Clustering Stores of Retailers via Consumer

Behavior
Thesis in Business Analytics and
Quantitative Marketing

Author:
Gijs van Rooij (360497)
Supervisor:
Gertjan van den Burg
Co-reader:
Dr. Michel van de Velden

Econometrics & Operations Research

Erasmus School of Economics
Erasmus University Rotterdam

February 2, 2017
 Abstract
These days most retailers define clusters of stores and set different prices in the clusters,
since it is not yet attractive to define store-by-store prices due to optimization and opera-
tional issues. However, retailers define clusters of stores solely based on local competition.
Existing clusters of stores could be further broken down and price management decisions
could be adjusted accordingly by using consumer behavior. Therefore, the price elasticity
is used which is a reflection of consumer behavior. In this way the retailer enables itself
to set different prices in smaller clusters of stores in order to attain higher revenue and
profit. This research provides a clustering solution that defines clusters of stores based
on price elasticities. This clustering solution proves potential with a projected increase in
revenue of 0.36% and a projected increase in profit of 0.76% by using data of one of the
major supermarket chains in the Netherlands.

Keywords: clustering, constrained clustering, cluster consensus, NACT

Contents

Abstract i

1 Introduction 1
1.1 Topic and data description . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Phase 1: Clusters of stores per product group . . . . . . . . . . . . 2
1.2.2 Phase 2: Final clusters of stores . . . . . . . . . . . . . . . . . . . 2
1.2.3 Phase 3: Clustering impact . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Structure paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Related work 5
2.1 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Covariates of price sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Data 8
3.1 Scanner data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Store-specific characteristics and trading area data . . . . . . . . . . . . . 9

4 Method 10
4.1 Dissimilarity measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2.1 Restricted K-means++ . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2.2 Cluster consensus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2.3 Cluster validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.4 Cluster evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 Regression analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.3.1 Regression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3.2 Variable selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5 Evaluation 22
5.1 Cluster definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.1.1 Cluster interpretation . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.1.2 Cluster evaluation: Jaccard . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.3 New price policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.4 Regression analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6 Conclusion 30

i
Bibliography 32

Appendices 35
A Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
B Impact clustering results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
C Panel data regression results . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1 | Introduction

In this chapter we propose the problem at hand and we briefly introduce the methods
applied to answer the research question. First, in Section 1.1 the topic of the research
alongside the research question and the context of the research are provided. Consequently,
in Section 1.2 the workflow of the research is described. Then, the applied methods are
briefly discussed in Section 1.3 and in Section 1.4 the structure of the paper is discussed.

1.1 | Topic and data description

Since it is not yet attractive – for optimization and operationally for managers – to define
store-by-store prices, retailers assign stores to clusters of stores. Retailers create clus-
ters of stores to set different prices for the same products in different clusters. Stores
assigned to the same group charge the same prices for the same products. Unfortunately
many suppliers rely too heavily on their internal perceptions with regard to their clus-
tering policy [29]. These days most retailers define clusters of stores solely based on
local competition whereas the variation in consumer behavior among stores is completely
neglected. Obviously, consumer behavior varies between different stores. Variance in con-
sumer behavior leads to differences in demand and therefore it is attractive for retailers
to set different prices in different stores for the same product. The aim of this research is
clustering stores based on price elasticity, which is a reflection of consumer behavior, to
prove that there is an opportunity to increase revenue and profit by using a new way of
clustering. In conclusion, since retailers in general exclusively focus on local competition
a great opportunity gets lost. This leads us to address the following research question:

How can we cluster stores by means of the differences in consumer behavior

such that the revenue and profit of the retailer increases?

The context of this research is supermarkets. We define a clustering framework using

data of the Jumbo supermarket chain. Jumbo owns over 600 stores spread all over the
country which makes them one of the major players in the Netherlands with regard to gro-
cery shopping. According to Nielsen marketing the market share amounted approximately
20% in 20151 . Jumbo defines four different clusters of stores based on local competition.
However, there is still a lot of variation in price elasticity within the clusters of stores and
especially in some specific groups of products (PGs) between stores. For example, the PG
Cola consists of all products related to Cola such as bottles of different volume from Pepsi
and Coca Cola. Each product group is defined by the retailer. This provides us with an
opportunity to boost sales and profit by defining smaller subsets of ‘similar’ stores within
existing clusters of stores based on the price elasticities.
1 http://www.distrifood.nl/service/marktaandelen

1
1.2 | Workflow
The workflow of this research consists of three phases, namely finding clusters of stores for
each specific product group (phase 1), obtaining the final clusters of stores (phase 2), and
analyzing for the impact of the obtained clusters of stores (phase 3). Each of these phases
raise different questions that need to be answered to get to the answer of the research
question.

1.2.1 Phase 1: Clusters of stores per product group

First we obtain clusters of stores for each product group separately, since consumer be-
havior among product groups differs [30]. Multiple clusterings impose different structures
on the data and therefore provide a wide range of information. As mentioned before, the
price elasticity reflects the consumer behavior. We use the price elasticities per store per
product which are called the price elasticities on store-item level. Since the price elasticity
on store-item level is the most specific level of price elasticities available, no information
gets lost in the process of aggregating to a higher level of price elasticities such as on store
level. In this case the information per product is no longer considered and therefore the
information is less comprehensive. Each store is assigned to a seperate cluster of stores
based on the store-item level price elasticities of all available products. In order to answer
the research question we first need to answer the following subquestion:

How can we cluster the stores per product group exclusively based on the
products available in the considered product group?

1.2.2 Phase 2: Final clusters of stores

Obviously, in phase 1 stores could end up in a different cluster of stores for the different
product groups. For example, store s could end up in the first cluster for product group g
and in the second cluster for product group h even after relabeling. In the end the retailer
searches for one specific set of clusters of stores instead of a clustering per product group
due to operational and optimization limitations. We could think about problems such
as the replacement of paper price tags and the computing speed limitations of computers
whereby price optimization could take ages. Therefore we need to combine the information
comprised in the clustering per product group into one final set of clusters of stores. This
leads us to address the following subquestion:

How can we obtain one final set of clusters of stores that combines the
information comprised in the clusters of stores found for each separate
product group?

2
1.2.3 Phase 3: Clustering impact
Price is the factor that provides immediate revenues [27]. Therefore, to prove the positive
impact of our framework on the revenue and the profit we have to adjust the current
prices according to the new formed clusters. We have to define a price policy at which
we set different prices for products in different clusters of stores. The price of a product
in a cluster is kept the same in all stores in that cluster. Note, the focus of this research
is not to find the optimal prices but finding the clusters of stores that fit the underlying
data the best. This raises the following subquestions to answer the research question:

If different prices are set in the clusters, what is the impact of the clustering
of stores for each of the separate product groups on the revenue and profit of
these product groups?

If different prices are set in the clusters, what is the impact of the final
clustering of stores on the revenue and profit in total?

1.3 | Method
The main focus of this research is to define new clusters of stores that use the differences
in consumer behavior among stores. To use differences in consumer behavior by means
of the variance in price elasticity on store-item level a two-stage framework is needed.
First, in phase 1 and the first step of the two-stage framework we obtain clusters of stores
based on the price elasticity on store-item level for each product group separately. The K-
means++ clustering algorithm by Arthur and Vassilvitskii [2] is used as a building block
for the Restricted K-means++ clustering algorithm which is proposed in this paper. The
K-means++ clustering algorithm is an easily implementable clustering algorithm that is
able to handle large datasets. The proposed Restricted K-means++ clustering algorithm
is bound to some restrictions for which K-means++ does not comply and therefore the
Restricted K-means++ clustering algorithm is an extension of the K-means++ clustering
algorithm. Stores should be assigned to clusters such that stores originating from the same
city/village are appointed to the same cluster. If stores from the same city/village end up
in different clusters our reassignment process ensures these stores in the end are assigned
to the same cluster. Furthermore, products that generate more revenue than others are
more important to the retailer. This is covered in the novel weighted dissimilarity measure
between stores proposed in this paper. The higher the weight, the more important the
product is to the retailer. Moreover, imagine we are interested in the dissimilarity between
two stores and only one of the stores sells a specific product. Although the price elasticity
of the product is not available in one of the stores it indicates a difference between the
stores because the assortment differs. To cope with this issue we add a correction term to
the novel weighted dissimilarity proposed in this paper that scales up the dissimilarity in

3
case data is missing. Secondly, phase 2 and the second step of the two-stage framework
includes combining the information comprised in the clusterings of stores from the separate
product groups by using the hard least squares Euclidean consensus algorithm [14]. The
result is the so-called cluster consensus which represents the final set of clusters of stores.
Finally, we conduct an extensive analysis using regressions which provides insights in the
drivers for differences in consumer behavior in order to make better decisions.

1.4 | Structure paper

In the remaining of this paper, first the related literature is discussed in Chapter 2. In
Chapter 3 the data used for evaluation is analyzed and in Chapter 4 the proposed method
regarding clustering is described. The results of the clustering are provided in Chapter 5.
In Chapter 6 the conclusion and some suggestions for future work are presented.

4
2 | Related work

In order to use the variation in price elasticities we propose a two-stage clustering frame-
work which consists of first finding new clusters of stores for each product group separately
and consequently finding the cluster consensus. The cluster consensus summarizes the in-
formation of all the found clusters of stores for each product group separately in one final
set of clusters. Additionally, we conduct an extensive analysis using regressions on the
formed clusters which provide insights in the drivers for differences in consumer behavior
in order to make better decisions. Existing methods are re-used and new ones are intro-
duced. Section 2.1 presents an overview of the literature on clustering. In Section 2.2 we
elaborate upon the literature related to the drivers of price elasticity.

2.1 | Clustering
The K-means clustering algorithm [12] is a clustering method that is the most commonly
used clustering algorithm in particular for its simplicity and its applicability to large
data sets. K-means suffers from the limitation that convergence to a local optimum
could produce unreliable results due to the choice of the initial centers. As such, the K-
means++ algorithm was proposed by Arthur and Vassilvitskii [2] to avoid the problem of
getting stuck in a local optimum. Moreover, the K-means++ algorithm outperforms the
K-means algorithm regarding speed as well. Additionally, in this research we are bound
to the domain-specific business rule that stores located in the same city/village should be
assigned to the same cluster. This business rules can be implemented in the clustering
algorithm via constraints. Related to it, constrained clustering [3, 4, 5] has been widely
researched the last decades.
Wagstaff et al. [40] implement constraints into the K-means clustering algorithm by
ensuring none of the constraints are violated while updating cluster assignments. In case
point s cannot be hosted by cluster C, they go through the list of clusters and search for
a cluster to which point s could be assigned. The must-link constraint, i.e., two instances
should be in the same cluster, corresponds to the business rule our research is bound to.
The disadvantage is that the algorithm is order-sensitive since the order of cluster centers
to which the stores are compared could influence the final clustering. Therefore the final
clusters could end up differently in separate runs if the order of cluster centers differs.
Basu et al. [3] needs supervisory information given as cluster labels a priori to initialize
the clustering algorithm. They propose to incorporate this form of semi-supervision in
the K-means algorithm by seeding. It uses labeled data and the constraints generated
from labeled data to initialize the clustering algorithm. This way so-called seed clusters
are generated to initialize the clustering algorithm. The labels of the seeded data are kept
the same during subsequent steps of the algorithm, whereas the non-seeded data labels

5
are estimated at each step. Additionally, they propose to apply the same technique using
the Expectation Maximization algorithm. During each Maximization step the conditional
distributions are kept the same for the seeded data and at each Expectation step the
conditional distributions for the non-seeded data are re-estimated. Experimental results
on a newsgroups dataset show the convenience of the aforementioned algorithms regarding
sensitivity and robustness over random seeding and COP-Kmeans, proposed by Wagstaff
et al. [40].
Another method for constrained clustering is the Constrained Complete Link algorithm
by Klein et al. [24]. This hierarchical agglomerative clustering method using complete
linkage is altered during initialization to cope for the must-link and cannot-link constraints,
i.e., two instances should not end up in the same cluster. In case instances are related by a
must-link constraint the distance between the instances is set to zero, while in case of the
cannot-link constraint the same distance is set to infinity. Consequently, new distances
between pairs of instances are found using shortest path.
In contrast to constructing a single clustering, multiple clusterings impose different
structures on the data and therefore provide a wide range of information. In order to
exploit the complementary nature of the data, different samples of input data can be
used. To combine clusterings, according to Vega-Pons and Ruiz-Scholcloper [39], roughly
two sorts of different methods exist, i.e., median partition based approaches [13, 39] and
object co-occurrence based approaches [14, 22, 38]. The basic idea of a median partition
based approach is to find a clustering P such that the similarity between P and all
the clusterings in the ensemble is maximized. One of the object co-occurrence based
approaches is the method by Strehl and Ghosh [36] for which first the similarity matrix
is constructed. Based on the adjacency matrix of a hypergraph the similarity matrix can
be deduced. If the adjacency matrix contains a 1 in the column it represents an object
(row) that is contained in that cluster. Next, any reasonable similarity-based clustering
algorithm can be used, such as K-medoids [23]. However, since the adjacency matrix of
a hypergraph is constructed they also propose to use the METIS algorithm [21] to yield
the combined clustering which then makes the algorithm a graph based method.

2.2 | Covariates of price sensitivity

The drivers of consumer behavior are especially interesting to the retailer to explain
differences in price elasticities between products and stores. Shifts in the demand curve
are caused by main determinants such as the disposable income of households and prices of
related goods. Along with these determinants, it is expected that the explanatory power
of the price elasticity rises by means of many other components. To define the covariates
of price elasticity a wide range of literature can be found.
Hoch et al. [16] managed, in contrast to the unsuccessful efforts of many other re-
searches [1, 34], to find a relationship between consumer characteristics and price elas-

6
ticity using scanner data of 18 product groups in 83 stores in Chicago. They discovered
they could explain two thirds of the variation in price elasticity by using eleven consumer
characteristics consisting of demographic and competitive variables. The information com-
prised in seven demographic variables related to life stage, education, family size, income,
ethnicity, value of the house, and the percentage of working women are exploited. More-
over, four competitive variables such as the sales of competitors and distances to other
supermarkets and warehouses are incorporated in the model. The demographic variables
proved to be more important than the competitive variables. However, the research dates
from 20 years ago and the retailing market has changed drastically. Collecting data is
way less expensive these days and therefore the data could contain more valuable infor-
mation. Moreover, since the data was collected in Chicago the competitive landscape and
consumer behavior are expected to differ from the competitive landscape and consumer
behavior in the Netherlands.
As stated before, price elasticity is broadly researched and all sorts of different deter-
minants to price elasticity are examined. Kumar and Karande [26] seek the effect of the
environment of a store on the retailer’s performance by means of the sales or productiv-
ity of stores located all over the United States. Most interestingly, they conducted the
analysis on store level and segmented stores offering useful insights in the determinants of
store performance. Situational price sensitivity is examined by Wakefield et al. [41]. They
found in case of social and hedonic consumption situations price sensitivity is weakened
compared to functional consumption. Huang et al. [19] found that low-income shoppers
appear to be most price sensitive and price sensitivity decreased in case market share
of brands increased. Last, Elrod and Winer [11] found weak significant influence of age,
education, and female headed households on price sensitivity.

