=Paper=
{{Paper
|id=Vol-2467/paper-13
|storemode=property
|title=Portfolio Management: How to Find Your Standard Variants
|pdfUrl=https://ceur-ws.org/Vol-2467/paper-13.pdf
|volume=Vol-2467
|authors=Daniel Jeuken,Frank Dylla,Thorsten Krebs
|dblpUrl=https://dblp.org/rec/conf/confws/JeukenDK19
}}
==Portfolio Management: How to Find Your Standard Variants==
https://ceur-ws.org/Vol-2467/paper-13.pdf
Portfolio Management:
How to Find Your Standard Variants
Frank Dylla and Daniel Jeuken and Thorsten Krebs 1
Abstract. necessarily), two trucks, i.e. spring mounted axles, and four wheels
Product portfolio management is one of the most important tasks with bearings. Optional components may be sliptape, paintings, ris-
for companies to secure their future competitiveness. A crucial as- ers, shock pads, nose/tail guards, etc. Consider that not all truck types
pect for portfolio management decisions is the volume of products fit to each deck and that not all wheel/truck combinations fit. An in-
sold and the sales numbers development over time – one could say: dividual composition of these components is sought by the customer
What are your current or upcoming best selling products, often used – leading to very few skateboards that are sold with the exact same
as “standard products” in sales? Especially for these products it is composition of deck, axes, wheels, and so on.
worthwhile to take actions in reducing costs and improving revenue. From our experience, for new multi-variant products it is common
Regarding discrete products the task is, simply said, looking for prod- that product managers guess which variants will be the top selling
ucts with the highest quantities or profit sold or significant changes in ones in future, i.e. the decision is based on their gut feeling. Evalu-
these quantities over a certain period of time (business intelligence). ation of the quality of their initial decision is barely feasible as only
In contrast, this approach does not work satisfactorily with complex standard BI techniques are available. These techniques are not suffi-
multi-variant products. An aggregated view on products, i.e. ignoring cient for portfolio planning of multi-variant products as they ignore
the sales numbers of the variants with their individual features, does the structural information of the variants themselves. Standard tech-
not give sufficient insights or may even lead to wrong decisions in niques typically analyze the list of sales over a certain period of time
portfolio management. The recurring combination of features across and use product identifiers as the key to identify which one is sold the
multiple types of products might be more important than the type of most and predict how this will change in future. But for variant-rich
the product itself. In this paper we investigate differences in identify- products that are sold in lot size 1 the product identifier cannot be
ing potential standard products in comparison to identifying potential used as a key criterion. It is rather important to compare characteris-
standard variants of products. Thereon we derive a high-level frame- tics and their values. For example, comparing the product ID, which
work how standard variants may be deduced from a given set of vari- identifies an individual composition, does not identify that a lot of
ants described by characteristics and provide an algorithmic sketch skateboards use the same wheels. Thus we consider it is important to
and discuss resulting challenges from a pragmatic perspective. use the configuration model - containing product data and rule sets -
as an input for a new kind of algorithm that does not compare on the
level of product identifiers but on the level of a set of product char-
1 Introduction acteristics, which supports better predictions of top-selling variants,
Portfolio management is a dynamic decision process evaluating, i.e. what the market really is willing to pay for.
prioritizing, reorganizing, cancelling, etc. products throughout their In order to support the step of evaluating past sales in comparison
lifecycle [6]. As managers have to deal with uncertain and changing to original plannings on the level of characteristics and their values,
information portfolio management is a complex task. One of the ma- we introduce the notion of central representative and propose a po-
jor difficulties in product portfolio management is predicting what tential calculation thereof. We discriminate against the term ”stan-
the customers are willing to pay for. This includes knowing the mar- dard product”, standard variants respectively, as this term describes
ket, i.e. knowing the current customer demand and knowing how it products which were actually built many times. As you will see later
will most likely change in future. Thus, product portfolio manage- a central representative does not need to have been built once. We are
ment is complex already when considering simple products, but gets convinced that central representatives will help to recognize changes
more complex when considering configurable and thus multi-variant in client behavior – or the market in general – over time and whether
products. adaptions are reasonable in order to meet the goals of portfolio man-
But what exactly is the challenging part of this task? Forecasts agement.
