two-tailed test). The restriction to a minimum of two
non-zero values ensures that all initial values can be calculated by the end of the calibration block, thereby allowing the
recursive formulae to proceed in the performance block. The
other restrictions were in keeping with the broadest range of
definitions of intermittence that the software company found
acceptable.
The forecast error statistics used for reporting results are:
the geometric root mean squared error (GRMSE) and the
average mean absolute error (MAE). As its name implies, the
GRMSE is based on squared errors and taking the appropriate
geometric mean as the summary measure. This summarization may be across time, across series or both. In this study,
the following approach is adopted: (i) calculate mean square
forecast error for each individual series (SKU) and then (ii)
multiply these values together for all n series and take the 2nth
root. This ensures that, when comparing two methods, the
effect of high errors for outlying SKUs cancel out. The properties of the GRMSE measure are discussed further by Boylan
and Syntetos (2006). The MAE averages errors, ignoring their
sign; it is summarized across series by its mean value. For
both measures, GRMSE and MAE, performance is measured
on all points in time and issue points only. The former corresponds to a re-order interval and the latter to a re-order level
system.
As discussed in the section on the purpose of the empirical
investigation, the estimators that are considered for the intermittent demand category (ie demand patterns associated with
a ‘low’ order frequency as determined by the break-point)
are Croston’s method and the SBA. For the non-intermittent
demand category (ie demand patterns with a ‘high’ order
frequency), SES and the SMA (13) are considered. Every
combination of those methods, for each possible break-point,
is tested. In Figure 4, the effect of break-point values is shown
for every pair of the estimators examined. These GRMSE-
Geometric Root Mean Square Error (GRMSE)
Industry
0.86
CR-SMA
CR-SES
SBA-SMA
SBA-SES
0.84
0.82
0.8
0.78
0.76
0.74
0.72
2
3
4
5
6
7
8
9
10
11
Break point (number of zeroes)
Figure 4 Categorization break-points for intermittent demand
(Data set 1).
based results were generated from the first data set, using
issue points only.
Results were also generated for the two smaller data sets
and using the mean MAE. The best break-points varied
slightly by data set and by error measure.
The recommended ranges of break-points are presented in
the following table. The ranges are consistent with the plateaus
shown in Figure 4 for Data set 1, but were recommended on
the basis of their consistency in yielding accurate forecasts
across all data sets and error measures.
Results were also generated for ‘all points in time’.
However, in this case, the results were consistent neither
across data sets nor, in some cases, across error measures.
This is an important element of the research agenda for
demand categorization.
The results in Table 2, for issue points only, indicate the
sensitivity of break-points to the choice of estimators. The
recommended range of break-points relating to the comparison of SES and the Syntetos–Boylan Approximation (SBA) is
consistent with theoretical expectations (Syntetos et al, 2005).
This is not true for the comparison of SES and Croston’s
estimator, in which case lower break-points for mean interdemand intervals were expected (Johnston and Boylan, 1996).
Nevertheless, consideration of the shapes of the curves in
Figure 4 results in an important operational conclusion, not
revealed in previous theoretical investigations. The curves are
478
Journal of the Operational Research Society Vol. 59, No. 4
Table 2
Suggested rules for identifying intermittence (Data sets 1, 2 and 3)
Intermittent
1.
2.
3.
4.
Non-intermittent
Recommended range of
break-point values
(number of zeroes)
Equivalent range of
mean inter-demand
intervals
SMA
SES
SMA
SES
5–7
6–8
2–3
2–4
1.63–2.17
1.86–2.60
1.18–1.30
1.18–1.44
Croston
Croston
SBA
SBA
quite flat for break-points from r = 2 to r = 6 showing that
forecast accuracy is insensitive to the choice of break-point in
this region. In the region from r = 7 (the old company breakpoint) to r = 13, forecast accuracy is highly sensitive to the
break-point value. This conclusion is confirmed by analysis
of mean MAE, where similar results are obtained.
This analysis strengthened the company’s resolve to change
this parameter from being hard-coded to being menu-driven
and to recommend r = 3 as an initial setting. This breakpoint consistently yielded accuracy that was close to the best,
for ‘issue points’, even when the optimal break-point was
somewhat higher. For ‘all points in time’, the setting of r = 3
performed well for Data set 1, but less so for Data sets 2 and
3. The need to customize this setting, based on client data,
remained for ‘all points in time’.
Empirical investigation: stock control
In the next stage of this investigation, stock control related
issues were considered. A demand forecasting system, such
as the one discussed in the previous section, may perform
well in terms of a given accuracy measure, but this does not
necessarily translate into excellent stock-control performance.
Simulation design and performance criteria
At this stage, the results were based mainly on one data
set (Data set 1, motor spare parts). The chemical data set
(Data set 3) was not used at all for stock simulations because
inventory-related data could not be made available. Moreover,
the aerospace spare parts data set (Data set 2) was of limited
use because, for many SKUs, the demand status switched very
frequently across different categories over time, leaving only
a small number (fewer than 30) that were consistently defined
as slow or lumpy. This also affected Data set 1, although to a
much lesser degree. Overall, many SKUs had to be discarded
in order to examine the characteristics of slow and lumpy
data. However, this enabled a more systematic investigation
on the remaining series.
