A Multicriterion Segmentation Approach Based on ...

A Multicriterion Segmentation Approach Based on CLV Components Mohamed Ben Mzoughia

Mohamed Limam

University of Tunis, Tunisia Telephone: (+216) 98-909-607 Email: [email protected]

University of Tunis, Tunisia and Dhofar University, Oman Email: [email protected]

Abstract—Most segmentation analyses use descriptive variables to group customers into homogenous segments in order to propose appropriate marketing actions and to optimize firms resources allocation. However, descriptive variables are usually fixed in time and lack actionability and responsiveness power. Some studies suggested that value based segmentation is the most significant from the standpoint of marketing activities. The customer lifetime value (CLV) metric, which aims to predict the future value of each customer, is often recommended as an interesting feature to segment customers. However, segmentation based on the two CLV components, number of transactions and lifetime, helps to better explain the customer behavior and to propose more effective marketing actions. In this work, we propose a Multicriterion segmentation approach based both on descriptive variables and on CLV components. The Multicriterion problem is solved using genetic algorithms by generating a set of Pareto-optimal solutions. The empirical analysis shows the ability of the proposed approach to characterize customer segments and to propose appropriate marketing actions.

I. I NTRODUCTION Customer segmentation is a fundamental approach in marketing, offering to managers the possibility to better fit customers needs, to optimize the firms marketing resources and to provide a snapshot of selected marketing strategies. The literature has extensively covered the issue of segmentation, providing a large number of methods including hierarchical clustering, K-means clustering, clusterwise regression, hierarchical Bayes, neural network, self-organizing map and many other methods. Traditional segmentation analysis uses only one set of variables to segment customers, especially descriptive variables, which are commonly used to identify the profile of each customers segment. When the market segmentation model uses more than one objective, we have multicriterion segmentation in which each segmentation base aims to maximize homogeneity not individually but together with other segmentation bases. An approach which is not supported by traditional clustering methods. The Multicriterion problem is defined as a set of optimization objectives or constraints. To solve this problem, a number of methods have been proposed. As a first solution, the Multicriterion problem was turned into a single optimization objective based on a weighted sum function. Then, a single objective simulated annealing heuristic was framed to get segmentation solutions [1]. Several studies have dealt with

the approach of transformation in Multicriterion segmentation problem. However, this approach presents several shortcomings that have not yet been resolved; this has led researchers to look for other ways to solve the Multicriterion segmentation problem. DeSarbo and DeSarbo [2] confirms that this kind of problem presents not only one solution but a set of Paretooptimal solutions. Finding a variety of solutions reflects the reality that there are many acceptable solutions for a customer segmentation problem. On the other hand, further studies have focused on the selection of criteria to be used for segmentation such as geographic, demographic, psychographics and other variables [3]. Zeithaml et al. [4] consider that traditional variables do not reflect the level of profitability of different segments. Hruschka and Natter [5] suggested that value based segmentation is the most significant from the standpoint of marketing activities. In the context of Multicriterion models, Wedel and Kamakura [6] proposed to segment customers simultaneously along two axes, both the predictive and the descriptive axes, especially as these two segmentation bases have little or no correlation. The CLV is an interesting customer level metric and in the same time a predictive variable that reflects the value of each customer. The CLV is typically used to identify profitable customers and it is proposed as an interesting base to segment customers [4]. The Pareto/NBD [7] is the most relevant CLV model in noncontractual context where the firm does not observe customer defection. This model is based on the prediction of two variables: the individual number of transactions modeled as a Poisson distribution with parameter λ and the customer lifetime with the firm modeled as an exponential distribution with dropout rate µ. It is true that segmentation based on CLV has been highly recommended by several studies, but the segmentation based on the two CLV components (number of transactions and lifetime) helps to explain better the customer behavior. For example, a low level of CLV can be explained either by a short customer lifetime or by a low number of transactions. These two explanations require completely different commercial actions. In this work, we propose a Multicriterion segmentation

approach based both on descriptive variables and on CLV components. Multicriterion problem is solved using genetic algorithms by generating a set of Pareto-optimal solutions. The remainder of this paper is organized as follows. Section II presents CLV measurements, with a focus on the Pareto/NBD model. Section III deals with the Multicriterion problem and the proposed segmentation approach. Section IV discusses the empirical study using real world data. Finally, we summarize the merits of our modeling approach in Section V. II. CLV MEASUREMENT The value of a customer has long been defined with regard to the longevity of his/her historical financial value. The concept of CLV attempts to account for the anticipated future profitability of each customer relationship. The CLV is defined as the discounted value of future profits yielded by a customer to the company [8]. The most recognized model in non-contractual setting is the Pareto-NBD, proposed by Schmittlein et al. in 1987 [7]. The Pareto/NBD model is based on the historical purchase behavior of each customer to forecast his future activity. Three past measures are required for every customer: the cohort T, which is the time from the entry of the customer of the company until now, the frequency x is the number of transactions that the customer has made after k time units and the recency tx which is the time between the entry date and the last purchase date. The Pareto/NBD model is based on six assumptions: 1) Customers go through two stages in their lifetime with a specific firm: they are alive for some period of time and then become permanently inactive; 2) While alive, the number of transactions made by a customer follows a Poisson process with transaction rate λ; 3) Heterogeneity in transaction rates across customers follows a gamma distribution (r, α); 4) Customers unobserved lifetime of length τ is exponentially distributed with dropout rate µ; 5) Heterogeneity in dropout rates across customers follows a gamma distribution (s, β); 6) The transaction rate λ and the dropout rate µ vary independently across customers. The classical resolution of the Pareto/NBD estimates the four parameters r, α, s and β. Our approach does not retain assumptions (3) and (5) and estimates the two parameters λi and µi for each customer i by maximizing the following likelihood function: L=