are created in order to plan the supply chain and production capac- We start with introducing our understanding of product configura-
ities. For simple products this is a rather straightforward task: one tion, which is constraint-based, and introduce diverse variant spaces
can assign a sales forecast to the product identifiers, e.g. material for later use (Sec. 2.1). We consider definitions of discrete standard
numbers, and use the bill of materials in order to get a list of compo- and basic products (Sec. 2.2) and elaborate how this relates to stan-
nents that are required. For variant-rich products such as skateboards, dards for multi-variant products (Sec. 2.3). We sketch our approach
however this is not that easy. In general necessary components of a in Section 3. To avoid misunderstandings with varying definitions of
skateboard2 are the deck, i.e. a plank (in general wooden, but not ‘standard’ we introduce the term central representative of a given
variant space described by characteristics (Sec. 3.1). In order to find
1 encoway GmbH, Germany, email: {dylla,jeuken,krebs}@encoway.de
such a central representative a measure of dissimilarity needs to be
2 see en.wikipedia.org/wiki/Skateboard (retrieved 8.5.2019)
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
defined (Sec. 3.2). In Section 3.3 we exemplify how a representative In more detail, if an assignment contains multiple values for one
can be computed and how a deviation can be derived thereon. We or more characteristics ki it contains at least two different atomic
summarize our considerations in an algorithm sketch (Sec. 3.4). We solutions. For example, given an assignment where a characteristic
discuss our approach from various pragmatic perspectives (Section contains a value, e.g. for deck A and deck B, this means that the
4). First, we revisit the choice of the set of product vectors P for customer at some configuration front-end can still decide for either
which the central representative should be computed (Sec. 4.1). Fur- deck A or B resulting in a valid assignment definitely. In the re-
thermore, in general data is not available in a well defined form in re- mainder of this paper we will use ki synonymously for referring to
ality, i.e. not all characteristics and values are defined in a consistent the characteristic itself as well as for its evaluation, i.e. value assign-
manner (Sec. 4.2). Additionally, multi-variant products are subject to ment, as the meaning becomes clear from the context in most cases.
change such that older products may falsify the results that should In case of ambiguities we clarify the meaning.
reflect the current state (Sec. 4.3). Finally, we consider derivation of In order to discuss notions of standard variant, we need to define
parameters and further prerequisites necessary in order to apply the several solution spaces based on the CSP definition.
algorithm presented to real data. (sec. 4.4).
Definition 3. Theoretical Configuration Space (S ∅ ): This space
contains all combinations of characteristics which are possible from
2 Theoretical background a mereological perspective, i.e. from all minimalist configurations
to all maximum configurations containing all optional components,
2.1 What is product configuration? but ignoring further constraints. In terms of CSP this is reflected by
⟨K, D, ∅⟩.
Felfernig et al. [8] base their understanding of configuration on a def-
inition in [18]: configuration is a special case of design activity where Consider the skateboard example. The minimalist configurations
the artifact being configured is assembled from instances of a fixed consist of a deck, two trucks, and four wheels as these components
set of well defined component types which can be composed conform- are necessary to obtain a functional skateboard from a mereologi-
ing to a set of constraints. A configuration task is the selection of the cal perspective. A configuration with two decks is not part of S ∅ ,
components and their properties to get a valid combination of the whereas configurations with different truck or wheel sizes are part
product components, the outcome is also called product variant [4]. of S ∅ , although this may make the skateboard unusable. Maximum
As a result the component types span a space of potential config- configurations consist of the above components plus all optional
urations which are further restricted by constraints, which limit the components which can be installed in parallel. As risers and shock
possibilities of how components can be combined. Practice shows pads are installed in the same place3 , there is no maximum config-
that the restrictions may arise from technical feasibility, legal re- uration containing both components. As we are interested in valid
quirements, product-design, or marketing purposes. In general, com- configurations in the end, we need to define a second configuration
ponents or properties of a product are described by characteristics in space.
formal product representations. There are additional notions to de-
scribe properties of components like attributes or features. For rea- Definition 4. Valid Configuration Space or variant space (S): This
sons of simplicity we will restrict to the term characteristics through- space contains only valid configurations, i.e. configurations that sat-
out this paper. Based on this we can define a product characteristics isfy all constraints of the underlying configuration model. Therefore
vector, product vector for short. it is given S ⊆ S ∅ . As valid configurations are also called variants,
we will talk of ’variant space’ in the remainder of this paper. The
Definition 1. Given a set of characteristics ki ∈ K with i ∈
variant space directly relates to the space of atomic solutions of a
{0, . . . , N − 1} with values from domain Di ∈ D each, we define
CSP.
[k0 , k1 , . . . , kN −1 ] as the product (characteristics) vector p⃗.