A positive trend of about 6% over 26 months was detected
at the aggregate level for the first data set. This trend was not
detectable at SKU level, but it is possible that it may have
affected the results.
For the purposes of this research, only the intermittent
demand category was evaluated, as improvements in that area
constituted the main objective of the software manufacturer.
The software features the continuous re-order point, order
quantity (s, Q) system, the periodic order-up-to-level (T, S)
system and the periodic order point order-up-to-level (T, s, S)
system. (For a discussion of these systems, see Silver et al,
1998.) In this research, detailed results were obtained only for
an (s, Q) system, in which orders of quantity Q are placed
when the stock falls below the re-order point (s). The simulations were not replicated on the other control systems since
preliminary results indicated no significant differences. This
conclusion is also supported by the findings of the empirical study conducted by Sani and Kingsman (1997) on the
combined performance of statistical estimators and periodic
stock control models.
The order-quantity, Q, was determined by the cumulative
forecast over the lead-time, and s by using an appropriate
distribution. For slow items, a Poisson distribution is assumed.
This is a natural choice for slow movers and reflected the
company’s existing practice. For lumpy items, the proprietary method developed by the company was investigated, in
addition to calculations based on the negative binomial
distribution (NBD). The NBD is included since it satisfies
both theoretical and empirical criteria (Syntetos and Boylan,
2006b). The forecasting methods considered, for both slow
and lumpy items, were: SBA and SMA(13). SMA(13) has
been included as it is the estimator currently employed in
the system. Croston’s method and SES were excluded on the
basis of a further forecasting analysis, the details of which
are beyond the scope of this paper.
The following measures were recorded: (i) individual
SKU time average stock-holding (in units and in value); (ii)
average of (i) over all SKUs; (iii) Customer service level
(CSL) achieved. The ‘CSL’ is defined as the ratio of the
fulfilled demand (total demand minus backorders) to the total
demand, calculated in terms of units. Default options for the
simulation experiment included: backorders carried forward
(ie no lost sales); time series are treated as demand rather
than sales; optimization of forecasting parameters over lead
time is based on the MSE.
To conduct this analysis, ‘intermittent demand’ was defined
as those SKUs with three or more zero demand periods over
the last 13 periods, following the outcome of the forecasting
investigation reported earlier. To distinguish between slow and
lumpy demand, the squared coefficient of variation of demand
size (CV2 ) was used. The evaluation of break-points, which
clients would use in practice, was problematic. Clients operate
JE Boylan et al—Classification for forecasting and stock control
Estimator
SMA(13)
SBA
Resulting inventory for slow demand-proposed scheme
(Data set 1)
Avg. stock
volume/units
Total stock
value (index)
CSL achieved (%)
1.454
1.325
100.0
88.3
96.75
93.37
differential service-level targets for slow and lumpy items,
and so the choice of break-point would largely depend on
service-mix requirements. In Data set 1, though, almost 50%
of the SKUs would be classified as slow, regardless of client
preferences, since these items had zero variance of demand
size. Classification of this subset of SKUs as slow, and the
remainder as lumpy, would provide a useful benchmark for
future analyses, taking client service-mix requirements into
account.
98.0
96.0
94.0
92.0
90.0
88.0
93.0
94.0
95.0
96.0
97.0
Target Customer Service Level %
Stock control implications of forecasting for slow items
SMA(13)
SBA
Target Service Level
Figure 5 Target and achieved service level—proposed scheme
(Data set 1).
Slow demand
1350
1300
Total Stock Volume (units)
The main objective of this analysis was to extend the
forecasting results to a stock control context, rather than
to conduct a detailed investigation of alternative standard
statistical demand distributions, as this issue has been often
addressed in the literature. The target CSL was initially set
to a commonly employed target, 95%, but was later treated
as a simulation parameter, with variation from 93 to 97%.
The SMA(13)–SBA comparison results (95% target) are
shown in Table 3. The figures that relate to the total inventory
value are presented as index numbers because the relevant
information is confidential.
Under the proposed scheme, the resulting stock from the
application of the SBA method is 8.9% less than that associated with SMA(13). Such a decrease in the volume of
stock translates to an 11.7% reduction in the total inventory
value. Nevertheless, the inventory-related savings occur at the
expense of a reduction in the achieved CSL, which drops
from 96.75 to 93.37%. These results conform to theoretical
expectations. Achieving a CSL higher than the target was
expected for SMA(13), owing to the bias (over-forecast) associated with this method after an issue-point ((LS, Q) system).
Similarly, some under-achievement of the target for the SBA
can be attributed to the fact that it slightly under-forecasts the
mean demand. The service level target was then varied, using
the same definitions of demand categories, and the same forecasting methods. This enabled the effect on the achieved CSL
to be observed (Figure 5).