λx+1 −(λ+µ)T λx µ −(λ+µ)tx e + e λ+µ λ+µ

(1)

The estimated parameters λˆi and µˆi reflect the customer’s behavior in two aspects, number of transactions and customer lifetime. Figure 1 shows that CLV components, λˆi and µˆi , explain better the customers value compared to CLV metric and allow taking more accurate marketing decisions.

Fig. 1.

CLV components interpretation

III. P ROPOSED SEGMENTATION APPROACH A. The multicriterion problem The proposed Multicriterion problem aims to segment customers simultaneously along two axes, namely: Descriptive variables: Age, income, multichannel usage Predictive variables: CLV components, number of transactions and customer lifetime. As described in Figure 2, we propose a segmentation approach based on the following two objectives: F1 Using descriptive variables, we create groups (centroids), which minimize the global distance between customers values and related centroids. The global function to minimize, noted F1, is the ratio of the within-segment sum of squares to the total sum of squares. A smaller F1 value represents a better segment homogeneity. This statistic will be used as the first objective of our multicriterion problem. F2 The obtained centroids allow to group in the same segments customers which are demographically similar. However, in order to obtain optimal marketing actions, we need the obtained groups to have different predictive specifications. Therefore, we propose as a second objective, denotes F2, to maximize the distance between the segments centroid regarding to predictive variables. The function F2 is calculated as the sum of squared distances between each couple of centroids. We describe the final multicriterion problem as follows: J is the number of descriptive variables; P is the number of predictive variables (in our case P=2); K is the number of segments; xij is the value of the descriptive variable j for customer i; i=1..I, I is the number of customers; xip is the value of the predictive variable p for customer i;

Fig. 3. Fig. 2.

Proposed Mutilcriterion objectives

-

I(k) is the set of customers in segment k and N(k) is the number of customer in segment k; cjk is the centroid value of the descriptive variable j for segment k; cpk is the average value of the predictive variable p for segment k; The two optimization objectives are defined as follows: PK PJ P 2 k=1 j=1 i∈I(k) (xij − cjk ) (2) F 1 = PJ PI P I 1 2 j=1 i=1 (xij − I i=1 xij ) F2 =

Graphic presentation of the Pareto front

K P X X

K X

(cpk1 − cpk2 )2

(3)

p=1 k1=1 k2=1,k26=k1

B. Problem resolution using genetic algorithm To solve this multicriterion problem, we propose to use genetic algorithms, which are particularly effective in providing solutions to these problems. The genetic algorithm is characterized by its own operators such as crossover, mutation and selection. The Crossover associates two individuals, or parents, in order to form a new individual, or child, for the coming generation. In our case we create children by a random weighted average of the parents. The selection function selects parents for the next generation in terms of their scaled values from the fitness functions. In our case we identify each parent by choosing individuals at random, and then selecting the best individual out of that set to be a parent. The mutation function makes small random changes in the individuals in the population, which provide genetic diversity and allow the genetic algorithm to search a larger space. In our case we use a Gaussian mutation function. The length of chromosome is K x J. The elements which constitute the chromosome correspond to the coordinates of the centroids of each of the classes. For example, the first element is the average value of the first descriptive variable for customers who belong to cluster number one, the second element is the average value of the second descriptive variable for customers who belong to cluster number two and so on. Since it is a multicriterion problem, we no longer talk about an optimal solution but a set of optimal solutions forming

a surface called a Pareto front. We call Pareto optimal each acceptable optimal solution to our multicriterion problem. Pareto optimal solutions set is more beneficial than one simple solution since they provide flexibility when considering the real life segmentation problem and allow decision makers to bring their experience when choosing the solution to be implemented. Figure 3 presents an illustrative solution set that optimizes both objectives F1 and F2. Each point crossed by the Pareto Front is an optimal solution. IV. E MPIRICAL ANALYSIS We propose to apply our Multicriterion segmentation approach using real-world data. We explore a data set based on credit card transactions provided by an important retail bank in North Africa. The data set focuses on a single cohort of customers who made their first purchase in the first month of 2011. The dataset contains customers card transaction data from January 2011 till December 2011. The total number of transactions is 67,750 made by 1,000 customers. The descriptive variables for each customer are also provided: age, income and the use of multi-channel products. Using the dataset, we estimate the Pareto/NBD parameters λˆi and µˆi , i=1...1000. Table I summarizes descriptive variables and estimated predictive parameters. Since the range of values of raw data varies widely, the objective functions will not work properly without normalization. We use feature scaling to standardize each range of variables as follows: xi 0 =

xi − min(xi ) max(xi ) − min(xi )