We note that N denotes the maximum number of possible charac- Taking the skateboard example again, configurations with differ-
teristics. Especially, if a characteristic is optional, a specific domain ent wheel sizes are not part of S, whereas configurations with differ-
value must be available defining that this characteristic is not chosen, ent wheel colors may be, depending whether such configurations are
evaluated respectively. As combinations of domain values are not re- permissible with reference to the configuration model.
stricted the product vector may reflect a product which is technically Other variant spaces may be defined on the ‘trading status’ of each
not feasible. p⃗ contained, for example:
Naturally, a configuration task can be considered as a constraint
satisfaction problem (CSP), see e.g. [8]. Definition 5. Offered variant space (S O ) and sold variant space
(S $ ): S O is defined as the space of all variants which have been
Definition 2. Constraint Satisfaction Problem (CSP): ⟨K, D, C⟩: A quoted to customers. S $ contains only those variants which have
CSP is defined as a set of variables ki ∈ K with i ∈ {0, . . . , N − 1} been sold.
with values from domain Di ∈ D together with a set of constraints
cj ∈ C and j ∈ {0, . . . , M −1} defining which combinations of values As in mass customization the variant space is rather large, in gen-
are allowed or not. A solution of a CSP is a consistent evaluation to eral it can be assumed that not all variants were sold or offered. Nev-
all variables (value assignment to all ki ), i.e. no constraint is vio- ertheless, in the very extreme case all possible variants have been
lated. Otherwise the assignment is called inconsistent. Furthermore, offered and sold and thus S $ ⊆ S O ⊆ S. Based on the presented def-
within an assignment values of ki do not need to be unique, i.e. that inition of variant space, an arbitrary number of variant spaces based
ki may contain multiple valid values which can be considered as al- on relevant criteria can be defined for investigation and comparison.
ternatives. Given a solution with a unique value per ki , it is called
3 between trucks and deck
an atomic solution or according to variant management a variant.
2.2 Discrete standard and basic products efficiency of mass production or as stated in [8]: . . . is based on the
idea of the customer-individual production of highly variant prod-
In the context of discrete products a central term for entrepreneurial ucts under near mass production pricing conditions. In general, in
considerations and decisions is standard product. this context products are multi-variant, i.e. there is more than one
According to the Lexico dictionary (Oxford)4 on a general level option available. One important question for variant management is
a standard is (a) a certain quality or attainment level reached or (b) how the variants can be compared in a reasonable manner. Buchholz
something considered exemplary or as a measure or model according states that all variants need to be considered with respect to their
to which others assess to (cf. benchmark, scale, guideline). product type and that relevant characteristics need to be selected for a
Following information given by Wikipedia a technical standard is reasonable comparison [2]. Buchholz also discusses the relationship
an established norm or requirement in regard to technical systems. between variants and standard. It is critically scrutinised whether a
It is usually a formal document that establishes uniform engineering standard variant is the one with maximum quantity, some sort of av-
or technical criteria, methods, processes, and practices. In contrast, erage or a yardstick for other variants. Nevertheless, it is specifically
a custom, convention, company product, corporate standard, and so emphasized that a standard variant is something special compared to
forth that becomes generally accepted and dominant is often called other variants. For comparison a measure of discrimination between
a de facto standard.5 variants is necessary, but not all characteristics are important such
Specifically considering discrete products a wide variety of def- that relevant characteristics need to be selected. In our notation this
initions is available which take different aspects into account. For means, that the product vector K = [k0 , k1 , . . . , kN −1 ] is abstracted
example, in the Gabler Wirtschaftslexikon standard product is de- to a reduced product vector K′ ⊂ K with N ′ < N .
fined with a focus on quality: Products that have a generally agreed Buchholz also presents different views from literature whether
(standardized) minimum quality. Product changes focus on quanti- such a standard variant needs to be part of the variant space itself
ties, prices and times. Standard products can be traded on the stock or not. For example, according to Boysen a basic or standard product
exchange.6 Other definitions base on the criteria whether they are may be a theoretical construct that has never been physically man-
ready for batch production.7 ufactured [1]. Whether it needs to be manufacturable at all remains
From our experience the term standard product is mainly used in unclear. For further details we refer to [2].
two different ways in manufacturing industry: On the one hand, to define a standard variant based on aggregated
1) Either as a label of a product which should be presented as a sales numbers over all variants of a variant space is unreasonable
standard (defined before product is sold at all) from our perspective as it exactly ignores the possible differences of
2) or as a product which is established on the basis of different cri- the available variants. Such an approach could be rather considered
teria e.g. it is sold the most within a given context, e.g. a region as a ’standard variant space’. On the other hand to only consider the
or a specific type of customer. sales numbers of each variant individually bears problems as well, it
even may lead to wrong interpretations. In general, the exact same
In order to dissolve this ambiguity we speak of a predefined standard
variant is not sold more than ’a few times’. For example, consider
in case of 1) and a derived standard in case of 2).