7
3 | Data

As we know retailers assign stores to clusters. Stores assigned to the same cluster charge
the same prices for the same products. As previously mentioned in Chapter 1 Jumbo
implements four unique clusters of stores based on local competition. Each of the formed
clusters of stores is called a priceline. The stores are assigned to a priceline based on the
nearest located competitor in the same domicile. In this research we focus on the priceline
represented by the largest competitor of Jumbo which is Albert Heijn due to availability
issues of the data. Within this priceline we conduct a clustering of stores. This cluster of
stores contains 305 stores out of the over 600 stores in total. These stores account for 53%
of the revenue of the Jumbo market chain. Stores that opened at most 3 months ago are
discarded from the research due to the limited amount of historical data. Furthermore,
only products which are sold in the last quarter (2016Q1) of the considered time span
are taken into account since products which are not sold anymore do no longer influence
the policy of a retailer. There are two sources of data used: the Jumbo database and
Statistics Netherlands (CBS). We use CBS data to retrieve information on demographics
related to the environment of the considered stores. The price elasticities on store-item as
well as on store level are provided by the retailer. Moreover, the data is roughly split into
two sets, the scanner data analyzed in Section 3.1 and the store-specific characteristics
and trading area data discussed in Section 3.2.

3.1 | Scanner data

We retrieve weekly scanner data at store-item level for a time span of 156 weeks from the
Jumbo database. We focus only on the non-alcoholic beverages again due to availability
issues. Furthermore, in general the product groups related to non-alcoholic beverages show
most variation in price elasticity. Therefore these product groups are most promising
regarding a boost in sales and profit. The non-alcoholic beverages account for 5% of
the euro sales volume. The considered product groups are displayed in Table 3.1. The
average price elasticity per product group per store is found by dividing the price elasticity
per product group per store by the number of stores that sell products of the considered
product group. The price elasticity per store per product group is provided by the retailer.
It can be easily seen that the product group Juices has the highest average price elasticity
per store, whereas Cola has the lowest average price elasticity per store. On average the
product groups contain 158 different products with 239 at a maximum for the product
group Kids youth and 66 at a minimum for the product group Energy.

8
 Table 3.1: The evaluated product groups with the number of products, number of
brands, average price elasticity per store and standard deviation of the price elasticity.

Product group Number of products Number of brands Average elasticity Standard deviation

Cola 108 6 -0.946 0.180

Energy 66 18 -0.964 0.116
Juices 233 28 -1.509 0.167
Kids youth 239 32 -1.056 0.130
Large soda 204 25 -1.044 0.139
Water 95 14 -1.016 0.096

This scanner data set comprises the retail prices, prices for substitutes and comple-
ments, as well as information on promotions such as price discounts. The extensive data
on promotional activity also incorporates indicators for the promotional channels such as
local media, flyers, and television commercials. Furthermore, the data contains informa-
tion on holidays, weather, and school vacations.

3.2 | Store-specific characteristics and trading area data

The Jumbo database and CBS provided us with data on store specifics and trading area
data which are composed of competition, socio-demographics, and socio-economic vari-
ables. All stores as accounted for in the scanner data set are represented. Moreover, to
get a grasp into the reasons for variation in price elasticity we retrieve information from
the database on store-specific characteristics such as franchise indicators, store offerings
being for example information on the presence of self scanners, the surface in square me-
ters of a store, the city-rural dummy and many more. The city-rural dummy is useful to
cope for population density within the trading area of specific stores. The trading area
is determined by competition among others. The competition is split into two separate
groups: supermarkets and miscellaneous such as liquor and drug stores. The retailer de-
fines the competitive environment of stores by collecting information on the competitive
supermarkets and the miscellaneous competitors within a radius of 15km from each store.
Note, the stores within a radius of 15km that belong to the supermarket chain of Jumbo
itself are also indicated as competitors since sales of these specific stores could transfer to
another Jumbo store due to the presence of another ‘competitive’ Jumbo store. The con-
sidered socio-economic variables comprise variables such as education, income, and social
class. The trade area characteristics take also socio-demographic variables into account
like household size. Additionally, from CBS we retrieve information on ethnicity in the
form of the percentage of western and non-western immigrants.

9
4 | Method

This research strives to use the variance in price elasticity to get to new clusters of stores
by conducting a two-stage clustering framework. Figure 4.1 shows there is still a lot of
variation in price elasticity within clusters of stores and especially in some specific product
groups between stores which proves the need for a new method.

25 % Cola
Energy
20 % Juice
Share of stores

Kids youth
Large soda
15 %
Water

10 %

5%

0%
−2.2 −2 −1.8 −1.6 −1.4 −1.2 −1 −0.8 −0.6 −0.4
Store-specific price elasticity

Figure 4.1: The share of stores by the store-specific price elasticity.

Differences in price elasticities on store-item level are studied [32] to find new clusters
of stores. We propose a novel dissimilarity measure in Section 4.1 that is used in the
clustering framework. Next, we discuss the clustering framework and the evaluation and
validation methods in Section 4.2. Finally, Section 4.3 shows an outline of the regression
model that is used for the analysis of the final set of clusters found by the clustering
framework. Note, we assume that each product only belongs to one product group. In
the remainder of this paper symbols i and j refer to products, whereas s, v, and y indicate
stores. The set of all stores is indicated by S and the set of all products by I. Furthermore,
G is the set of product groups. Then,

G
[
I= Pg (4.1)
g=1

where Pg is the set of products in the product group with index g. The input data for
the clustering algorithm Γ = {ei,s ∀i ∈ I, s ∈ S} comprises all price elasticities ei,s per
product i in store s. The clustering function for each product group indicated by g can
be described as:
λg : S → {1, ..., kg }, ∀g ∈ {1, ..., G}, (4.2)

10
with kg is the number of clusters for product group g and subsequently the set of clusterings
is defined as follows:
Λ = {λg : g = 1, ..., G}. (4.3)

This way we define a clustering of stores for each product group separately via Λ based on
the price elasticities on store-item level. The information comprised in Λ is used to find
the final optimal clustering λ∗ by means of the hard least squares Euclidean consensus
algorithm. In the appendix, Table A.1 shows an overview of all symbols used for the
dissimilarity measure and the clustering method.

4.1 | Dissimilarity measure

For the dissimilarity measure between stores, which is used in the clustering method, two
conditions should be taken into account: first product importance and second not available
values (NA). That is why the commonly used Euclidean distance for clustering does not
suffice as dissimilarity measure. First obviously, products with relatively high revenue
are most valuable to the retailer which makes us introduce weighted dissimilarities. The
higher the weight, the more important we consider a specific product. Weight wi is defined
as follows:
ψi di
wi = P , (4.4)
i∈N (s,y) ψi di

where N (s, y) is the set of all products in a product group sold in both stores s and y,
ψi equals the average revenue per store for product i, and di represents the number of
stores in which product i is sold. Weight wi corresponds to the total revenue of product i
divided by the total revenue of all products sold in both stores s and y in its corresponding
product group such that 0 ≤ wi ≤ 1. Consequently, the result is the following preliminary
weighted dissimilarity measure between store s and store y:
X
D0 (s, y) = wi |ei,s − ei,y |, (4.5)
i∈N (s,y)

where |ei,s − ei,y | is the absolute difference between the price elasticities of product i sold
in store s and store y. The sum is exclusively evaluated over the set N (s, y) since it is only
possible to subtract price elasticities in case both stores sell the product. If a product is
solely sold in one of both stores, the price elasticity of the product is not available in one
of the stores and we can not subtract the price elasticities of the products as simply one
of them misses. Note, if both stores do not sell the considered product there will be no
difference in assortment and therefore there is no indication for a difference between the
stores regarding the considered product.

11
 Second, again imagine we are interested in the dissimilarity between two stores and
only one of the stores sells a specific product. Although the price elasticity of the product
is not available in one of the stores it indicates a difference between the stores because
the assortment differs. Therefore, Porro et al. [33] suggest to address the problem before
the classifier is built. They propose to adjust the dissimilarity measure to cope for the
not available values by using the available data only. The Not Available Correction Term
(NACT) is proposed to correct for products which are solely sold in one of the two con-
sidered stores. The NACT is represented by the fraction ψ∪ /ψ∩ (s, y) and consists of the
following terms:
X
ψ∪ = ψj dj (4.6)
j∈Pg

and
X
ψ∩ (s, y) = ψi di , (4.7)
i∈N (s,y)

where ψ∪ is the total revenue of all products sold in a product group, whereas ψ∩ (s, y)
is the total revenue of all products exclusively sold in both stores. Accordingly, the final
domain-specific dissimilarity measure is as follows:

ψ∪ X
D(s, y) = wi |ei,s − ei,y |. (4.8)
ψ∩ (s, y)
i∈N (s,y)

This way the NACT is responsible for the relative importance of the set of products sold
in both stores in a product group versus the set of products exclusively sold in one of both
considered stores in a product group. The following hypothetical example provides insight
in the NACT. Imagine we compare two stores s and y. There are three products sold in
the union of products sold in stores s and y in the considered product group. Product 1
is exclusively sold in store s and has a revenue of 10 in total. Moreover, products 2 and 3
have a revenue of 20 and 30 in total in both stores, respectively. Therefore, the numerator
of the NACT equals 60 and the denominator equals 50 which results in a NACT of 60/50.
This means the dissimilarity measure is scaled up since one of the products is exclusively
sold in one store. We want to take this products as well into account with regard to
the dissimilarity between two stores since the assortment differs. Finally, the weight wi
addresses the relative importance of products sold in both stores relative to each other.
Note, the denominator of the NACT and weight wi are the same, i.e, ψ∩ (s, y).

4.2 | Clustering
This section provides the two-stage clustering framework along with the method for clus-
tering validation and evaluation. Subsection 4.2.1 introduces the novel Restricted K-
means++ clustering algorithm and Subsection 4.2.2 the process of finding the cluster

12
consensus. Subsection 4.2.3 enumerates the methods for determining k the number of
clusters. The cluster evaluation method with regard to robustness of the algorithm and
the price policies are shown in Subsection 4.2.4.

4.2.1 Restricted K-means++

K-means++ algorithm
K-means aims to partition n observations into k clusters such that each observation is
assigned to the closest cluster center that serves as a prototype for the cluster. As K-
means could produce unreliable results due to the choice of the initial centers, K-means++
proposes to use the randomized seeding technique that copes with the issue of ending up
in local optima. This way initial centers are seeded at random. At first initial center c1
is picked uniformly at random concerning the randomized seeding technique. Next, let
Cl = {c1 , ..., cl } ⊆ C be the current set of cluster centers. Then, store y is the next cluster
center cl+1 with probability:

min D(y, c)2

c∈Cl
P (cl+1 = y) = P , ∀y ∈
/ Cl , (4.9)
min
s∈S c∈C D(s, c)2
l

where S is the set of all stores, Cl is the current set of cluster centers, and minc∈Cl D(y, c)
is the shortest distance of store y to the closest center c that is already chosen. This way
if the distance of a store to the closest center c that is already chosen becomes higher, the
higher the probability becomes that this store is chosen as the following cluster center cl+1 .

Cluster centers
As stated before we have to deal with products which are not sold in certain stores resulting
in values which are not present in the data. Apart from the problem these values cause
with regard to the dissimilarity measure it interferes with the calculation of the cluster
centers. Cluster centers are normally represented by the cluster means in the K-means++
clustering algorithm. However, since not all values of the price elasticities are available we
can not simply acquire the cluster mean. Therefore, the original K-means++ clustering
algorithm does not suffice and the assignment of new cluster centers in the Restricted
K-means++ clustering algorithm proposed in this paper should be conducted differently.
The cluster center is found with regard to the following optimization criterion:

1 X
cz = argmin D(s, y), (4.10)
y∈Sz |Sz |
s∈Sz

where Sz is the set of stores assigned to the cluster with label z and D(s, y) represents the
dissimilarity between store s and y. This means an existing store serves as a cluster center.
Most importantly note that K-means++ can yield empty clusters due to the assignment

13
of cluster means. However, since our method does not simply compute the cluster means,
but according to Equation 4.10 returns the store which on average has minimum distance
to the other stores within a cluster, we prevent this from happening. The algorithm of
the K-means++ clustering algorithm with a modification to the process of finding cluster
centers can be found in Algorithm 1.

Algorithm 1 K-means++
Initialize kg the number of clusters for PG g
Initialize S the set of stores
Initialize iterM ax the number of iterations of K-means
Pick first initial center c1 uniformly at random from S
for l = 1 to kg − 1 do
minc∈Cl D(y,c)2
Pick new center cl+1 from S with probability P (cl+1 = y) = P 2
s∈S minc∈Cl D(s,c)
end for
for n = 1 to iterM ax do
for z = 1 to kg do
if s ∈ S is closest to center cz then
Assign s to cluster with center cz
end if
Set new cluster center argmin |S1z | s∈Sz D(s, y)
P
y∈Sz
end for
end for

Retailer specifics
To define the clusters retailers operate in compliance with domain-specific business rules.
One of the these business rules that we should take into account during clustering is
that stores originating from the same domicile should be assigned to the same cluster.
This makes us propose the Restricted K-means++ clustering algorithm as found in Al-
gorithm 2. To alter the original clustering algorithm for domain-specifics, the constraint
should be handled with care during initialization or assignment [10]. Since we can easily
depict manually which stores should be assigned to the same clusters according the afore-
mentioned geographical business rule a simple adaption of the assignment of stores should
suffice. Assume V is the set of stores located in the same domicile. Inspired by Wagstaff
et al. [40], assign store v, ∀v ∈ V , to the cluster with center cz according the following
optimization criterion:
1 X
cz = argmin D(v, c). (4.11)
c∈C |V |
v∈V

Hence, Equation 4.11 represents the average distance of the stores located in the same
domicile to the closest cluster center. Thus, all stores located in the same domicile are
assigned to a cluster if these stores are closest on average to the center of that cluster.
This means at first all stores are separately clustered and subsequently cluster centers are

14
determined as proposed in Equation 4.10. Last, taking into account the business rule,
stores are re-assigned according Equation 4.11.

Robustness
Additionally, we focus on building a robust system by conducting the Restricted K-
means++ clustering nStart times taking the clustering r∗ that minimizes the total within
sum-of-squares (TWSS) of the clusters. The TWSS is a measure of internal cohesion and
is the sum of distance functions for all clusters of each point in the cluster to the k th
center. This way we avoid that little bit of randomness that slips into the system by
picking a first cluster center uniformly at random during random seeding.