(4)

We solve multicriterion problem for K=3...7 (K is the number of clusters). Figure 4 shows a graphic presentation of the set of Pareto-optimal solutions, for the case K=5, and reflects the reality that there are many optimal solutions for our multicriterion segmentation problem. Each optimal solution minimizes the distances from centroids with respect to descriptive variables, and maximize the distance between centroids with respect to the CLV components. By putting all optimal solutions together, for K=3...7, the decision maker can choose the appropriate solution that satisfies his need according to the two objectives. In our case,

TABLE I D ESCRIPTIVE STATISTICS OF PREDICTIVE AND DESCRIPTIVE VARIABLES

TABLE II P REDICTIVE AND DESCRIPTIVE SPECIFICATIONS OF CLUSTERS

Variable

Min

Max

Mean

Std. dev.

Class

Descriptive variables

CLV components.

Age Incomes ($/month) Multi-channel use Transactions parameter λˆi Dropout rate µˆi

24 353 0 0.03 0.00

77 9,900 1 2.61 0.84

46 1,275 0.2 0.82 0.03

11 999 0.4 0.48 0.05

C1

Elderly, low income, low use of multi-channel

C2

Elderly, high income, high use of multi-channel Young, low income, high use of multi-channel

Average transactions frequency and high churn risk Average transactions frequency and low churn risk Average transactions frequency and high churn risk Low transactions frequency and high churn risk High transactions frequency and average churn risk

Fig. 4.

C3

C4

Elderly, high income, low use of multi-channel

C5

Young, high income, high use of multi-channel

The Pareto front (K=5)

we select K=5 and the optimal solution F1=0.176 and F2=2.15. Figure 5 shows that the distance between centroids Ci, i=1...5 is important and allows taking different marketing decisions. Table II presents the descriptive and predictive specifications of each group of customers. We propose some examples of marketing decisions: A. Cross selling strategy Table I shows that customers who do not use Multi-channel products present a higher churn risk. The idea is to develop a cross selling strategy by offering, for example free of charge for one year, some multi-channel products to clusters C1, C4 and C5. This action enables them to extend their lifetime with the firm and then increase their lifetime value. B. Targeting strategy Cluster C5 presents a very high transaction frequency and an average churn risk. This class contains young customers with high income. We propose to create for them a specific product with appropriate trade dress and target potential customers with similar descriptive characteristics. C. Retention strategy Clusters C1 and C3 present a high churn risk and a low income level. These customers are often sensitive to price and change from a bank to another for a low price difference. It is possible to retain these customers either by decreasing prices or by proposing a loyalty program with benefits that increase with the customer lifetime and which are lost as soon as the customer registers a substantial period of inactivity.

Fig. 5.

Centroids position, with respect to CLV components

V. C ONCLUSION Market segmentation is a key approach in marketing giving managers the ability to meet customers needs and to develop a strategic action plan. Several studies show that value based segmentation is important from the standpoint of marketing activities and that CLV metric represents an interesting feature to segment customers. In this work we proposed a multicriterion segmentation approach based on descriptive variables and on CLV components. A two-objective problem is solved using genetic algorithms by performing a set of Pareto-optimal solutions. The empirical analysis shows the ability of the proposed approach to characterize customer segments and take appropriate marketing actions. Further investigation is needed as an improvement of this approach is to identify the optimal number of clusters. R EFERENCES [1] J. Brusco, Michael , J. Dennis Cradit, and Armen Tashchian, ”Multicriterion clusterwise regression for joint segmentation settings: An application to customer value,” Journal of Marketing Research, vol. 40, no. 2, pp. 225-234, 2003. [2] S. DeSarbo, Wayne and F. Christian DeSarbo, ”A generalized normative segmentation methodology employing conjoint analysis,” Conjoint Measurement, Springer Berlin Heidelberg, pp.473-504, 2003.

[3] T. Bock and M. Uncles, ”A taxonomy of differences between consumers for market segmentation,” International Journal of Research in Marketing, vol. 19, no. 3, pp. 215-224, 2002. [4] V.A. Zeithaml, R.T. Rust, and K.N. Katherine, ”The customer pyramid: creating and serving profitable customers,” California Management Review, vol. 43, no. 4, pp. 118-142, 2001. [5] H. Hruschka and M., ”Comparing performance of feedforward neural nets and K-means for cluster-based market segmentation,” European Journal of Operational Research, vol. 114, no. 2, pp. 346-353, 1999. [6] R. Calantone, Market segmentation: conceptual and methodological foundations, 2000. [7] D.C. Schmittlein, D.G. Morrison and R. Colombo. ”Counting Your Customers: Who-Are They and What Will They Do Next?,” Management science, vol. 33, no. 1, pp. 1-24, 1987. [8] R.T. Rust, V.A. Zeithaml and K. N. Lemon, Driving customer equity: How customer lifetime value is reshaping corporate strategy, Simon and Schuster, 2001.