100 skateboards of 96 different variants sold. This means that most
Furthermore, a basic product – also called generic product – is
variants were sold once and two may have been sold three times each.
defined to realize the core benefit of the product. This implies that
This also means that the standard variants may change within a few
a basic product cannot be further reduced without losing the possi-
new sales. Therefore, from our perspective it would not be useful to
bility of intended product usage.8 In case of a skateboard this is the
define these ”top selling” variants as standard variants.
ability to ride on such a board with pushing oneself forward by foot.
From the perspective of the product management and with the aim
A basic product may not be saleable, e.g. due to legal restrictions. An
of an efficient portfolio handling, it is also useful for multi-variant
extended product is one which offers additional benefit to customers.
products on the one hand to offer and place a standard variant in the
In the context of manufacturing companies ... a basic product might
market and on the other hand to analyze which product variant is sold
be a rather simple good that experiences relatively consistent con-
most or is never sold at all.
sumer demand ....9 Sometimes a core product is differentiated from
From our point of view the notion of a basic product can be di-
the product: The core product of a book is information. It is not the
rectly transferred to a basic variant: to cover the basic functionality
book itself.10 The book itself is then the basic product.
necessary characteristics must be set with corresponding values re-
flecting a ”basic” quality. In case of a skateboard a deck, two trucks,
2.3 Multi-variant products and standard variants and four wheels each of rather low quality. In case only one compo-
The term mass customization defines the challenge of anticipating nent (characteristic) is missing, it is no variant of a skateboard any-
individualized products to be manufactured simultaneously with the more as it is non-functional. In addition top-level variants can be
4
given: variants with a maximum number of characteristics evaluated
www.lexico.com/en/definition/standard (retrieved
with corresponding values reflecting a high level of quality, i.e. based
2.8.2019)
5 en.wikipedia.org/wiki/Technical_standard (retrieved on the configuration model no further feature can be selected with-
2.5.2019) out deselecting at least one other feature. In some cases, depending
6 wirtschaftslexikon.gabler.de/definition/ on the context, it might appear that not more options are chosen in
standardprodukte-42877 (retrieved 6.5.2019, in German) case of a professional board compared to a basic one, but components
7 e.g. www.lawinsider.com/dictionary/standard-products
(retrieved 2.5.2019) of better quality, e.g. the material types of the deck or the wheels. In
8 wirtschaftslexikon.gabler.de/definition/ the end this must be reflected in the underlying metrics.
produkt-42902 (retrieved 2.5.2019, in German) In Figure 1 we depict relations between basic (bi ), top-level (ti ),
9 www.businessdictionary.com/definition/ and ‘regular’ (pi ) product variants. Furthermore, each variant may
basic-product.html (retrieved 8.5.2019)
10 www.marketing91.com/five-product-levels/ (retrieved also be computed or defined as a standard variant (marked with ☆ ).
8.5.2019) The level, i.e. the number of selected characteristics and ’rank’ of
t0 t☆2 S ∅ , S, S O and S $ (see Sec. 2.1) we already defined specific P,
i.e. sets where all p⃗j fulfill certain properties. As we are interested
t1
in the ”best representative” of P we define a central representative
p9
of P based on a measure of similarity or dissimilarity.
p6 p10
Definition 6. Central representative r⃗P and deviation ν⃗P : r⃗P is the
p5
product vector of a product space P which has the overall minimal
p☆7 p8 dissimilarity to all p⃗j ∈ P considering a measure M. Furthermore,
p0 we define the deviation ν⃗P to be the vector of the individual devia-
tions νi of assigned values per characteristic ki (see Figure 2).
p1
p3 p4 Simplified, one could say r⃗P is the average product of P regarding
the measure M or more specific, the one that minimizes the dissimi-
p2
larity to all pi ∈ P. The deviations νi can be defined in multiple ways.
We detail this in Section 3.3. We note that, based on this definition, it
is not necessary, that r⃗P ∈ P. Furthermore, as several solutions may
have the same aggregated distance regarding pi ∈ P based on M,
b0 b☆1 ⋯ bn−1 bn
there may be no unique central representative r⃗P . We sketch how a
measure M can be defined below.