Algorithm 2 Domain-specific Restricted K-means++

Initialize kg the number of clusters for PG g
Initialize S the set of stores
Initialize iterM ax the number of iterations of K-means
Initialize V the set of stores per domicile
Pick first initial center c1 uniformly at random from S
for l = 1 to kg − 1 do
minc∈Cl D(y,c)2
Pick new center cl+1 from S with probability P (cl+1 = y) = P
minc∈Cl D(s,c)2
s∈S
end for
for n = 1 to iterM ax do
for z = 2 to kg do
if s ∈ S is closest to center cz then
Assign s to cluster with center cz
end if
Set new cluster center argmin |S1z | s∈Sz D(s, y)
P
y∈Sz
end for
if V ⊂ S closest to center cz subject to cz = argmin |V1 | v∈V D(v, c) then
P
c∈C
Assign v, ∀v ∈ V to cluster with center cz
end if
end for

Note, the Restricted K-means++ clustering algorithm is conducted for all product groups
that are considered separately.

4.2.2 Cluster consensus

As mentioned before, the behavior among product groups differs and therefore we found
different clusters of stores for each product group separately. However, in the end the
retailer searches for one specific clustering of stores due to operational and optimization
limitation. The information in the separate clusterings of product groups is captured in
a single relation by means of the hard least squares Euclidean consensus algorithm [17]
through the CLUE package in open source software package R.

15
 Before the actual clustering consensus can be found the definition of dissimilarities
between clusterings should be considered. The main issue to calculating dissimilarities
between clusterings is that the cluster labels may be mixed up in different clusterings,
whereas the underlying structure of the data does not change. Therefore we have to
find a permutation of the cluster labels in such a way that agreement between clusters
is maximized. In order to assess the problem of cluster labels permutation matrix Π
is used to replace λ by λΠ. This relabeling procedure assures the cluster labels of λ
are reassigned without changing the underlying structure of the data. Since searching
through all possible permutations is very time-consuming Dimitriadou et al. [8] defined
the following Euclidean clustering dissimilarity between λ and λ:
e

e = minkλ − λΠk,
d(λ, λ) e (4.12)
Π

where k·k is the Frobenius norm. This distance measure is simply equivalent to maxi-
mizing the number of objects with the same class id in both clusterings. For proof see
Hornik [17]. Now, Hornik proposed to find the optimal Π using the Hungarian method [25]
since we have to deal with the linear sum assignment problem (LSAP). Subsequently, all
information in the elements of the cluster ensemble Λ needs to be incorporated into the
so-called cluster consensus. The cluster consensus is the single clustering of stores we are
looking for. Consensus candidates λ are compared to the cluster ensemble. The optimal
cluster consensus λ∗ is defined as follows:
X
λ∗ = argmin xg d(λ, λg )p , (4.13)
λ
λg ∈Λ

which is equivalent to
X
λ∗ = argmin xg minkλ − λg Πg kp ., (4.14)
λ Πg
λg ∈Λ

where xg is the PG-specific weight. Moreover, weights are based on the revenue of a
specific product group: P
j∈Pg ψj dj
xg = PG P . (4.15)
h=1 j∈Ph ψj dj
Then, xg represents the total revenue of product group g divided by the total revenue
of all product groups such that 0 ≤ xg ≤ 1. If p = 2, we use least squares consensus
clusterings. Now define λe as the weighted average of λg Πg and fix Πg . The weighted
average of λg Πg is equivalent to:

G
e= P 1
X
λ G
x g λ g Πg . (4.16)
g=1 xg g=1

16
Then, Hornik. [17] proves the optimal λ which is λ∗ , is given by λ.
e Moreover, since we
have to find multiple optimal permutations for the separate partitions we no longer assess
the LSAP but it becomes a multi-dimensional assignment problem (MAP) which is solved
using the DWH (Dimitriadou, Weingessel and Hornik) algorithm from the CLUE package
in R. This algorithm is an extension of the greedy algorithm described in Dimitriadou et
al. [8]. Note that without going back to the information contained in the original data or
the Restricted K-means++ clustering algorithm we obtain a final clustering.

4.2.3 Cluster validation

In general there are two different validity tests to determine the number of clusters that
fits the underlying data the best: internal indices versus external indices [42]. Internal
indices are used to measure the goodness of a clustering structure without respect to
external information [37]. On the contrary, external indices are used when cluster labels
are known a priori [9]. For our purpose we use internal indices as cluster labels are
unknown beforehand. A lot of research is conducted for cluster validity from which we
selected the most commonly applied elbow method [31] as a decision rule to determine kg
the number of clusters for product group g 1 . The number of clusters used for the cluster
consensus k ∗ is found by using the weighted average of the number of clusters found for
the separate product groups:

G
X
k ∗ = round( xg kg ), (4.17)
g=1

where round(·) is the nearest integer function, xg is the weight for product group g and
kg the number of clusters indicated for product group g.

4.2.4 Cluster evaluation

The price policies applied in this paper embody a simplified version of reality where no
price optimization method comes in play. The main focus is proving usefulness of our
clustering framework by searching for the impact of the acquired clusters of stores and
not so much to find optimal prices.
The main goal of the price setting procedure is to create price differences for the prod-
ucts between the clusters. The price setting process comprises two steps: label products as
elastic, regular, or inelastic and subsequently change prices of elastic and inelastic labeled
products. Therefore, we choose to label products based on predefined product-specific
intervals. The average price elasticity µi and standard deviation σi of product i are found
and used as input to construct the product-specific interval (µi ± σi ), see Figure 4.2.
1 The silhouette index [35] and the Hartigan index [15] are used for confirmation. In case both the

silhouette index and Hartigan index do not agree on the number of clusters kg found by the elbow method
for product group g, the number of clusters is reconsidered.

17
 Price elasticity
µi − σi µi µi + σi
elastic inelastic

Figure 4.2: The illustration of the product-specific interval.

Next, labels are assigned to each product within a specific cluster. The average price
elasticity µi,c of product i in cluster c is found and compared to the product-specific
interval. In case µi,c exceeds the lower bound of the interval and µi,c is smaller than -1
the product is assigned the label ‘elastic’. The cluster-specific average price elasticity of
a specific product should exceed -1, otherwise a product is in principle not elastic at all.
Whenever µi,c exceeds the upper bound of the interval and µi,c ∈ (−1, 0) the product
is assigned the label ‘inelastic’. In all other cases the product is assumed ‘regular’. The
labeling procedure is summarized in Algorithm 3.

Algorithm 3 Labeling procedure

Initialize Pg the set of products in a PG
Initialize C the set of cluster centers
for i ∈ Pg do
Find average µi and st.dev. σi of the price elasticity of product i
for c ∈ C do
Find average µi,c of the price elasticity of product i
cluster with cluster center c
if µi,c < µi − σi and µi,c < −1 then
Label product i in cluster with cluster center c as ‘elastic’
else if µi,c > µi + σi and −1 < µi,c < 0 then
Label product i in cluster with cluster center c as ‘inelastic’
else
Label product i in cluster with cluster center c as ‘regular’
end if
end for
end for

The following step is to set prices for a new price policy based on the labeling procedure.
Current prices are used as a starting point. Obviously, the prices of inelastic labeled
products are raised and prices of elastic labeled products are cut. Since we have the data
of Jumbo at our disposal we have to take into account their business rules. Therefore,

18
prices should not exceed the lowest prices of the competition within the same domicile.
This leads to a price increase in inelastic products up to the prices of the competition
with a maximum of 5%. The price decrease of elastic products is limited to a maximum
of 5%. Both the percentage changes are set according the policy of the retailer. Last,
price elasticities are used to find the projected sales after the price setting procedure is
conducted. Keep in mind that we force price differences between clusters in order to be
able to prove the value to the retailer to set different prices in different clusters of stores.
To conduct a robustness analysis for the clustering we use the Jaccard (dis)similarity
[20]. The Jaccard similarity is developed to find the similarity between sets of categorical
variables, such as the similarity between the cluster consensus and the separate clusterings
of each product group. This measure is specifically chosen since the distances between
the cluster labels which represent cluster membership are irrelevant. In Equation 4.19 the
formula of the Jaccard similarity can be seen, where λg (S) and λ∗ (S) are the clustering
for product group g and the cluster consensus representing cluster membership:

|λg (S) ∩ λ∗ (S)|

J(λg (S), λ∗ (S)) = (4.18)
|λg (S) ∪ λ∗ (S)|
where λg (S) ∩ λ∗ (S) = the intersection of sets λg (S) and λ∗ (S) and λg (S) ∪ λ∗ (S) = the
union of sets λg (S) and λ∗ (S). The opposite of the Jaccard simmilarity is obviously the
Jaccard dissimilarity which is as follows:

|λg (S) ∩ λ∗ (S)|

J(λg (S), λ∗ (S)) = 1 − . (4.19)
|λg (S) ∪ λ∗ (S)|

Below we give an example of the (dis)similarity calculation between the cluster mem-
bership for a specific product group λg (S) and the cluster consensus λ∗ (S). Imagine
hypothetically we have 8 different stores assigned to two different clusters.

h iT
λg (S) = 2 1 1 2 1 2 2 2
h iT (4.20)
λ∗ (S) = 1 1 1 2 2 2 2 1

It can be easily seen that the Jaccard similarity equals 5/8 and the Jaccard dissimilarity
equals 3/8. This means that for the evaluated product group 5 out of the 8 stores end up
in the same cluster as in the cluster consensus.

4.3 | Regression analysis

Next, we acquire the drivers of price elasticity by conducting regression models for each of
the separate clusters. This way we can prove the differences in consumer behavior among
the clusters and gain insight in the underlying factors that affect consumer behavior such

19
the retailer can make better decisions. In order to discover the drivers of differences in
consumer behavior among clusters panel data models [28] are conducted for the clusters,
inspired by Hoch et al. [16]. Therefore socio-demographic as well as socio-economic vari-
ables and competitional characteristics among others are used [26]. In Subsection 4.3.1 the
theoretical background on regression models is elaborated. Subsection 4.3.2 explains the
variables that are made available and discusses the selection procedure of these variables
for the regression models.

4.3.1 Regression model

We consider a unique regression model for each of the four different clusters. The regres-
sion model serves descriptive purposes [18] for the price elasticity of stores per cluster.
So, in each of these models the dependent variable is the price elasticity per store. For
each regression model the price elasticities per store of the stores that are assigned to the
considered cluster are used. Since time contributes to the diversity of the data we con-
sider panel data regression models for each of the formed clusters. We use time-variant
as well as time-invariant characteristics. The step wise decision process to acquire the
final regression model leads us to the considered random effects models. The following
model postulates the relationship between price elasticities per store per cluster, es,t , and
covariates, xs,t , as follows:
es,t = δ + x0s,t γ + us,t , (4.21)

with us,t = (δs − δ) + ηs,t , δs ∼ i.i.d.(δ, σδ2 ), and ηs,t ∼ i.i.d.(0, ση2 ). The price elasticities
per store per cluster are found by aggregating the sales of all products part of all six
considered product groups in a specific store. Note, the price elasticities considered in the
regression models are no longer per product per store since we are especially interested
in the drivers that separate the stores and not so much in product specifics. The feasible
generalized least squares estimation (FGLS) is used to estimate the parameters in the
random effects model.

4.3.2 Variable selection

The extensive background information on store-specifics and trading area comprises socio-
economic variables, socio-demographics and competitive characteristics among others. An
overview of all the variables used during the regression can be found in Table A.2 in the
Appendix. We conduct a step wise regression with forward selection. To counterbalance
the problem of multiple comparisons we need to assure the family-wise error rate (FWER)
is controlled at the significance level (F W ER ≤ α). The controlling procedure we use to
encounter this problem is the classical Bonferroni correction [6]:

α
pi ≤ (4.22)
m

20
where pi is the newly found significance level for hypothesis i, α is the desired significance
level, and m is the number of hypotheses tested. In general, the significance level α is set
to 5%.
With regard to the time-dependent variables we have to deal with aggregation issues.
Since the data is made available at store-item level per week we need to aggregate over
the products sold in a store to acquire store level data per week. Moreover, for the prices
of substitutes and the prices of complements the average price during a week is used. For
the promotional variables the percentage of products on promotion is composed.

21
5 | Evaluation

In this chapter the results of the proposed methods are discussed. First, the cluster
definition is elaborated in Section 5.1. Next, in Section 5.2 the results of the sensitivity
analysis for different price policies are considered. In Section 5.3 we discuss the results of
the new price policy. Finally, in Section 5.4 we take a closer look at the results from the
regression analysis.

5.1 | Cluster definition

This section provides the cluster definition. We show the cluster validation of the clus-
tering algorithm and the interpretation of each of the found clusters in Subsection 5.1.1.
Next, we evaluate the robustness of the clustering method using the Jaccard dissimilarity
in Subsection 5.1.2.

5.1.1 Cluster interpretation

The number of clusters indicated by the elbow method for each of the separate product
groups is presented in the elbow plot in Figure 5.1 by means of the TWSS1 . Results show
to remain four clusters for each of the product groups. Therefore, we set the number of
clusters for the cluster consensus to four as well.

Cola
Energy
Juice
10
Kids youth
TWSS

Large soda
Water
5

0
2 3 4 5 6 7 8 9 10
Number of clusters

Figure 5.1: The figure presents the number of clusters per product group indicated by
the elbow method by means of the total within sum of squares (TWSS).

The first cluster contains 102 stores represented by an environment with a relatively
high percentage of consumers part of the low social class, see Table A.3 in the Appendix for
1 The silhouette and Hartigan index confirm the number of clusters indicated by the elbow method.

22
more information on social classes. Moreover, the percentages of youth and non-western
immigrants are large. The second cluster consists of 105 stores mostly situated in the
South of the country. As well as for the fourth cluster, which consists of 41 stores, the
percentage of consumers part of the high social class and families with kids are relatively
high. These clusters differ in particular in the share of youth which is highest in cluster
4. Last, the remaining 57 stores belong to cluster 3 and are mostly situated in the upper
North of the country in the rural areas which is reflected in the small share of immigrants
and the fact that supermarkets are relatively far apart. As well as for cluster 1 the
percentage of consumers part of the low social class is relatively high. An overview of
the cluster means of some of the characteristics of the different clusters can be found in
Table 5.1.

Table 5.1: The table presents the cluster means of some of the characteristics of the
different clusters (in percentages).

Characteristic Cluster 1 Cluster 2 Cluster 3 Cluster 4

Low social class 54 46 60 45

High social class 46 54 40 55
Non-western immigrants 8 5 4 5
Western immigrants 8 10 5 9
Youth 9 7 7 11
Families with kids 17 20 15 20
Average distance to supermarket (in m) 500 590 685 530

5.1.2 Cluster evaluation: Jaccard

Throughout Subsection 4.2.4 we have discussed the Jaccard dissimilarity. This measure is
used as an indication of the robustness of the clustering method. Note, the results provided
in Table 5.2 are measured with regard to the cluster consensus. This way each of the
dissimilarities found in the table represents a comparison between the cluster membership
of the listed product group and the cluster consensus.