Figure 5 shows that SMA consistently attains a service
level above the target. Although this is desirable, it is at the
expense of high inventory levels (see Figure 6). The SBA
attains service levels that are close to targets above 95%. For
lower targets, there is a wider discrepancy. The effect of target
service levels on inventory is shown in Figure 6.
Figure 6 shows marked savings in inventory arising from
the application of the SBA for all service level targets. This is
Slow demand
100.0
Achieved Customer Service Level %
Table 3
479
1250
1200
1150
1100
1050
1000
950
900
850
93.0
94.0
95.0
96.0
97.0
Target Customer Service Level %
SMA(13)
Figure 6 Target service level and
(volume)—proposed scheme (Data set 1).
SBA
resulting
inventory
consistent with theoretical expectations and with the empirical findings of Eaves and Kingsman (2004). The software
company was greatly encouraged by these results for slow
items. Their view was that clients would prefer small undershoots to overshoots of the target CSL if large inventory
savings could be achieved.
480
Journal of the Operational Research Society Vol. 59, No. 4
Stock control implications of forecasting for lumpy items
Conclusions
The lumpy demand category is evaluated in terms of the
impact of forecasting methods and of subsequent calculations
for stock-control. The target CSL for this demand category is
70%. All combinations of methods examined failed to achieve
this target. In terms of the subsequent calculations, the possibility of using the NBD instead of the current empirically
driven approach was assessed, as discussed earlier. Comparison results between the use of NBD and the currently used
procedure indicated a very similar performance.
The philosophy of categorization by comparison of
methods depends upon having good methods for each of
the categories. In this evaluation, the broadest definition of
lumpy demand was used, including SKUs with very modest
variability in demand size. Nevertheless, it was not possible
to attain the target service level or to get close to it. In the
absence of a good approach for lumpy demand, it is not
possible to determine the appropriateness of the companypreferred classification variable (squared coefficient of variation of demand size) in a stock-control context.
Since it was not possible to improve on the current proprietary method, no changes were recommended to the system,
although the NBD may be made available as an alternative
for lumpy demand.
The development of demand categorization schemes has not
received as much academic attention as it deserves. Demand
categorization rules dictate the forecasting and stock control
methods to be used for different SKUs. Consequently, these
rules have significant implications in terms of stock and
customer satisfaction.
In the empirical investigation, it has been found that the
company’s old break-point for intermittence (seven or more
zeroes in the last 13) was not the best and that, for forecasts
after ‘issue points’, a parameter value between two and six
would be better. Within this range, forecast accuracy is not
sensitive to the exact break-point value. The company were
persuaded by a priori arguments that the average demand
should not be used to distinguish slow from lumpy demand.
To replace this parameter, they preferred the squared coefficient of variation of demand size, since it is dimensionless
and would fit in with potential developments in categorization of intermittence. Inventory assessments showed substantial savings by using the SBA for slow demand, with a slight
undershoot of the target CSL. The software manufacturer has
changed from hard-coding to a menu-driven approach for classification according to the number of zeroes, and dropped the
old rule of at least seven zeroes out of 13. Although more work
remains to be carried out on lumpy demand, the company
has also introduced the CV2 parameter to distinguish between
slow and lumpy demand, accompanied by facilities for client
experimentation.
Research agenda
In this paper, the effect of demand categorization on both forecasting and stock-control has been evaluated empirically. In
previous research, based on forecasting only, it was found that
categorization schemes should take into account the number
of zero demand periods as well as the coefficient of variation of demand size (Syntetos et al, 2005). In this research,
the number of zero demand periods has been confirmed as
an effective categorization parameter for forecasting, at least
for forecasts after an issue-point. The results show forecast
accuracy to be relatively insensitive to the exact choice of the
break-point value for the number of zero periods. The results
on forecasts for ‘all points in time’ were less conclusive, and
further research is required to assess the sensitivity of forecast
accuracy to categorization methods in this case. The interaction of forecasts at ‘all points in time’ with re-order interval
systems also requires detailed examination.
The results for lumpy data show that, for all combinations
of methods, the target CSLs were not achieved. Further work
in this area should include a wider selection of forecasting and
inventory approaches and analysis of alternative categorization variables, such as the ratio of variance to mean of demand.
An overall optimization of forecasting and stock-control
categories has not been considered. It is important to undertake such an analysis, to understand the effect of overall
optimization on inventory system performance. Moreover,
extension of this work to other inventory methods would
allow the interaction between forecasting and stock-control
methods to be understood more fully.
Acknowledgements — We acknowledge financial support for this project
from the company involved and the DTI. The empirical findings of
the paper emerged from a Knowledge Transfer Partnership between the
company and Buckinghamshire Chilterns University College. Also, we
thank the participants in the Intelligent Management Systems in Operations
(IMSIO) III conference (Salford, June 28–29, 2005) for their comments
on an earlier draft of this paper.
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Received October 2005;
accepted July 2006 after one revision