Figure 1. Schematic structure of basic (bi ), top-level (ti ), and standard
(pi ) variants inbetween. Variants of any of these levels can be designated as
a standard variant (☆ ). P
ν0 r⃗P
corresponding values is reflected by height. The edges depict that
the variants differentiate in a single characteristic.11 Naturally, basic ν1
variants are rather at the bottom and top-level variants at the top of
the figure. Nevertheless, it is possible to have feature combinations
that aren’t separable and so basic as well as top-level variants can
exist on different levels. But irrevocably basic variants must not have Figure 2. Schematic depiction of a variant space P with its central
another connected variant ‘below’ them, top-level variants ‘above’ representative r⃗P and its deviation ν⃗ = [ν0 , ⋯, νn−1 ] with n = 2
respectively. All other variants inbetween have ‘smaller’ predeces-
sors and ‘larger’ successors. Standard variants can be defined on any
of these levels. Consider our skateboard example. We define a basic
variant as standard skateboard for beginners, a mid-range skateboard
as a standard for trained half pipe skaters and a top-level variant as a
3.2 Measure M: Dissimilarity of variants
standard for skate competitions. M could be either a measure of similarity or dissimilarity. Although
M can be defined arbitrarily, e.g. based on ∑, ∏, min, max or some
3 Approach complex aggregation function, we stick to a specific distance based
measure, and thus dissimilarity, for reasons of simplicity. For future
We believe that the availability of a standard variant in the sense of research a promising link is given by case-based reasoning (CBR) as
an average product of the most selling variants is very helpful in port- the notion of similarity is central to this approach [9, 16, e.g.]. Nev-
folio management. In order to prevent misunderstandings with other ertheless, although CBR has been applied to product configuration,
definitions (see Sec. 2.2 and 2.3) we will talk of a central representa- to our knowledge specific product similarities have not been exten-
tive of a variant space instead. One possibility to exploit the central sively investigated in the literature; exceptions are [12, 21, 20]. As-
representative in portfolio management is to compare it with prede- pects of similarity have been studied in the context of CSP [7, 5, e.g.]
fined standards and adapt them accordingly. In order to discuss the resulting in the need of Euclidian distance measures from a practical
challenges in defining such a central representative in the context of perspective. In the following of this section we summarize aspects of
multi-variant products, we need to give some formal definitions re- similarity measures relevant to our approach.
garding configuration spaces (Section 3.1). We define a measure M A Euclidian distance measure δ for some entities o, p and q is
(Sec. 3.2) for computation of a central representative (Sec. 3.3). We reflexive: δ(p, p) = 0, symmetric: δ(p, q) = δ(q, p), and transitive:
close this section with an algorithmic sketch, integrating definitions δ(o, q) ≤ δ(o, p) + δ(p, q). For reasons of simplicity, we will talk of
from preceding subsections (Sec. 3.4). distance in the remainder of this paper.
In order to define a distance measure M consider a variant space,
3.1 Definition of a central representative of a e.g. S, and a subset thereof, e.g. S $ (S $ ⊆ S). This implies that p⃗ ∈ S
variant space and q⃗ ∈ S $ contain the same characteristics kx with x ∈ {0, ⋯, N −1}
in the same order. First, we need a distance between values from the
In Section 2.1 we introduced the notion of a product (configuration) same characteristic δx for all x ∈ {0, ⋯, N − 1}, for example:
vector p⃗, which holds all characteristics which define a certain prod-
uct. Let P = {⃗p0 , p⃗1 , . . . , p⃗P −1 } be a set of P product vectors. With δx (kxp , kxq ) = ∣kxp − kxq ∣ (1)
11 For reasons of simplicity we neglect that connected variants may differ in with kxp denoting the value of the x-th characteristic of product
more than one characteristic as they are inseparable due to the rule set. vector p⃗, kxq of q⃗ respectively. Depending on the type of scale of
the characteristic (i.e. nominal, ordinal, interval or ratio scale) cer- N −1
tain calculations may not be possible, e.g. subtraction or addition on r, p⃗i ) with p⃗i ∈ S $
r⃗S $ = argmin ∑ ∆(⃗ (5)
⃗∈S
r i=0
nominal scale is not reasonable. On nominal scale only the equality
between values can be determined, i.e. are two values the same or In the first case (Eq. 4) r⃗ has been sold itself as r⃗ ∈ S $ , whereas
not. If a level of similarity is required at least an ordinal scale for the in the second case (Eq. 5) r⃗ is a general technically feasible variant
values must be available, i.e. a linear order for the values for the def- r ∈ S). One could even relax that the representative not even needs
(⃗
inition of a median. For interval or ratio scale a mean can be defined. to be technically feasible, and thus select r⃗ ∈ S ∅ (cf. 2.3).
This results in a distance vector of distances per characteristic In conjunction with the central representative it is also of interest
’how large’ or ’how widespread’ the set is, which it represents. For
⎡ δ0 (k0p , k0q ) ⎤ ⎡ d0 ⎤
⎢ ⎥ ⎢ ⎥ this we need a notion of deviation, diameter, or variance. For now,
⃗ p , q⃗) = ⎢
δ(⃗ ⎢ ⋮
⎥ ⎢
⎥=⎢ ⋮
⎥
⎥ (2)
⎢ ⎥ ⎢ ⎥ we stick with the notion of average deviation per characteristic (νi )
⎢δN −1 (kN
p
−1 , kN −1 )
q ⎥ ⎢dN −1 ⎥ for all p⃗j ∈ P as it suffices our needs.