Table 5.2: The Jaccard dissimilarities of the cluster memberships of the product
groups versus the cluster consensus.

Clusters Cola Energy Juices Kids youth Large soda Water

All stores 0.039 0.026 0.026 0.020 0.007 0.026

Cluster 1 0.056 0.064 0.019 0.057 0.019 0.073
Cluster 2 0.076 0.028 0.057 0 0 0.019
Cluster 3 0.070 0 0.035 0.068 0 0.070
Cluster 4 0.128 0.146 0.128 0.049 0.049 0.049

23
 In general, the Jaccard dissimilarity of the product groups with the cluster consensus
seems strikingly low with 0.039 as a high for Cola. This indicates an overall difference of
12 out of 305 stores appointed to different clusters. This means the deviation of each of
the clusterings of the product groups from the cluster consensus is small and the stores
for the most part end up in the same cluster. Noteworthy is for example the fact that
for both Kids youth and Large soda the stores in the second cluster do not differ from
the cluster consensus. This could be due to the large number of products together with
the relatively small spread in price elasticity in these product groups, see Table 3.1. This
makes clustering relatively easy compared to the other product groups. Considering the
results of the Jaccard dissimilarity the proposed Restricted K-means++ clustering method
is very robust and only indicates minor differences between the clusterings of the product
groups versus the cluster consensus. The consumer behavior seems to be split roughly
the same for each of the product groups since we are using the most specific level of price
elasticities.

5.2 | Sensitivity analysis

In Figure 5.2 we provide the initial average revenue and profit per product of the evaluated
product groups as a reference point for the upcoming results. The average revenue and
profit are based on the current out-of-the-door prices, also called regular prices. The
average revenue as well as the average profit are at a maximum for the product group
Cola while these numbers are at a minimum for the product group Kids youth. Cola can be
seen as one of the most popular product groups since the sales of the individual products
are relatively high. From Figure 5.2 it follows the average profit share per product is 27%.
That is why the average profit share per product of 32% for Energy stands out since the
margin per product is relatively high.

Cola 328 93
Energy 199 63
Water 159 46
Large soda 133 38
Juice 126 32
Kids youth 118 25

Figure 5.2: The initial situation of the average revenue (l) and average profit (r) per
product of the products within a product group (in thousands of euros).

We work step by step towards a new price policy as discussed in Subsection 4.2.4.
After each product is indicated as being ‘elastic’, ‘inelastic’ or ‘regular’, new prices are set
for the different clusters. To recap, the prices of inelastic products are increased up to a
maximum of 5% and the price cut of elastic products is also limited to 5%. Moreover, price

24
elasticities are used to find the projected sales after new prices are set. If we change prices
we have to reckon with competition since prices are not supposed to exceed the prices of
the competition and Jumbo has the ‘lowest price guarantee’, which basically means that
prices of a specific product for all stores in a cluster are set as low as necessary by the
supermarket in a way that there is still sufficient profit left.
First, we take a closer look at the effect of price changes of elastic products on the
revenue and profit. Obviously, by increasing the percentage change of prices of both
the elastic and inelastic products the revenue increases. On the other hand this is not
by definition the case considering the profit. Results show that cutting prices of elastic
products by a predefined percentage in general is not profitable in the end. The reason
is that prices are bounded to the business rule of the lowest price guarantee. There is
no longer space for price cuts without harming the profit due to the negligible difference
between the cost price and out-of-the-door price in general. If we cut prices it does not
lead to sufficient increases in the sales such the profit grows.
Now, we take a closer look at the the effect of price changes of inelastic products on
the revenue and profit. From now on, we consider a maximum price increase in inelastic
products, indicated by ‘max+5%’, as the price increase which is bounded by the price of
that product charged by the competition within the same domicile. For example, product
i and j are priced e1 in our store. The price of the competition for product i is e1,05
and the price of the competition for product j is e1,10. The price of product i can be
raised up to e1,04, since the new price can not exceed the price of the competition. This
results in a price increase of 4%. For product j we can raise the price up to e1,09 which
represents a price increase of 9%. However we are bounded to a maximum increase of 5%
of the current price resulting in a new price of e1,05 for product j. Results show that
changing prices of inelastic products results in more revenue and more profit in the end.
In conclusion, a price change of elastic products in general does not lead to an increase
in profit, but price changes of elastic products prove to be valuable in case of the revenue.
On the other hand, the price increase in inelastic products is valuable to the revenue and
is profitable. Thus, the optimal profit can be found by not changing prices of elastic
products and changing prices of inelastic products up to the maximum of +5%. In the
end we are dealing with a trade-off between revenue and profit. The increase in revenue
can be related to more customers and therefore more relevance of the retailer in the eyes
of the customer. On the other hand profit is important for the retailer itself. The impact
on the revenue and profit by means of the step wise percentage change in price of inelastic
and elastic products can be found in Table B.1 and B.2 in the Appendix, respectively.

25
 Table 5.3: The projected increase in revenue and profit for different price policies (in
percentages).
Elastic Inelastic Revenue Profit

-0% max+5% 0.19 1.1

-1% max+5% 0.28 0.93

-2% max+5% 0.36 0.76

-3% max+5% 0.45 0.57

-4% max+5% 0.52 0.37

-5% max+5% 0.6 0.15

Table 5.3 presents the sensitivity analysis for the projected increase in revenue and
profit for different price policies in percentages. As mentioned before, we noticed that
changing prices of elastic products results in an increase in revenue and in a decrease in
profit generally. However, looking at price changes of inelastic products both revenue and
profit result in an increase. We impose a trade-off between revenue and profit. To find
middle ground, from this moment onward we focus on the price policy where prices of
elastic products are cut by 2% and prices of inelastic products are raised by max+5%. In
this case, the projected increase in revenue and profit of the considered product groups
are 0.36% and 0.76%, respectively.

5.3 | New price policy

Now, we are going to highlight some of the results of the new price policy discussed in
Section 5.2. Tables 5.4 and 5.5 present the projected increase in revenue and profit per
product group by cluster, respectively. Note, we are taking a closer look at the projected
increase in revenue and profit and not at the total effective absolute values of revenue and
profit. Thereby it can happen that the increase in revenue exceeds the increase in profit
which could seem counter intuitive. This has everything to do with the co-existence of
the change in sales and change in total cost both found using the price elasticity. The
moment we set new prices according the price elasticity, the sales change and therefore
the total cost of these products change.

26
 Table 5.4: The projected increase in revenue per product group by cluster with
competition taken into account and 2% price change of elastic products.

Product group Cluster 1 Cluster 2 Cluster 3 Cluster 4 Total

Cola 18,528 (0.15) 76,274 (0.63) 23,222 (0.39) 10,505 (0.20) 128,529 (0.36)
Energy 531 (0.01) 3,605 (0.08) 13,626 (0.60) 6,506 (0.49) 24,268 (0.18)
Juice 7,960 (0.08) 47,689 (0.52) 38,157 (0.62) 18,141 (0.43) 111,947 (0.38)
Kids youth 32,077 (0.34) 36,784 (0.39) 40,109 (0.63) 9,693 (0.32) 118,663 (0.42)
Large soda 9,953 (0.12) 54,504 (0.53) 34,461 (0.61) 8,973 (0.32) 107,891 (0.40)
Water 6,692 (0.14) 17,170 (0.29) 16,120 (0.65) 8,312 (0.44) 48,294 (0.32)

Total 75,741 (0.15) 236,026 (0.46) 165,695 (0.58) 62,130 (0.34) 539,772 (0.36)

Table 5.4 gives the projected increase in revenue per product group by cluster. In line
with our expectations the relative increase in revenue of cluster 3 is highest compared
to the other clusters by reason of the substantial share of products indicated as elastic
or inelastic, namely 19.2%. However, in absolute terms cluster 2 outperforms cluster 3
since it consists of almost double the number of stores. The average number of products
indicated as inelastic and elastic per cluster is 17.5%. For more information on the number
of products indicated as elastic or inelastic see Table B.4 in the Appendix. In addition,
outstanding is the minor increase in revenue for cluster 1 despite the large amount of stores
in cluster 1. The number of products indicated as inelastic (6%) is strikingly low. Further
notice that Kids youth experiences the most growth in relative terms and in particular
cluster 1 stands out with regard to the other product groups.

Table 5.5: The projected increase in profit per product group by cluster with
competition taken into account and 2% price change of elastic products.

Product group Cluster 1 Cluster 2 Cluster 3 Cluster 4 Total

Cola 27,256 (0.79) 9,807 (0.28) 23,112 (1.34) 2,512 (0.18) 62,687 (0.63)
Energy -71 (-0.00) -714 (-0.01) 16,238 (2.13) -2,319 (-0.56) 13,134 (0.31)
Juice 4,869 (0.19) 21,703 (0.94) 29,692 (1.92) 69 (0.00) 56,333 (0.76)
Kids youth 18,063 (0.92) 41,332 (2.01) 2,176 (0.16) 4,320 (0.67) 65,890 (1.10)
Large soda 11,878 (0.50) 28,838 (1.01) 35,322 (2.15) 428 (0.01) 76,465 (0.99)
Water -1,022 (-0.07) 12,973 (0.78) 10,984 (1.49) 2,747 (0.51) 25,683 (0.59)

Total 60,973 (0.46) 113,939 (0.83) 117,524 (1.52) 7,757 (0.16) 300,193 (0.76)

Then, the projected increase in profit per product group by cluster is depicted in
Table 5.5. In general the different clusters of each of the product groups are more profitable
than the initial situation. Nonetheless, we can find some clusters, such as cluster 2 of the
product group Energy and cluster 1 of the product group Water, which result in a decrease
in profit. Especially for cluster 2 of the product group Energy this is not surprising since
exclusively some products are indicated as elastic and as we have seen before price changes

27
of elastic products usually result in a decrease in profit. Cluster 3 outperforms cluster 2
although the projected increase in revenue for cluster 2 is higher. This indicates the cost
of goods sold changes in favor of cluster 3. In absolute terms as well as in relative terms
cluster 4 is least profitable among other things because of the small number of stores that
end up in cluster 4. Then, the projected increase in profit in relative terms is highest for
the product group Kids youth. Likewise, the projected increase in profit of the product
group Kids youth is highest.
Finally, results show a projected increase in revenue of 0.36% and a projected increase
in profit of 0.76% in total for the considered product groups. Cluster 3 is most profitable
as a result of the large amount of inelastic indicated products (11%) despite the fact that
cluster 2 generates a higher projected increase in revenue. With regard to the product
groups, especially the profit increase in Kids youth attracts attention endorsed by the
projected increase in revenue.

5.4 | Regression analysis

At last we are interested in the drivers of consumer behavior and thereto this section
discusses the results of the panel data regressions2 . To recall regression analysis is con-
ducted such we can prove the differences in consumer behavior among the clusters and
gain insight in the underlying factors that affect consumer behavior such the retailer can
make better decisions. Note, when interpreting the signs of the coefficients of the inde-
pendent variables it is important that the dependent variable is a negative number. If
the independent variable grows, a positive sign results in a shrinking effect on the price
elasticity, whereas a negative sign indicates an enlarging effect.
Table 5.6 presents a few of the covariates of the price elasticities per store per cluster.
First, the holidays Father’s and Mother’s day are considered which show various effects
on the price elasticity. Father’s day has an enlarging effect on the price elasticity, whereas
Mother’s day has a shrinking effect. The considered advertisement channels in this section
comprise instore flyers and national folders since they prove the difference in behavior
among clusters. Generally, these advertisement channels increase price sensitivity, however
in particular cluster 3 behaves differently. The price of substitutes seems to have an
enlarging effect in general on the price elasticity, however for cluster 2 this is not the case.
Interesting is the fact that time-independent variables usually have significant effect on the
price elasticities in exclusively one of the clusters. Outstanding is the difference in effect
of unemployment on clusters 1 and 2. The unemployment rate results in an increasing
effect of price sensitivity for cluster 1 and a decreasing effect for cluster 2. Summarizing,
these covariates provide sufficient evidence to assume that consumer behavior among
clusters differs and therefore pricing decisions should be adjusted accordingly. The full
2 Linear time-independent regressions were also attempted but yielded no significant results.

28
 results of the panel data regression models with regard to the clusters can be found in
Table C.8 in the Appendix. Additionally, the panel data regression models per product
group per cluster are also elaborated in Appendix C to show differences within each
product group between the four found clusters. Furthermore, this Appendix contains
the results of regression models for the different product groups to show differences in
consumer behavior among product groups.

Table 5.6: The table presents some of the coefficients (and standard errors) of the
variables of the panel data regression models on store-item level for all clusters to
declare the dependent variable of price elasticities. Note, that the significance level is set
to 5% and only variables indicated by ‘-’ are not significant.

Panel data regression model

Cluster 1 Cluster 2 Cluster 3 Cluster 4
Independent variables

Father’s day -0.025 (0.004) -0.033 (0.005) -0.027 (0.005) -0.027 (0.008)
Mother’s day 0.050 (0.006) 0.054 (0.007) 0.029 (0.007) 0.069 (0.012)
Price ratio substitute 1 -1.083 (0.039) 0.316 (0.033) -1.183 (0.049) -0.387 (0.064)
Instore flyer -0.446 (0.12) -0.469 (0.139) 0.000 (0.000) -0.786 (0.247)
National folder -1.203 (0.140) -0.640 (0.120) 0.000 (0.000) -0.551 (0.216)

Percentage high education -0.105 (0.035) - - -

Percentage unemployed -0.410 (0.202) 0.789 (0.202) - -
Percentage regular visitor competitor -0.050 (0.023) - - -
R2 0.622 0.649 0.651 0.802

29
6 | Conclusion

In this paper we proposed a two-stage clustering framework using differences in consumer

behavior to define new clusters of stores which are not solely based on local competition.
This way we can boost the revenue and profit of a retailer. The context used is one of the
major supermarket chains in the Dutch market. We defined clusters of stores within the
already existing clusters of stores as there appears to be a difference in consumer behavior
among stores within product groups reflected in the variance in price elasticities. First,
we proposed the Restricted K-means++ clustering algorithm to find the clusterings of
stores for each product group separately. Retailer specifics are implemented under the
guise of a geographical restriction such that each store situated in the same domicile is
appointed to the same cluster. Second, we combined the information comprised in these
separate clusterings into a general clustering called the cluster consensus. That way, all
information on the price elasticity at store-item level is used and no information iss lost
in the process due to aggregation issues. In the following, we highlight our contributions
and propose suggestions for future work.
First, the clustering in general is very accurate and robust since the Jaccard dissim-
ilarity indicates small differences between the clusterings of the product groups and the
cluster consensus. Stores are by and large appointed to the same cluster within each of
the product groups which indicates using price elasticities on store-item level seems an
appropriate choice. Then, most retailers set different prices in clusters of stores based on
the competition in proximity of the considered stores. Our research provides an easily
implementable and fully automated clustering method to find groups of ‘similar’ stores
which are not exclusively driven by local competition. The results show the influence of
competition, store-specifics and trading area data on the price sensitivity, proving con-
sumer behavior is driven by these factors on a day-to-day basis. Thus, depending on the
extent of the influence of the aforementioned characteristics the pricing decision should
be informed accordingly. Furthermore, the algorithm is not order-sensitive by reason of
the random seeding technique. Moreover, we know that K-means can yield empty clusters
however by constructing cluster centers as we propose in this research this can not happen.
The algorithm is not limited to the singular data set used in this research. Furthermore, it
is not even limited to the context of supermarkets. The only information really needed to
apply the algorithm are the price elasticities on store-item level and the revenue per prod-
uct per store which makes the algorithm transparent. The revenue per product per store
is needed to find the product importance and NACT proposed in this paper. The NACT
provides a convenient way to cope with not available values. Altogether, the sensitivity
analysis for the considered product groups suggests potential of defining new clusters of
stores based on consumer behavior enhanced by the projected increase in revenue of 0.36%
and the projected increase in profit of 0.76%.

30
 The follow-up step is to consider if and how the analysis could be extended to the
complete store, which means taking all product groups present in the store in considera-
tion. Moreover, in this research we focus exclusively on the first cluster and are limited
to the results that belong to this cluster. Therefore, an opinion on operational feasibility
should be formed concerning the extension to complete stores and all existing pricelines.
In general, it seems obvious to reconsider the time span of pricing optimization as price
sensitivity changes over time. For example, price elasticity differs from ‘regular’ weeks
around the holidays proven by the panel data analysis. These days prices are optimized
mostly 2-3 times per year whereas it could be interesting and profitable to update prices
more regularly. Although outside the scope of this research, one could think about ap-
plying the method by Brombin et al. [7] to search for the covariates of price elasticity
if interested in the drivers of the differences between clusters. This simulation method
provides an elegant way to find the independent variables for models of price elasticity.
This way the overall process of regression could be fully automated like the clustering
algorithm without interference of the end-user selecting the variables by hand.

31
Bibliography

[1] Allenby, G.M., Rossi, P.E.: A marginal-predictive approach to identifying household

parameters. Marketing Letters 4(3), 227–239 (1993)

[2] Arthur, D., Vassilvitskii, S.: k-means++: The advantages of careful seeding. In:
Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms.
pp. 1027–1035. Society for Industrial and Applied Mathematics (2007)

[3] Basu, S., Banerjee, A., Mooney, R.: Semi-supervised clustering by seeding. In: In Pro-
ceedings of 19th International Conference on Machine Learning (ICML-2002. Citeseer
(2002)

[4] Basu, S., Banerjee, A., Mooney, R.J.: Active semi-supervision for pairwise con-
strained clustering. In: SDM. vol. 4, pp. 333–344. SIAM (2004)

[5] Basu, S., Bilenko, M., Mooney, R.J.: A probabilistic framework for semi-supervised
clustering. In: Proceedings of the tenth ACM SIGKDD international conference on
Knowledge discovery and data mining. pp. 59–68. ACM (2004)

[6] Bonferroni, C.E.: Teoria statistica delle classi e calcolo delle probabilita. Libreria
internazionale Seeber (1936)

[7] Brombin, C., Finos, L., Salmaso, L.: Adjusting stepwise p-values in generalized linear
models. In: International Conference on Multiple Comparison Procedures.–see step.
adj () in the R someMTP package (2007)

[8] Dimitriadou, E., Weingessel, A., Hornik, K.: A combination scheme for fuzzy cluster-
ing. International Journal of Pattern Recognition and Artificial Intelligence 16(07),
901–912 (2002)

[9] Dudoit, S., Fridlyand, J.: A prediction-based resampling method for estimating the
number of clusters in a dataset. Genome biology 3(7), 1–21 (2002)

[10] Eduardo, M., Brea, A., et al.: Constrained clustering algorithms: Practical issues
and applications (2013)

32
[11] Elrod, T., Winer, R.S.: An empirical evaluation of aggregation approaches for devel-
oping market segments. The Journal of Marketing pp. 65–74 (1982)

[12] Forgy, E.W.: Cluster analysis of multivariate data: efficiency versus interpretability
of classifications. Biometrics 21, 768–769 (1965)

[13] Ghaemi, R., Sulaiman, M.N., Ibrahim, H., Mustapha, N., et al.: A survey: clustering
ensembles techniques. World Academy of Science, Engineering and Technology 50,
636–645 (2009)

[14] Gordon, A.D.: Classification, (chapman & hall/crc monographs on statistics & ap-
plied probability) (1999)

[15] Hartigan, J.A.: Clustering algorithms (1975)

[16] Hoch, S.J., Kim, B.D., Montgomery, A.L., Rossi, P.E.: Determinants of store-level
price elasticity. Journal of marketing Research pp. 17–29 (1995)

[17] Hornik, K.: A clue for cluster ensembles. Journal of Statistical Software 14(11) (2005)

[18] Hsiao, C.: Analysis of panel data. No. 54, Cambridge university press (2014)

[19] Huang, M.H., Hahn, D.E., Jones, E., et al.: Determinants of price elasticities for
store brands and national brands of cheese. In: American Agricultural Economics
Association Annual Meeting, Denver, Colorado. August. pp. 1–4 (2004)

[20] Jaccard, P.: The distribution of the flora in the alpine zone. New phytologist 11(2),
37–50 (1912)

[21] Karypis, G., Kumar, V.: Multilevelk-way partitioning scheme for irregular graphs.
Journal of Parallel and Distributed computing 48(1), 96–129 (1998)

[22] Karypis, G., Kumar, V.: Parallel multilevel series k-way partitioning scheme for
irregular graphs. Siam Review 41(2), 278–300 (1999)

[23] Kaufman, L., Rousseeuw, P.: Clustering by means of medoids. North-Holland (1987)

[24] Klein, D., Kamvar, S.D., Manning, C.D.: From instance-level constraints to space-
level constraints: Making the most of prior knowledge in data clustering (2002)

[25] Kuhn, H.W.: The hungarian method for the assignment problem. Naval research
logistics quarterly 2(1-2), 83–97 (1955)

[26] Kumar, V., Karande, K.: The effect of retail store environment on retailer perfor-
mance. Journal of Business Research 49(2), 167–181 (2000)

[27] Lagin, M., Gebert-Persson, S.: Defining the links between retail price strategies and
price tactics (2015)

33
[28] Maddala, G.S., Lahiri, K.: Introduction to econometrics, vol. 2. Macmillan New York
(1992)

[29] Marn, M.V., Roegner, E.V., Zawada, C.C.: Pricing new products. McKinsey Quar-
terly (3), 40–49 (2003)

[30] Monroe, K.B.: Measuring price thresholds by psychophysics and latitudes of accep-
tance. Journal of Marketing Research pp. 460–464 (1971)

[31] Ng, A.: Clustering with the k-means algorithm. Machine Learning (2012)

[32] Petrick, J.F.: Segmenting cruise passengers with price sensitivity. Tourism Manage-
ment 26(5), 753–762 (2005)

[33] Porro-Muñoz, D., Duin, R.P., Talavera, I.: Missing values in dissimilarity-based clas-
sification of multi-way data. In: Progress in Pattern Recognition, Image Analysis,
Computer Vision, and Applications, pp. 214–221. Springer (2013)

[34] Rossi, P.E., Allenby, G.M.: A bayesian approach to estimating household parameters.
Journal of Marketing Research pp. 171–182 (1993)

[35] Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of
cluster analysis. Journal of computational and applied mathematics 20, 53–65 (1987)

[36] Strehl, A., Ghosh, J.: Cluster ensembles—a knowledge reuse framework for combining
multiple partitions. Journal of machine learning research 3(Dec), 583–617 (2002)

[37] Thalamuthu, A., Mukhopadhyay, I., Zheng, X., Tseng, G.C.: Evaluation and com-
parison of gene clustering methods in microarray analysis. Bioinformatics 22(19),
2405–2412 (2006)

[38] Tumer, K., Agogino, A.K.: Ensemble clustering with voting active clusters. Pattern
Recognition Letters 29(14), 1947–1953 (2008)

[39] Vega-Pons, S., Ruiz-Shulcloper, J.: A survey of clustering ensemble algorithms. In-
ternational Journal of Pattern Recognition and Artificial Intelligence 25(03), 337–372
(2011)

[40] Wagstaff, K., Cardie, C., Rogers, S., Schrödl, S., et al.: Constrained k-means clus-
tering with background knowledge. In: ICML. vol. 1, pp. 577–584 (2001)

[41] Wakefield, K.L., Inman, J.J.: Situational price sensitivity: the role of consumption
occasion, social context and income. Journal of Retailing 79(4), 199–212 (2003)

[42] Wang, K., Wang, B., Peng, L.: Cvap: validation for cluster analyses. Data Science
Journal 8, 88–93 (2009)

34
Appendices

35
 A | Variables

Table A.1: The symbols used in the clustering method.

Symbol Description Equation

z Cluster indicator -
n Iteration indicator -
i, j Product indicator -
r Results indicator -
s, v, y Store indicator -
t Time indicator -
k Number of clusters -
kg Number of clusters in PG g -
k∗ Number of clusters in cluster consensus -
g Product group indicator -
iterM ax Number of iterations K-means -
nStart Number of iterations Restricted K-means++ -
G Number of product groups -

I Set of all products 4.1

Pg Set of all products sold in PG g 4.1 & 4.6 & 4.15
Λ Set of final clustering results for each PG 4.3 & 4.13
N (s, y) Set of all products in a PG sold in store s and y 4.4 & 4.5 & 4.7 & 4.8
S Set of all stores 4.9
Cl Set of current cluster centers 4.9
Sz Set of stores assigned to the cluster with label z 4.10
V Set of all stores located in the same domicile 4.11
C Set of cluster centers -
Γ Set of input for the clustering of price elasticities on store-item level -

wi Weight of product i 4.4 & 4.5 & 4.8

ψi Average revenue per store for product i 4.4 & 4.6 & 4.7 & 4.15
di Number of products in which product i is sold 4.4 & 4.6 & 4.7 & 4.15
D(s, y) Distance between store s and y 4.5 & 4.8 & 4.9 & 4.11
ei,s Price elasticity of product i sold in store x 4.5 & 4.8
ψ∪ Total revenue of all products sold in a PG 4.6 & 4.8
ψ∩ (x, y) Total revenue of all products exclusively sold in both stores x and y 4.7 & 4.8
cz Cluster center z with z the number of the cluster 4.9 & 4.11
λ Potential clustering of stores 4.12 & 4.13 & 4.14
λg Cluster function of product group g 4.2 & 4.3 & 4.13 & 4.14 & 4.16
Π Permutation matrix 4.12
λ
e Cluster membership of stores 4.12 & 4.16
λ∗ Cluster consensus, final clustering 4.13 & 4.13 & 4.14
xg Weight of product group g 4.13 & 4.14 & 4.16 & 4.15
Πg Permutation matrix for PG g 4.14 & 4.16

36
 Table A.2: The variables used in the regression analysis.

Variable Description

Ascension day holiday, when holiday date falls in week then 1 else 0
Back to school school, when holiday date falls in week then 1 else 0
Carnival holiday, when holiday date falls in week then 1 else 0
Easter holiday, when holiday date falls in week then 1 else 0
Father’s day holiday, when holiday date falls in week then 1 else 0
Autumn school, when holiday date falls in week then 1 else 0
Krokus school, when holiday date falls in week then 1 else 0
Liberation day holiday, when holiday date falls in week then 1 else 0
New year holiday, when holiday date falls in week then 1 else 0
Pre-Easter holiday, when holiday date falls in week then 1 else 0
Pre-Pentecost holiday, when holiday date falls in week then 1 else 0
Pre-Christmas holiday, when holiday date falls in week then 1 else 0
Queen’s day holiday, when holiday date falls in week then 1 else 0
Mother’s day holiday, when holiday date falls in week then 1 else 0
Olympus holiday, when holiday date falls in week then 1 else 0
Pentecost holiday, when holiday date falls in week then 1 else 0
Sinterklaas holiday, when holiday date falls in week then 1 else 0
Christmas holiday, when holiday date falls in week then 1 else 0

Price ratio competition Competitor price vs. average competitor price

Price ratio regular price Regular price vs. average regular price
Price ratio substitute 1 Regular price substitute 1 vs. average regular price substitute 1
Price ratio substitute 2 Regular price substitute 2 vs. average regular price substitute 2
Price ratio complement 1 Regular price complement 1 vs. average regular price complement 1

Discount price Discount amount on regular price

Trips Number of transactions
Seasonality Captures the overall sales trend
Rain Total mm rain in a week
Temperature Average temperature in Kelvin in a week

Instore flyer Promotion dummy

Signing on shelf Promotion dummy
Openings flyer Promotion dummy
Dynamic newsletter Promotion dummy
Entrance poster Promotion dummy
National folder Promotion dummy
Buy-1-get-1-free Promotion dummy
Second placing Promotion dummy
Online radio Promotion dummy
Store radio Promotion dummy

Average family size Number of persons versus the number of household

City-rural dummy When city then 1 else 0
Franchise dummy Own store indicator
Holiday indicator (e.g. Christmas) When holiday date falls in week then 1 else 0
No. competitive stores in 15km Number of competitors in a radius of 15km from a store
Percentage high income Share of consumer with high income (above 1.5x modal)
Percentage high social class Share of of consumers part of the high social class
Percentage high education Share of high educated consumers
Percentage low education Share of low educated consumers
Percentage regular visitor competitor Share of consumers that regularly visits the biggest competitor
Percentage unemployed Share of unemployed consumers
Percentage western immigrants Share of western immigrants
Percentage non-western immigrants Share of non-western immigrants
Region East Stores situated in the East of the country
Region South Stores situated in the South of the country
Region West Stores situated in the West of the country
Self-scan dummy When self-scanner available then 1 else 0
Surface in sqm Surface of supermarket in square meters

37
 Table A.3: The social class, the division is based upon the breadwinner of a family.
Horizontally we can see the study degree according the Dutch education system and
vertically the profession.

Division social classes

WO HBO HAVO/VWO MBO MAVO LBO/VMBO LO and not specified
Profession breadwinner

Business owner
A (high) A A A B1 B2 C
(leads 10 or more persons)
Business owner
A A A A B1 B2 C
(leads less than 10 persons)
Farmer / gardener A A B1 B1 B2 C C
Free professions A A A B1 B2 C C
Scientist and higher; manager A B1 B1 B1 B2 C C
Scientist and higher; no manager A B1 B1 B1 B2 C C
Secondary technical and vocational
A B1 B1 B1 B2 C C
education (SBC 4); manager
Secondary technical and vocational
A B1 B1 B2 B2 C C
education (SBC 4); no manager
Elementary school and lower technical and
B1 B2 B2 C C C C
vocational education (SBC 1 en 2)

Early retirement (dutch: VUT) /

A A B1 B1 B2 C D
vocational Retirement
Unemployed / Disabled /
B1 B2 C C C C D
Social welfare provision
Student / Other B1 B2 C C D D D (low)

38
B | Impact clustering results

Table B.1: The step wise revenue without taking competition into account, the
horizontal percentage change represents the price increase in inelastic products and the
vertical percentage change represents the price cut of elastic products (in thousands of
euros).