⎣ ⎦ ⎣ ⎦
The next step is to aggregate these individual distances into a sin- 1 P −1
gle distance value describing the distance between two product vec- νi = ∑ δi (ri , ki )
j
(6)
P j=0
tors. It needs to be reflected that not all characteristics are equally
important. Therefore a weighting factor wi needs to be integrated Then ν⃗ = [ν0 , . . . , νN −1 ] denotes a vector of all deviations per char-
for each characteristic. If characteristic ki should not be considered, acteristic.
the corresponding wi needs to be set to zero. Furthermore, not all It is not beneficial if a central representative covers a ’too wide
distances for individual characteristics may have the same range and range’ of variants, i.e. one or several νi are rather high for some
thus, one characteristic may dominate others, therefore a normaliz- characteristics ki , as it would not give much help for portfolio op-
ing factor vi is necessary. For example, consider a distance vector timization, especially if members of the set of product vectors are
with N = 3 where d0 represents a binary distance (d0 ∈ {0, 1}), not distributed uniformly. Consider the case depicted in Figure 4.
d1 represents a distance between zero and five (d1 ∈ [0, 5]), and d2 Products were sold in two rather distant regions of the variant space.
represents a distance between zero and thousand (d2 ∈ [0, 1000]). Considering them as one set would lead to a representative which
In most cases d2 would dominate or overrule d1 , which in turn also does not reflect the situation at hand (orange space). We need to look
dominates d0 . Therefore, it is import that all value ranges of the ki for separate subsets, i.e. clusters, instead, to come to a result depicted
are normalized, e.g. to values between zero and one. This results in a by the two separate regions S0$ and S1$ (light blue). As we have de-
distance between two product vectors p⃗ and q⃗. fined a central representative and a deviation thereof, various cluster
1 N −1 analysis methods are applicable, e.g. centroid-based or density based
p , q⃗) =
∆(⃗ ∑ wi vi di (3) clustering. For an overview of existing clustering methods we refer
N i=0
to [13, 23, 17, e.g.]. The adequate selection of a clustering method
We give a schematic impression of a distance ∆ between two will be a crucial task for the successful application of the approach
product vectors r⃗S and r⃗S $ in Figure 3. Nevertheless, it still remains proposed.
open how central representatives like r⃗S and r⃗S $ can be determined For pragmatic reasons we restrict our considerations to clustering
based on ∆. parameters (assuming a clustering method given) to maximum de-
viation per characteristic and a minimum number of members per
cluster. Therefore, a vector of thresholds θ⃗ = [θ0 , . . . , θN −1 ] for the
S corresponding characteristics ki and θ# for the minimum number
needs to be given.
r⃗S
∆
r⃗S $ S $
S
r⃗S S $
r⃗S $ r⃗S $
1 S1$ r⃗S $ 0
S0$
Figure 3. Schematic depiction of a general variant space (S, dark blue)
rS ) and sales variant space (S $ , light blue)
and its central representative (⃗
rS $ ). The ∆ depicts the difference
also with its central representative (⃗
between r⃗S and r⃗S $ .
Figure 4. Schematic depiction of cluster splitting due to high variance in
single cluster consideration.
3.3 Calculation of central representatives
We defined the central representative r⃗P as a variant which minimizes
the overall dissimilarity (cf. Definition 6). Furthermore, it is not a
3.4 An algorithm sketch
requirement that r⃗P is itself an element of P. Consider these two We summarize the parts of how to find adequate representatives for
definitions of central representatives of S $ . a given set of product vectors P (e.g. sold variants S $ ) out of an-
N −1
other given set of product vectors Q (e.g. the overall variant space
r⃗S $ = argmin ∑ ∆(⃗
r, p⃗i ) with p⃗i ∈ S $ (4) S) in Algorithm 1. In the beginning only the single cluster P exists
⃗∈S $
r i=0 for which central representative r⃗P and deviation ν⃗P is calculated.