+0% +1% +2% +3% +4% +5%

-0% 148,406 148,491 148,574 148,656 148,737 148,817
-1% 148,537 148,622 148,706 148,788 148,869 148,949
-2% 148,664 148,748 148,832 148,914 148,995 149,075
-3% 148,785 148,869 148,953 149,035 149,116 149,196
-4% 148,900 148,985 149,069 149,151 149,232 149,312
-5% 149,011 149,096 149,179 149,262 149,343 149,422

Table B.2: The step wise profit without taking competition into account, the horizontal
percentage change represents the price increase in inelastic products and the vertical
percentage change represents the price cut of elastic products (in thousands of euros).

+0% +1% +2% +3% +4% +5%

-0% 39,661 39,792 39,921 40,049 40,175 40,301
-1% 39,597 39,727 39,856 39,984 40,111 40,236
-2% 39,527 39,657 39,787 39,914 40,041 40,166
-3% 39,452 39,582 39,712 39,839 39,966 40,091
-4% 39,372 39,502 39,631 39,759 39,886 40,011
-5% 39,287 39,417 39,546 39,674 39,801 39,926

39
 Table B.3: The projected increase in profit with competition vs. without competition
taken into account and 2% price change of elastic products, between brackets the
relative change can be found.

Product group Competition No competition

Cola 62,687 (0.63%) 171,021 (1.71%)

Energy 13,134 (0.31%) 15,301 (0.37%)
Juice 56,333 (0.76%) 65,075 (0.88%)
Kids youth 65,890 (1.10%) 85,699 (1.43%)
Large soda 76,465 (0.99%) 126,722 (1.65%)
Water 25,683 (0.59%) 41,388 (0.95%)

Total 300,193 (0.76%) 505,207 (1.26%)

Table B.4: The share of products labeled as inelastic or elastic by the labeling
procedure (in percentages).

Cola Energy Juices Kids youth Large soda Water

Clusters
Inelas. Elas. Inelas. Elas. Inelas. Elas. Inelas. Elas. Inelas. Elas. Inelas. Elas.
Cluster 1 10% 13% 0% 2% 3% 17% 7% 11% 5% 18% 10% 14%
Cluster 2 5% 3% 6% 18% 3% 2% 4% 3% 21% 7% 3% 3%
Cluster 3 23% 8% 12% 11% 7% 10% 4% 16% 5% 2% 8% 9%
Cluster 4 9% 11% 3% 9% 17% 14% 13% 5% 7% 8% %11 10%
Total 11% 8% 4% 8% 7% 9% 8% 7% 9% 7% 7% 8%

40
C | Panel data regression results

Table C.1: The table presents the coefficients (and standard errors) of the variables of
the panel data regression models for Cola on store-item level for all clusters to declare
the dependent variable of price elasticities. Note, that the significance level is set to 5%.

Panel data regression model

Cluster 1 Cluster 2 Cluster 3 Cluster 4
Independent variables

Intercept 1.120 (0.050) -1.755 (0.059) -0.011 (0.062) -0.127 (0.100)

Ascension day 0.022 (0.005) 0.044 (0.006) 0.009 (0.006) 0.026 (0.009)
Back to school 0.004 (0.004) 0.017 (0.005) 0.008 (0.005) -0.004 (0.007)
Carnival 0.025 (0.005) 0.000 (0.006) 0.005 (0.006) 0.023 (0.009)
Easter 0.007 (0.004) 0.024 (0.005) 0.000 (0.005) 0.011 (0.007)
Father’s day -0.025 (0.004) -0.033 (0.005) -0.027 (0.005) -0.027 (0.008)
Autumn 0.013 (0.004) 0.031 (0.005) 0.027 (0.005) 0.017 (0.007)
Krokus -0.001 (0.004) -0.024 (0.005) 0.004 (0.005) -0.012 (0.007)
Liberation day -0.005 (0.004) -0.020 (0.005) -0.012 (0.005) -0.001 (0.008)
New year 0.045 (0.004) 0.021 (0.005) 0.035 (0.005) 0.055 (0.007)
Pre-Easter -0.019 (0.004) 0.004 (0.005) -0.018 (0.005) -0.013 (0.007)
Pre-Pentecost -0.020 (0.004) -0.016 (0.005) -0.022 (0.005) -0.024 (0.008)
Pre-Christmas 0.033 (0.007) 0.053 (0.010) 0.034 (0.010) 0.052 (0.014)
Queen’s day -0.011 (0.004) -0.005 (0.005) -0.013 (0.005) 0.003 (0.008)
Mother’s day 0.050 (0.006) 0.054 (0.007) 0.029 (0.007) 0.069 (0.012)
Olympus 0.111 (0.007) 0.086 (0.008) 0.110 (0.008) 0.082 (0.012)
Pentecost -0.001 (0.004) 0.009 (0.005) 0.007 (0.005) 0.000 (0.008)
Sinterklaas 0.046 (0.004) 0.062 (0.005) 0.027 (0.005) 0.066 (0.007)
Christmas 0.048 (0.006) 0.070 (0.008) 0.057 (0.008) 0.083 (0.010)

Price ratio complement 1 0.010 (0.017) 0.031 (0.020) -0.053 (0.020) -0.091 (0.032)
Price ratio competition -0.636 (0.049) 0.348 (0.064) -0.224 (0.066) -0.179 (0.096)
Price ratio regular price 0.145 (0.062) 1.773 (0.078) 1.004 (0.082) 0.912 (0.121)
Price ratio substitute 1 -0.884 (0.015) -0.591 (0.018) -0.834 (0.019) -0.662 (0.024)
Price ratio substitute 2 -0.780 (0.032) -1.202 (0.038) -0.921 (0.044) -1.127 (0.069)

Discount price -0.005 (0.000) -0.006 (0.000) -0.005 (0.000) -0.004 (0.001)
Trips 0.006 (0.000) 0.003 (0.000) 0.005 (0.000) 0.012 (0.000)

Dynamic newsletter 0.000 (0.000) 0.643 (0.106) 0.463 (0.111) 1.366 (0.153)
Entrance poster -1.647 (0.502) -5.129 (0.593) -1.856 (0.586) 0.000 (0.000)
National folder 0.825 (0.114) 0.704 (0.145) 0.765 (0.162) 0.876 (0.229)
Instore flyer -0.348 (0.042) -0.806 (0.091) -0.602 (0.095) -1.428 (0.133)
Online radio 0.134 (0.029) -0.116 (0.035) 0.162 (0.039) 0.237 (0.057)
Openings flyer -1.979 (0.124) -2.005 (0.148) -0.875 (0.143) -1.356 (0.138)
Signing on shelf 1.341 (0.064) 0.362 (0.079) 1.042 (0.081) 0.759 (0.125)
Second placing -0.814 (0.071) 0.471 (0.089) -0.239 (0.095) 0.620 (0.138)
Store radio 3.76 (0.486) 6.577 (0.580) 2.586 (0.573) 0.000 (0.000)

Rain (x1000) 0.017 (0.003) 0.015 (0.004) 0.012 (0.005 ) 0.035 (0.007)
Temperature (x1000) 0.221 (0.019) 0.617 (0.016) 0.213 (0.016) 0.644 (0.023)
Seasonality 0.098 (0.006) 0.155 (0.009) 0.130 (0.007) 0.000 (0.000)

Percentage high education -0.306 (0.069) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Percentage high income 0.158 (0.05) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
City-rural dummy -0.035 (0.012) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
No. competitive stores in 15km 0.000 (0.000) -0.013 (0.003) -0.005 (0.002) 0.000 (0.000)

R2 0.575 0.443 0.562 0.625

41
Table C.2: The table presents the coefficients (and standard errors) of the variables of
the panel data regression models for Energy on store-item level for all clusters to declare
the dependent variable of price elasticities. Note, that the significance level is set to 5%.

Panel data regression model

Cluster 1 Cluster 2 Cluster 3 Cluster 4
Independent variables

Intercept 1.562 (0.061) 0.315 (0.056) 1.045 (0.086) 0.957 (0.087)

Ascension day 0.076 (0.007) 0.064 (0.005) 0.060 (0.009) 0.049 (0.010)
Back to school -0.001 (0.006) -0.014 (0.004) 0.017 (0.009) 0.005 (0.009)
Carnival 0.013 (0.008) 0.015 (0.006) 0.022 (0.011) 0.007 (0.012)
Easter 0.045 (0.006) 0.018 (0.004) 0.031 (0.008) 0.022 (0.009)
Father’s day 0.017 (0.007) 0.012 (0.004) 0.019 (0.009) 0.001 (0.010)
Autumn -0.063 (0.007) -0.023 (0.005) -0.070 (0.009) -0.025 (0.009)
Krokus 0.023 (0.006) 0.015 (0.004) 0.024 (0.008) 0.017 (0.009)
Liberation day 0.017 (0.007) -0.006 (0.005) 0.016 (0.009) -0.004 (0.010)
New year -0.060 (0.006) -0.030 (0.004) -0.084 (0.008) -0.057 (0.009)
Pre-Easter 0.045 (0.006) 0.021 (0.004) 0.050 (0.008) 0.029 (0.009)
Pre-Pentecost 0.029 (0.007) 0.026 (0.005) 0.026 (0.010) 0.020 (0.010)
Pre-Christmas -0.010 (0.012) -0.013 (0.009) -0.008 (0.017) -0.029 (0.018)
Queen’s day 0.073 (0.007) 0.037 (0.005) 0.074 (0.009) 0.033 (0.010)
Mother’s day 0.105 (0.011) 0.038 (0.007) 0.092 (0.013) 0.066 (0.016)
Olympus 0.253 (0.013) 0.099 (0.008) 0.239 (0.015) 0.173 (0.024)
Pentecost 0.053 (0.007) 0.041 (0.004) 0.041 (0.009) 0.019 (0.010)
Sinterklaas -0.040 (0.006) -0.019 (0.004) -0.033 (0.008) -0.038 (0.009)
Christmas -0.012 (0.009) 0.005 (0.007) -0.009 (0.012) 0.016 (0.013)

Price ratio competition -1.464 (0.045) -0.541 (0.031) -1.263 (0.061) -0.531 (0.053)
Price ratio regular price -0.390 (0.071) -0.550 (0.051) -0.047 (0.100) -1.404 (0.106)
Price ratio substitute 1 -0.361 (0.029) -0.362 (0.020) -0.158 (0.039) -0.319 (0.040)
Price ratio substitute 2 -0.564 (0.025) -0.330 (0.016) -0.742 (0.032) -0.337 (0.035)

Discount price 0.016 (0.003) 0.015 (0.002) 0.016 (0.006) 0.033 (0.006)
Trips 0.001 (0.000) 0.004 (0.000) -0.008 (0.000) 0.001 (0.000)

Rain (x1000) -0.083 (0.006) -0.032 (0.004) -0.101 (0.008) -0.084 (0.009)
Temperature (x1000) 0.620 (0.020) 0.608 (0.013) 0.690 (0.030) 0.620 (0.028)
Seasonality 0.232 (0.01) 0.178 (0.004) 0.236 (0.014) 0.252 (0.006)

National folder -6.656 (0.391) -4.993 (0.255) -6.690 (0.502) -6.671 (0.502)
Instore flyer -0.795 (0.147) -0.757 (0.096) -1.231 (0.186) -1.203 (0.196)
Online radio 0.221 (0.035) 0.084 (0.022) 0.286 (0.049) 3.332 (0.173)
Signing on shelf 2.612 (0.138) 2.328 (0.089) 2.585 (0.172) 0.776 (0.076)
Second placing 0.480 (0.053) 0.639 (0.035) 0.401 (0.075) 0.000 (0.000)

Region East 0.000 (0.000) 0.115 (0.055) 0.000 (0.000) 0.000 (0.000)
Region South 0.000 (0.000) 0.139 (0.042) 0.000 (0.000) 0.000 (0.000)
City-rural dummy 0.000 (0.000) -0.061 (0.019) 0.000 (0.000) 0.000 (0.000)
Percentage high education 0.000 (0.000) 0.000 (0.000) 0.500 (0.124) 0.334 (0.018)
No. competitive stores in 15km 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.002 (0.001)

R2 0.576 0.683 0.555 0.657

42
Table C.3: The table presents the coefficients (and standard errors) of the variables of
the panel data regression models for Kids youth on store-item level for all clusters to
declare the dependent variable of price elasticities. Note, that the significance level is set
to 5%.