If there is any deviation νi which is above its defined threshold θi P Maimon state that a focus on relevant characteristics has several ad-
needs to be splitted in two clusters.12 In the next iteration at least two vantages [3]. For example, removal of irrelevant characteristics im-
clusters need to be considered. At some point clusters with only few proves efficiency as well results are more conclusive and easier to
members are computed (< θ# ). We ignore these clusters from fur- interpret due to the focus on key features. Nevertheless, a too lim-
ther consideration in this iteration. We continue with increasing the ited choice of characteristics leads to information loss and reduces
number of clusters until we obtain a set of clusters with each con- the quality of the results. For further information on feature selection
taining a central representative with each deviation per characteristic methods we refer to [22]. If a characteristic is considered irrelevant
below the given threshold (∀i νi ≤ θi ). We note, that we increase the for an evaluation at hand wi (cf. Eq. 3) should be set to zero in the
number of clusters iteratively and start the cluster splitting from the calculations. For all characteristics with wi > 0 the relative relevance
original set P on purpose. If not doing so the order of considering needs to considered very carefully as slight changes may lead to sig-
pi ∈ P might have an effect and thus, would lead to different results nificant changes in the classification of the data. For example, if the
if pi are represented in a different order. results are designed for adapting standard products a slight change in
the parameters might lead to a different variant.
Input: P, Q, θ,⃗ M, θ#
Result: S ∶= set of central representatives for P out of Q
no of clusters ∶= 1 ;
S = {P}; 4.2 Data preparation
R ∶= calculate list of representatives from Q for all sj ∈ S based
on M;
Θ ∶= calculate list of all deviations for corresponding rj and sj Practice shows that within companies often master data is not co-
based on M; ordinated. In general, this leads to multiple characteristics contain-
while ∃i, j with νij ∈ Θ > θi for any sj ∈ S do ing the same information, potentially represented differently, e.g. us-
no of clusters ∶= no of clusters +1 ; ing different text strings, numbers, or different units. As products
S ∶= clusterSplitting(P, M, no of clusters); are subject to permanent change, the inconsistency of data increases
delete all sj ∈ S from S where ∣sj ∣ < θ# ; over time. In order to ease and automatize analysis in the long run,
R ∶= calculate list of representatives from Q for all sj ∈ S data synchronization is inevitable. Nevertheless, considering given
based on M; data, data cleansing is essential to prevent bad decisions based on
Θ ∶= calculate list of all deviations for corresponding rj and bad analysis results [24]. Maletic described the data preparation as
sj based on M; a multistep procedure comprising (1) definition of error types, (2)
end finding instances of these errors, and (3) correction of them [11]. He
Algorithm 1: Algorithmic sketch for deducing central representa- emphasizes that each of these steps is a complex task in itself.
tives out of the variant space Q based on the variants given by the To give an idea of the effort that needs to be taken, we present a
variant space P. non-exhaustive list of different error types in (master) data below. A
common error type is conditioned by different notions or represen-
tations, i.e. characteristics and values holding the same information,
but represented with different spellings. These errors often arise from
4 Pragmatic considerations inconsistent usage of blanks, hyphens, prefixes, suffixes or abbrevia-
Not all characteristics of product vectors must be considered as rele- tions. Different units may also be used, e.g. due to different intended
vant information might be covered by other characteristics (Sec. 4.1). usage. Characteristics holding complex information, i.e. connected
In general, data provided by companies needs some preparation as information, are problematic as well as further processing might be
this data is often not consistent concerning characteristics’ and val- limited. A common example is a combined string representation of
ues’ denomination (Sec. 4.2). We consider temporal restriction of length, width, and height (sometimes without a given unit) instead of
data and how observations over time can be derived (Sec. 4.3). Be- having individual numerical characteristics for each of them. A tricky
fore Algorithm 1 can be applied value ordering and weighting factors type of errors comprises misleading value specifications, e.g. frame
for each characteristic must be available 4.4. sizes termed with numerical values which have to be interpreted in
a specific manner so that naive calculation is not possible. Consider
frame sizes 5, 8, and 12 which reflect three consecutive frame sizes.
4.1 Contentual evaluation The physical difference in size cannot be calculated from these val-
In order to support a business question a contentual focus on data is ues, instead other data like length, width, and height of certain com-
necessary. Simplified, two levels of contentual constraints can be dif- ponents need to be considered. Furthermore, the conceptual distance
pi ) can be considered.
ferentiated. First, the context of each variant (⃗ cannot be calculated from these ’values’: as the categories are con-
Context can be defined on different perspectives, e.g. in which shop secutive the distance is 1 and not 3 and 4. In order to prevent trim-
or region the variant has been generated, by whom, whether it has ming of leading zeros, such terms may be even stored as strings.
been sold, only offered, or never even offered (cf. S, S O , S $ in Sec. Elimination of errors of this type requires very specific semantic
2.1), or for which application, domain respectively, it was bought if knowledge, which makes it not only hard to spot these errors, but
this information is available. Second, the relevance of each charac- also to correct them. For further information on data cleansing and
teristic should be checked as consideration of all characteristics may data quality we refer to [14, 15].
block the view on relevant information, for example, the color of the As a result of data preparation we get a set P of product vectors
trucks or some non-visible strings on some component. Chizi and p⃗i with consistent [k0 , k1 , . . . , kN −1 ], i.e. with comparable informa-
tion stored in the same characteristic with the same value for every
12 How this is actually done depends on the clustering algorithm chosen.
product variant.