Panel data regression model

Cluster 1 Cluster 2 Cluster 3 Cluster 4
Independent variables

Intercept -0.637 (0.059) -0.393 (0.056) -0.808 (0.078) -1.000 (0.084)

Ascension day -0.004 (0.006) 0.026 (0.005) 0.002 (0.007) 0.004 (0.010)
Back to school 0.001 (0.006) 0.042 (0.005) -0.028 (0.007) -0.008 (0.010)
Carnival -0.021 (0.007) -0.027 (0.006) -0.023 (0.009) -0.017 (0.012)
Easter -0.046 (0.006) -0.056 (0.005) -0.062 (0.007) -0.050 (0.009)
Father’s day -0.086 (0.006) -0.039 (0.005) -0.098 (0.007) -0.079 (0.010)
Autumn -0.015 (0.006) -0.025 (0.005) -0.026 (0.007) -0.017 (0.009)
Krokus 0.028 (0.006) 0.022 (0.005) 0.045 (0.007) 0.036 (0.009)
Liberation day -0.001 (0.006) -0.013 (0.005) -0.021 (0.007) -0.024 (0.010)
New year -0.021 (0.006) -0.082 (0.006) -0.005 (0.008) -0.058 (0.010)
Pre-Easter -0.061 (0.005) -0.045 (0.005) -0.076 (0.007) -0.073 (0.009)
Pre-Pentecost -0.003 (0.006) 0.013 (0.005) -0.001 (0.008) -0.004 (0.010)
Pre-Christmas 0.087 (0.011) 0.053 (0.010) 0.061 (0.014) 0.071 (0.018)
Queen’s day -0.009 (0.006) -0.015 (0.006) -0.031 (0.008) -0.023 (0.011)
Mother’s day -0.010 (0.008) -0.028 (0.007) 0.006 (0.010) -0.032 (0.014)
Olympus 0.078 (0.008) 0.031 (0.007) 0.097 (0.009) 0.063 (0.014)
Pentecost 0.054 (0.006) 0.036 (0.005) 0.041 (0.007) 0.043 (0.010)
Sinterklaas -0.022 (0.006) -0.036 (0.005) -0.012 (0.007) -0.018 (0.009)
Christmas -0.029 (0.008) -0.019 (0.008) -0.015 (0.011) -0.035 (0.013)

Price ratio competition -0.379 (0.096) -0.554 (0.088) 0.176 (0.121) -0.566 (0.163)
Price ratio regular price 0.420 (0.089) 0.267 (0.080) -0.199 (0.113) 0.676 (0.152)
Price ratio substitute 1 0.601 (0.050) -0.404 (0.041) 0.251 (0.069) 0.413 (0.079)
Price ratio substitute 2 -1.024 (0.048) 0.115 (0.039) -0.715 (0.062) -0.769 (0.077)

Discount price 0.002 (0.004) 0.031 (0.003) 0.013 (0.005) 0.003 (0.009)
Trips 0.027 (0.001) 0.007 (0.000) 0.025 (0.001) 0.022 (0.001)

National folder -0.499 (0.207) -0.351 (0.181) -1.579 (0.260) -0.093 (0.330)
Instore flyer 1.598 (0.132) 0.681 (0.113) 1.494 (0.169) 1.288 (0.218)
Online radio 0.087 (0.038) 0.619 (0.032) 0.073 (0.049) 0.264 (0.062)
Signing on shelf -2.588 (0.139) -1.661 (0.121) -2.626 (0.175) -2.033 (0.222)
Second placing 0.087 (0.113) 0.769 (0.109) 0.724 (0.147) -0.025 (0.178)
Openings flyer 2.362 (0.078) 1.205 (0.072) 1.774 (0.102) 2.169 (0.122)

Rain (x1000) 0.014 (0.002) -0.037 (0.005) 0.000 (0.000) 0.021 (0.009)
Temperature (x1000) 0.325 (0.019) 0.260 (0.018) 0.351 (0.023) 0.500 (0.030)
Seasonality 0.034 (0.008) 0.110 (0.009) 0.000 (0.000) 0.082 (0.007)

No. competitive store in 15km 0.007 (0.002) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Percentage unemployed -1.619 (0.333) -1.721 (0.373) 0.000 (0.000) 0.000 (0.000)
Percentage regular visitor competitor -0.137 (0.039) -0.143 (0.048) 0.156 (0.061) 0.086 (0.025)
Percentage high education 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.199 (0.033)
Percentage high income 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) -0.144 (0.029)

R2 0.530 0.328 0.520 0.602

43
Table C.4: The table presents the coefficients (and standard errors) of the variables of
the panel data regression models for Large soda on store-item level for all clusters to
declare the dependent variable of price elasticities. Note, that the significance level is set
to 5%.

Panel data regression model

Cluster 1 Cluster 2 Cluster 3 Cluster 4
Independent variables

Intercept 2.114 (0.055) 0.887 (0.050) 2.524 (0.07) 1.918 (0.093)

Ascension day 0.043 (0.006) 0.039 (0.005) 0.035 (0.008) 0.036 (0.011)
Back to school -0.020 (0.005) -0.019 (0.005) -0.023 (0.007) -0.033 (0.010)
Carnival 0.071 (0.007) 0.036 (0.006) 0.113 (0.009) 0.045 (0.013)
Easter 0.055 (0.005) 0.053 (0.005) 0.043 (0.007) 0.036 (0.009)
Father’s day -0.001 (0.006) -0.009 (0.005) 0.001 (0.008) -0.016 (0.011)
Autumn -0.043 (0.005) -0.043 (0.005) -0.031 (0.007) -0.053 (0.010)
Krokus 0.011 (0.005) 0.017 (0.005) -0.009 (0.007) 0.001 (0.010)
Liberation day 0.031 (0.006) 0.013 (0.005) 0.030 (0.008) 0.013 (0.011)
New year 0.057 (0.005) 0.066 (0.005) 0.016 (0.007) 0.075 (0.010)
Pre-Easter 0.092 (0.005) 0.162 (0.005) 0.027 (0.007) 0.101 (0.009)
Pre-Pentecost 0.000 (0.006) 0.026 (0.005) -0.015 (0.008) 0.006 (0.011)
Pre-Christmas 0.066 (0.011) 0.072 (0.010) 0.040 (0.014) 0.096 (0.019)
Queen’s day -0.004 (0.006) 0.02 (0.005) -0.011 (0.008) -0.016 (0.011)
Mother’s day 0.004 (0.009) -0.002 (0.007) 0.007 (0.011) 0.018 (0.017)
Olympus 0.141 (0.007) 0.086 (0.006) 0.128 (0.009) 0.147 (0.015)
Pentecost 0.069 (0.006) 0.055 (0.005) 0.060 (0.007) 0.056 (0.010)
Sinterklaas -0.070 (0.005) -0.046 (0.005) -0.096 (0.007) -0.059 (0.010)
Christmas 0.031 (0.008) 0.030 (0.008) 0.028 (0.011) 0.056 (0.014)

Price ratio competition -0.343 (0.091) -0.221 (0.080) -0.892 (0.130) -0.189 (0.175)
Price ratio regular price -3.586 (0.114) -2.459 (0.100) -3.226 (0.168) -3.386 (0.226)
Price ratio substitute 1 -0.282 (0.059) -0.266 (0.048) -0.413 (0.080) -0.267 (0.105)
Price ratio substitute 2 0.308 (0.039) 0.213 (0.031) 0.403 (0.053) 0.041 (0.065)
Price index complement 1 0.601 (0.043) 0.474 (0.035) 0.549 (0.057) 0.472 (0.078)

Discount price 0.071 (0.002) 0.042 (0.001) 0.038 (0.002) 0.102 (0.006)
Trips 0.014 (0.001) 0.019 (0.000) 0.013 (0.001) 0.009 (0.001)

National folder -0.820 (0.203) -0.870 (0.168) -0.639 (0.283) -0.621 (0.392)
Instore flyer 0.812 (0.184) 0.888 (0.153) 0.842 (0.259) 0.605 (0.353)
Online radio 0.011 (0.028) -0.151 (0.023) 0.269 (0.036) -0.116 (0.051)
Signing on shelf -1.036 (0.246) -1.206 (0.205) -1.412 (0.354) 0.084 (0.461)
Second placing 1.106 (0.143) 1.201 (0.121) 1.044 (0.208) 0.363 (0.264)
Openings flyer -0.154 (0.091) 0.279 (0.077) -0.135 (0.127) 0.000 (0.000)

Rain (x1000) -0.049 (0.005) -0.040 (0.005) -0.057 (0.007) -0.040 (0.010)
Temperature (x1000) -0.129 (0.020) -0.037 (0.018) -0.242 (0.028) 0.000 (0.000)
Seasonality 0.170 (0.007) 0.203 (0.007) 0.122 (0.010) 0.145 (0.010)

No. competitive stores in 15km -0.006 (0.002) -0.005 (0.002) 0.000 (0.000) 0.000 (0.000)
Region East -0.029 (0.013) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Region South -0.072 (0.017) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
City-rural dummy -0.051 (0.012) 0.000 (0.000) -0.074 (0.027) 0.000 (0.000)
Self-scan dummy -0.041 (0.012) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Percentage unemployed 0.000 (0.000) -1.345 (0.413) 0.000 (0.000) 0.000 (0.000)
Percentage non-western immigrants 0.000 (0.000) 0.567 (0.189) 0.000 (0.000) 0.000 (0.000)
Percentage western-immigrants 0.000 (0.000) -0.304 (0.146) 0.000 (0.000) 0.000 (0.000)

R2 0.550 0.580 0.543 0.612

44
Table C.5: The table presents the coefficients (and standard errors) of the variables of
the panel data regression models for Juices on store-item level for all clusters to declare
the dependent variable of price elasticities. Note, that the significance level is set to 5%.

Panel data regression model

Cluster 1 Cluster 2 Cluster 3 Cluster 4
Independent variables

Intercept -4.936 (0.070) -5.774 (0.086) -5.009 (0.106) -4.848 (0.121)

Ascension day 0.125 (0.010) 0.111 (0.010) 0.122 (0.012) 0.132 (0.015)
Back to school -0.047 (0.009) -0.042 (0.009) -0.074 (0.012) -0.046 (0.014)
Carnival -0.045 (0.011) -0.042 (0.011) -0.043 (0.014) -0.046 (0.017)
Easter 0.099 (0.009) 0.125 (0.009) 0.098 (0.011) 0.099 (0.012)
Father’s day 0.090 (0.010) 0.090 (0.009) 0.070 (0.012) 0.079 (0.014)
Autumn 0.056 (0.009) 0.078 (0.009) 0.050 (0.011) 0.032 (0.013)
Krokus 0.016 (0.009) -0.017 (0.009) 0.055 (0.011) 0.028 (0.013)
Liberation day 0.012 (0.010) 0.010 (0.009) 0.013 (0.012) 0.013 (0.014)
New year 0.006 (0.009) -0.012 (0.009) 0.015 (0.012) 0.016 (0.013)
Pre-Easter 0.111 (0.009) 0.182 (0.009) 0.045 (0.011) 0.136 (0.013)
Pre-Pentecost 0.107 (0.010) 0.136 (0.010) 0.059 (0.012) 0.105 (0.015)
Pre-Christmas 0.072 (0.018) 0.059 (0.018) 0.111 (0.023) 0.138 (0.027)
Queen’s day 0.022 (0.009) 0.029 (0.009) 0.025 (0.012) 0.017 (0.014)
Mother’s day -0.001 (0.014) -0.023 (0.012) 0.028 (0.016) -0.002 (0.021)
Olympus -0.159 (0.013) -0.177 (0.011) -0.069 (0.015) -0.170 (0.020)
Pentecost 0.028 (0.009) 0.018 (0.009) 0.032 (0.012) 0.039 (0.014)
Sinterklaas 0.019 (0.009) -0.006 (0.009) 0.081 (0.011) 0.074 (0.013)
Christmas 0.132 (0.013) 0.155 (0.014) 0.129 (0.018) 0.094 (0.019)

Price ratio competition 0.807 (0.104) 1.017 (0.098) 0.192 (0.132) 0.644 (0.164)
Price ratio regular price 3.308 (0.138) 3.184 (0.129) 4.186 (0.178) 2.991 (0.206)
Price ratio substitute 1 1.773 (0.045) 1.859 (0.040) 1.224 (0.054) 1.700 (0.072)
Price ratio substitute 2 -2.984 (0.045) -2.81 (0.040) -2.868 (0.057) -2.746 (0.066)

Discount price 0.129 (0.013) 0.045 (0.006) 0.021 (0.005) 0.122 (0.015)
Trips 0.024 (0.001) 0.017 (0.001) 0.030 (0.001) 0.016 (0.001)

Instore flyer 0.945 (0.193) 0.584 (0.169) 1.425 (0.24) 0.655 (0.291)
Online radio -0.587 (0.047) -0.319 (0.044) -0.842 (0.058) -0.537 (0.071)
Signing on shelf 2.286 (0.365) 2.027 (0.333) 2.502 (0.476) 2.463 (0.537)
Second placing -0.006 (0.317) 1.209 (0.291) -0.101 (0.418) 0.092 (0.473)
Openings flyer -0.612 (0.223) -1.829 (0.212) -0.535 (0.293) -1.136 (0.310)

Rain (x1000) 0.064 (0.008) 0.090 (0.009) 0.051 (0.011) 0.089 (0.013)
Temperature (x1000) -0.123 (0.028) 0.000 (0.000) -0.225 (0.037) 0.000 (0.000)
Seasonality 0.285 (0.015) 0.343 (0.015) 0.319 (0.019) 0.306 (0.014)

Franchise dummy -0.052 (0.022) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Percentage high education 0.000 (0.000) 0.195 (0.077) 0.000 (0.000) 0.000 (0.000)
Region East 0.000 (0.000) 0.188 (0.061) 0.000 (0.000) 0.000 (0.000)
Region South 0.000 (0.000) 0.285 (0.049) 0.000 (0.000) 0.000 (0.000)
Percentage high social class 0.000 (0.000) 0.000 (0.000) 0.312 (0.130) 0.000 (0.000)
Percentage regular visitor competitor 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.312 (0.096)

R2 0.563 0.531 0.613 0.589

45
Table C.6: The table presents the coefficients (and standard errors) of the variables of
the panel data regression models for Water on store-item level for all clusters to declare
the dependent variable of price elasticities. Note, that the significance level is set to 5%.

Panel data regression model

Cluster 1 Cluster 2 Cluster 3 Cluster 4
Independent variables

Intercept -0.938 (0.030) -1.585 (0.036) -0.782 (0.036) -1.097 (0.059)

Ascension day 0.026 (0.004) 0.020 (0.005) 0.040 (0.005) 0.019 (0.008)
Back to school -0.005 (0.004) -0.020 (0.004) -0.011 (0.005) 0.006 (0.008)
Carnival -0.006 (0.005) -0.032 (0.006) -0.002 (0.006) -0.009 (0.010)
Easter 0.015 (0.004) 0.015 (0.004) 0.011 (0.005) 0.023 (0.007)
Father’s day -0.007 (0.004) -0.006 (0.004) -0.004 (0.005) -0.011 (0.008)
Autumn -0.009 (0.004) -0.001 (0.004) 0.009 (0.005) -0.008 (0.008)
Krokus 0.014 (0.004) -0.003 (0.004) 0.012 (0.005) 0.009 (0.008)
Liberation day 0.006 (0.004) 0.016 (0.005) -0.023 (0.005) -0.002 (0.008)
New year -0.025 (0.004) -0.027 (0.005) -0.041 (0.005) -0.030 (0.007)
Pre-Easter 0.018 (0.004) 0.021 (0.004) 0.013 (0.005) 0.019 (0.007)
Pre-Pentecost 0.027 (0.004) 0.041 (0.005) 0.012 (0.005) 0.032 (0.009)
Pre-Christmas 0.058 (0.008) 0.073 (0.009) 0.093 (0.010) 0.056 (0.015)
Queen’s day 0.018 (0.004) 0.016 (0.005) 0.031 (0.005) 0.001 (0.008)
Mother’s day -0.017 (0.006) -0.039 (0.006) -0.005 (0.007) -0.020 (0.012)
Olympus -0.001 (0.007) -0.013 (0.008) 0.021 (0.009) 0.042 (0.016)
Pentecost 0.023 (0.004) 0.025 (0.004) 0.029 (0.005) 0.028 (0.008)
Sinterklaas 0.012 (0.004) 0.045 (0.004) 0.001 (0.005) 0.017 (0.007)
Christmas 0.045 (0.006) 0.066 (0.007) 0.031 (0.007) 0.046 (0.011)

Price ratio competition -0.065 (0.032) -0.218 (0.039) -0.105 (0.038) -0.320 (0.060)
Price ratio regular price -0.089 (0.041) 0.563 (0.048) -0.363 (0.050) 0.339 (0.081)
Price ratio substitute 1 0.079 (0.037) -0.310 (0.04) 0.508 (0.044) -0.530 (0.077)
Price ratio substitute 2 -0.365 (0.024) 0.086 (0.027) -0.770 (0.030) 0.187 (0.052)

Discount price -0.015 (0.006) 0.005 (0.003) 0.019 (0.004) -0.020 (0.009)
Trips 0.006 (0.000) 0.008 (0.000) 0.010 (0.000) 0.000 (0.000)

Instore flyer 2.570 (0.445) 3.033 (0.460) 3.045 (0.475) 2.084 (0.819)
Online radio -0.135 (0.018) -0.158 (0.020) 0.047 (0.023) -0.050 (0.035)
Signing on shelf -0.177 (0.027) -0.303 (0.03) 0.095 (0.033) -0.174 (0.057)
Second placing -0.172 (0.392) 0.762 (0.425) -0.398 (0.504) 0.773 (0.821)
Openings flyer -0.444 (0.388) -1.578 (0.421) -0.726 (0.494) -0.864 (0.811)
National folder -1.504 (0.434) -1.773 (0.446) -1.706 (0.462) -1.631 (0.792)

Rain (x1000) -0.028 (0.004) -0.019 (0.004) -0.053 (0.005) -0.036 (0.008)
Temperature (x1000) 0.625 (0.015) 0.583 (0.019) 0.483 (0.020) 0.909 (0.027)
Seasonality 0.224 (0.004) 0.234 (0.005) 0.238 (0.005) 0.229 (0.006)

No. competitive stores in 15km -0.007 (0.001) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
City-rural dummy 0.054 (0.011) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Franchise dummy 0.000 (0.000) 0.000 (0.000) -0.074 (0.028) 0.000 (0.000)
Self-scan dummy 0.000 (0.000) 0.000 (0.000) 0.061 (0.019) 0.000 (0.000)

R2 0.684 0.609 0.763 0.828

46
 Table C.7: The table presents the coefficients (and standard errors) of the variables of
the panel data regression models on store-item level for all product groups to declare the
dependent variable of price elasticities. Note, that the significance level is set to 5%.

Panel data regression model

Cola Energy Large soda Kids youth Juices Water
Independent variables

Intercept 0.031 (0.054) 0.847 (0.097) 1.873 (0.037) -0.418 (0.082) -5.100 (0.044) -1.183 (0.024)

Ascension day 0.030 (0.003) 0.064 (0.004) 0.038 (0.003) 0.011 (0.003) 0.120 (0.006) 0.026 (0.003)
Back to school 0.009 (0.003) -0.003 (0.003) -0.024 (0.003) 0.004 (0.003) -0.056 (0.005) -0.012 (0.003)
Carnival 0.016 (0.003) 0.017 (0.004) 0.063 (0.004) -0.015 (0.004) -0.038 (0.006) -0.013 (0.003)
Easter 0.013 (0.003) 0.028 (0.003) 0.055 (0.003) -0.052 (0.003) 0.110 (0.005) 0.015 (0.002)
Father’s day -0.030 (0.003) 0.011 (0.003) -0.005 (0.003) -0.074 (0.003) 0.086 (0.005) -0.006 (0.003)
Autumn 0.025 (0.003) -0.037 (0.003) -0.047 (0.003) -0.017 (0.003) 0.057 (0.005) -0.004 (0.003)
Krokus -0.005 (0.003) 0.017 (0.003) 0.015 (0.003) 0.034 (0.003) 0.011 (0.005) 0.009 (0.002)
Liberation day -0.013 (0.003) 0.008 (0.004) 0.023 (0.003) -0.012 (0.003) 0.011 (0.005) 0.003 (0.003)
New year 0.029 (0.003) -0.054 (0.003) 0.061 (0.003) -0.043 (0.004) 0.009 (0.005) -0.034 (0.003)
Pre-Easter -0.012 (0.003) 0.034 (0.003) 0.113 (0.003) -0.059 (0.003) 0.128 (0.005) 0.019 (0.002)
Pre-Pentecost -0.023 (0.003) 0.022 (0.004) 0.013 (0.003) 0.005 (0.004) 0.111 (0.006) 0.033 (0.003)
Pre-Christmas 0.044 (0.005) -0.010 (0.007) 0.072 (0.006) 0.069 (0.006) 0.085 (0.011) 0.082 (0.005)
Queen’s day -0.006 (0.003) 0.055 (0.004) 0.005 (0.003) -0.019 (0.004) 0.025 (0.005) 0.018 (0.003)
Mother’s day 0.050 (0.004) 0.077 (0.005) 0.007 (0.005) -0.016 (0.005) -0.007 (0.007) -0.026 (0.004)
Olympus 0.096 (0.004) 0.183 (0.006) 0.119 (0.004) 0.062 (0.004) -0.150 (0.007) 0.003 (0.005)
Pentecost 0.003 (0.003) 0.041 (0.003) 0.064 (0.003) 0.044 (0.003) 0.027 (0.005) 0.027 (0.003)
Sinterklaas 0.054 (0.003) -0.033 (0.003) -0.065 (0.003) -0.026 (0.003) 0.029 (0.005) 0.022 (0.003)
Christmas 0.059 (0.004) -0.003 (0.005) 0.039 (0.005) -0.023 (0.005) 0.138 (0.008) 0.046 (0.004)

Price ratio competition -0.258 (0.035) -0.955 (0.023) -0.292 (0.051) -0.231 (0.056) 0.762 (0.059) -0.162 (0.021)
Price ratio regular price 1.023 (0.043) -0.481 (0.038) -3.179 (0.065) 0.075 (0.052) 3.353 (0.078) 0.220 (0.027)
Price ratio substitute 1 -0.731 (0.010) -0.316 (0.015) -0.288 (0.033) 0.052 (0.028) 1.697 (0.025) -0.086 (0.023)
Price ratio substitute 2 -0.984 (0.022) -0.498 (0.013) 0.239 (0.021) -0.395 (0.027) -2.845 (0.025) -0.188 (0.016)
Price ratio complement 1 -0.017 (0.011) 0.000 (0.000) 0.530 (0.024) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)

Discount price -0.005 (0.000) 0.019 (0.002) 0.052 (0.001) 0.016 (0.002) 0.047 (0.004) 0.008 (0.002)
Trips 0.004 (0.000) 0.000 (0.000) 0.014 (0.000) 0.018 (0.000) 0.022 (0.000) 0.005 (0.000)

Instore flyer -0.362 (0.029) -1.014 (0.073) 0.177 (0.039) -0.347 (0.081) 0.841 (0.106) 3.166 (0.269)
Online radio 0.061 (0.020) 0.000 (0.000) 0.000 (0.000) 0.346 (0.022) -0.517 (0.026) -0.109 (0.012)
Signing on shelf 0.635 (0.026) 2.839 (0.064) -0.339 (0.093) -0.782 (0.074) 2.307 (0.205) -0.154 (0.013)
Openings flyer -1.779 (0.084) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) -1.086 (0.126) -0.827 (0.067)
Store radio 4.652 (0.326) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Entrance poster -2.965 (0.336) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Second placing 0.000 (0.000) 0.552 (0.027) 1.011 (0.081) 0.517 (0.068) 0.347 (0.178) 0.000 (0.000)
National folder 0.879 (0.082) -5.877 (0.194) 0.000 (0.000) -0.999 (0.119) 0.000 (0.000) -1.944 (0.261)
Dynamic newsletter 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 1.825 (0.044) 0.000 (0.000) 0.000 (0.000)

Rain (x1000) 0.013 (0.003) -0.066 (0.003) -0.049 (0.003) -0.007 (0.003) 0.079 (0.005) -0.035 (0.002)
Temperature (x1000) 0.405 (0.008) 0.630 (0.010) 0.000 (0.000) 0.282 (0.011) -0.040 (0.020) 0.709 (0.010)
Seasonality 0.152 (0.004) 0.220 (0.003) 0.135 (0.004) 0.088 (0.004) 0.283 (0.007) 0.217 (0.002)

Percentage high education -0.212 (0.077) -0.242 (0.051) -0.211 (0.052) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Percentage high income -0.323 (0.078) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Franchise dummy -0.060 (0.020) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) -0.043 (0.015) -0.036 (0.010)
Percentage non-western immigrants 0.593 (0.221) 0.839 (0.168) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.369 (0.096)
Percentage western immigrants -1.449 (0.225) -0.658 (0.212) 0.000 (0.000) -0.790 (0.144) 0.000 (0.000) 0.000 (0.000)
Region South 0.000 (0.000) -0.066 (0.016) -0.166 (0.014) 0.000 (0.000) 0.000 (0.000) -0.043 (0.009)
Average family size 0.000 (0.000) 0.102 (0.037) 0.000 (0.000) -0.144 (0.033) 0.000 (0.000) 0.000 (0.000)
Percentage unemployed 0.000 (0.000) 0.000 (0.000) -0.858 (0.363) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
City-rural dummy 0.000 (0.000) 0.000 (0.000) -0.036 (0.016) 0.000 (0.000) 0.000 (0.000) 0.044 (0.009)
Percentage regular visitor competitor 0.000 (0.000) 0.000 (0.000) -0.093 (0.037) 0.062 (0.028) 0.105 (0.033) 0.000 (0.000)
Percentage high social class 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.254 (0.046) 0.000 (0.000) 0.000 (0.000)
Surface in sqm 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) -0.011 (-0.002) 0.000 (0.000) -0.006 (0.001)
Self-scan dummy 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.036 (0.014) 0.043 (0.009)
R2 0.463 0.560 0.541 0.427 0.552 0.660

47
Table C.8: The table presents the coefficients (and standard errors) of the variables of
the panel data regression models on store-item level for all clusters to declare the
dependent variable of price elasticities. Note, that the significance level is set to 5%.

Panel data regression model

Cluster 1 Cluster 2 Cluster 3 Cluster 4
Independent variables

Intercept -0.215 (0.041) -1.219 (0.038) -0.532 (0.050) -0.781 (0.065)

Ascension day 0.052 (0.003) 0.049 (0.003) 0.036 (0.004) 0.043 (0.005)
Back to school 0.006 (0.003) 0.007 (0.003) -0.018 (0.004) -0.009 (0.005)
Carnival -0.003 (0.004) -0.007 (0.003) 0.005 (0.005) 0.001 (0.006)
Easter -0.001 (0.003) 0.019 (0.003) 0.008 (0.004) 0.006 (0.004)
Father’s day -0.023 (0.003) -0.009 (0.003) -0.038 (0.004) -0.029 (0.005)
Autumn -0.006 (0.003) 0.003 (0.003) -0.006 (0.004) -0.007 (0.005)
Krokus 0.002 (0.003) -0.010 (0.003) 0.018 (0.004) 0.008 (0.005)
Liberation day -0.015 (0.003) -0.014 (0.003) -0.012 (0.004) -0.020 (0.005)
New year -0.004 (0.003) 0.004 (0.003) 0.015 (0.004) -0.006 (0.005)
Pre-Easter -0.023 (0.003) 0.044 (0.003) -0.028 (0.004) 0.002 (0.005)
Pre-Pentecost -0.009 (0.003) 0.024 (0.003) -0.013 (0.004) 0.005 (0.005)
Pre-Christmas 0.031 (0.006) 0.073 (0.006) 0.048 (0.008) 0.064 (0.009)
Queen’s day 0.015 (0.003) 0.030 (0.003) 0.013 (0.004) 0.008 (0.005)
Mother’s day 0.016 (0.004) 0.013 (0.004) 0.017 (0.006) 0.009 (0.007)
Olympus 0.030 (0.005) 0.019 (0.004) 0.044 (0.006) 0.028 (0.008)
Pentecost 0.044 (0.003) 0.036 (0.003) 0.053 (0.004) 0.038 (0.005)
Sinterklaas -0.027 (0.003) -0.001 (0.003) -0.002 (0.004) 0.005 (0.005)
Christmas 0.050 (0.004) 0.065 (0.004) 0.082 (0.006) 0.051 (0.007)

Price ratio competition -0.823 (0.054) -0.197 (0.053) -1.040 (0.070) -0.798 (0.095)
Price ratio regular price 1.847 (0.074) 1.303 (0.067) 2.197 (0.100) 1.762 (0.123)
Price ratio substitute 1 -1.083 (0.039) 0.316 (0.033) -1.183 (0.049) -0.387 (0.064)
Price ratio substitute 2 -0.371 (0.038) -1.165 (0.033) -0.411 (0.050) -0.823 (0.060)
Price ratio complement 1 -0.644 (0.027) -0.477 (0.023) -0.442 (0.034) -0.591 (0.044)

Discount price -0.002 (0.002) -0.011 (0.001) 0.002 (0.002) -0.007 (0.003)
Trips 0.013 (0.000) 0.002 (0.000) 0.011 (0.000) 0.006 (0.000)

Rain (x1000) -0.002 (0.001) -0.015 (0.003) -0.011 (0.003) -0.002 (0.001)
Temperature (x1000) 0.000 (0.000) 0.500 (0.010) 0.327 (0.015) 0.430 (0.015)
Seasonality 0.194 (0.005) 0.205 (0.005) 0.126 (0.006) 0.219 (0.006)

Instore flyer -0.446 (0.12) -0.469 (0.139) 0.000 (0.000) -0.786 (0.247)
Signing on shelf 1.227 (0.098) 0.191 (0.096) 0.958 (0.059) 0.686 (0.186)
Openings flyer 1.429 (0.695) 0.000 (0.000) 0.000 (0.000) -0.923 (0.26)
Dynamic newsletter 1.568 (0.138) 1.463 (0.158) 0.968 (0.067) 1.583 (0.266)
Entrance poster -1.998 (0.688) -13.168 (2.328) 0.000 (0.000) 0.000 (0.000)
National folder -1.203 (0.140) -0.640 (0.120) 0.000 (0.000) -0.551 (0.216)
Buy-1-get-1-free -0.618 (0.171) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Second placing 0.000 (0.000) 0.952 (0.130) 0.000 (0.000) 0.713 (0.237)
Online radio 0.000 (0.000) -0.244 (0.029) 0.000 (0.000) 0.000 (0.000)
Store radio 0.000 (0.000) 12.317 (2.326) 0.000 (0.000) 0.000 (0.000)

Franchise dummy -0.020 (0.008) -0.026 (0.010) 0.000 (0.000) 0.000 (0.000)
No. competitive stores in 15km -0.003 (0.001) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Percentage high education -0.105 (0.035) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Percentage unemployed -0.410 (0.202) 0.789 (0.202) 0.000 (0.000) 0.000 (0.000)
Self-scan dummy -0.026 (0.008) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Percentage regular visitor competitor -0.050 (0.023) 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)
Percentage high social class 0.000 (0.000) 0.000 (0.000) 0.125 (0.042) 0.000 (0.000)
Percentage non-western immigrants 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 1.276 (0.360)
City-rural dummy 0.000 (0.000) 0.000 (0.000) 0.000 (0.000) 0.040 (0.023)
R2 0.622 0.649 0.651 0.802

48