4.3 Temporal evaluation interval and ratio scale data naturally a distance is given – assum-
ing the characteristic is not misinterpreted as such and is ’only’ on
Products are subject to permanent change. They are designed, devel- ordinal scale (cf. Sec. 4.2). For ordinal data this is not the case, a
oped, sold, and refined, potentially several times. Such refinements linear ordering has to be defined manually. Although, an ordering of
and changes in expectations of the market may result in changes of terms like ”basic”, ”advanced”, ”expert”, and ”professional” might
central representatives. Therefore, regardless whether from technical be considered trivial in the first place, it is a tricky, currently man-
or sales perspective, it is not reasonable to consider outdated data, ual and time consuming task and thus, also error prone. Looking at
which leads to the application of methods from time series analysis. the terms ”expert” and ”professional” the question is whether ”ex-
Furthermore, as sales numbers for the products of interest may vary pert” is before or after ”professional” or equal in the end as they
significantly over time, consideration of single time points (or rather relate to completely different aspects of the product. It may be pos-
small time intervals only) may show varying results for each of these sible that a reasonable distance between terms like ”basic” and ”ad-
time points. vanced” is definable, i.e. how far is ”basic” from ”advanced”, ”ad-
One applicable method in order to generate smoothed results is vanced” from ”expert” and so forth. We refrain from this as the re-
the sliding window approach (SWA), see for example [10]. The ba- sulting costs would not be in a reasonable cost-benefit relation for
sic idea is to evaluate overlapping intervals, so called windows, to an industrial company. For a start an equidistant conceptual distance
get smoother and more consistent results. We depict relevant param- measure should suffice, i.e. all preceding and succeeding terms in a
eters for the SWA in Figure 5. Let d denote the overall period under linear order have the same distance.
review (one year in the given example). The window size is denoted In business intelligence it is common to not only consider the num-
by w (three month) with w ≪ d and the corresponding step size by ber of sold units, but also profit or the number of sold units per quote
s (1 month) with s ≤ w. Analysis is then performed for data in each is part of the analysis for example. On the one hand a pragmatic way
window separately. without changing the algorithm is to modify the original set by re-
The choice of specific values for d, w and s is very crucial and ducing or multiplying the number of equal product vectors in P. On
must be considered carefully, especially if conclusions on future de- the other hand an additional weighting factor per pi could be intro-
velopments are drawn. For example, if d is chosen too small the duced, which would be much more efficient regarding run-time of
corresponding data set may be too small to generate significant re- the algorithm.
sults. Statistical or learning methods support a reasonable choice,
[19, e.g.].
Algorithm 1 can be extended in such a way that not only a sin- 5 Summary and Outlook
gle time point is considered (P), but subsequent sets, i.e. subsequent
windows. On this basis developments of the central representatives To support portfolio management for multi-variant products we ex-
and their corresponding deviations can be observed: how they ’won- amined definitions of ’standard’ for discrete and multi-variant prod-
der around’ and how the number of clusters increases or decreases. ucts. To differentiate from these definitions we introduced the term
central representative of a variant space. We derived an algorithmic
d sketch based on a measure M to calculate representatives for clusters
with reasonable size. Finally, we discussed tasks necessary before the
algorithm can be applied to real data.
As the work on central representatives for a variant space is in an
early stage many tasks and questions remain open. The straightfor-
jan feb mar apr may jun jul aug sep oct nov dec ward next step is to experiment with large scale real data instead of
few small toy examples. Furthermore, the determination of weighting
w factors wi is a challenging task. We need to investigate to what ex-
s w tent learning methods, either supervised or unsupervised, may ease
the task. Once real data is available it will be a worthwhile task to
reconsider alternative definitions of distance functions, e.g. investi-
Figure 5. Sliding window approach with d denoting the overall period gating the impacts of choosing ∏, min, max or some other function
considered, w denoting the window size and s the step size.
as aggregation operators. In theory it is possible that multiple central
representatives are available. If this case also appears with real data,
we need to investigate how to deal with it.
4.4 Weighting factors and value ordering Acknowledgement
The approach is significantly based on the definition of the measure
We thank the anonymous reviewers for critically reading the
M containing the distances δ and ∆, which in turn contains weight-
manuscript and providing helpful comments for clarification and im-
ing factors wi for each characteristic. First experiments have shown
provement of the manuscript.
that distance measures on nominal data very much influences the re-
sults significantly as the distance can be only either zero or one. A
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