顧客價值分析之隨機模型建立及實證

郭瑞祥; 蔣明晃; 陳宏毅

doi:10.6504/JOM.2004.21.05.07

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P675 - 692

社会科学 > 管理学

DOI： 10.6504/JOM

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顾客价值分析之随机模型建立及实证

Stochastic Modeling and Validation of Customer Value Analysis

郭瑞祥(Ruey-Shan Guo) ；蒋明晃(David Chiang) ；陈宏毅(Hung-Yi Chen)

管理学报； 21 卷 5 期 (2004 / 10 / 01) ， P675 - 692

繁体中文 DOI： 10.6504/JOM.2004.21.05.07

顾客价值分析；马可夫链；贝氏统计； Customer's value analysis ； Markov chain ； Bayesian statistics

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摘要 │ 参考文献 (21) │ 被引用文献 (4) │ 国际计量

摘要〈TOP〉

并列摘要〈TOP〉

In today business, enterprises must maintain close relationship with their customers and focus on key customers for higher profits. How to estimate customers’ lifetime value and distinguish between valuable customers from non-valuable customers has become an important issue. With the rapid progress of information technology and development of related algorithms, customers’ lifetime value can now be better estimated. To fill the gap of the current literature lacking both systematic methodologies and empirical studies, the goal of this paper is to propose a systematic method to estimate customers’ lifetime value and conduct empirical validation.
This research consists of the following steps: 
Step 1: Construct a stochastic model of customers’ purchasing behavior and propose the underlying probability distributions of customers’ purchasing frequency and money amount. Six assumptions are assumed about the underlying distributions which include (1) the distribution of purchasing frequency and money amount are independent; (2) customers’ purchasing behavior is modeled as a Markov chain; (3) customers’ purchasing frequency follows a Poisson distribution with average equal to λ; (4) the average purchase frequency (λ) as used in (3) follows a Gamma distribution; (5) customers’ purchasing money amount follows a Gamma distribution with average equal to u/θ; (6) the parameter (θ) as used in (5) follows a Gamma distribution. With assumptions (3) and (4), customers’ purchasing frequency is modeled as a negative binomial distribution. With assumptions (5) and (6), customers’ purchasing money amount is modeled as a Gamma-Gamma distribution.
Step 2: Model the customer’ purchasing behavior as a Markov chain and the associated transition states based on the RFM (recency-frequency-monetary) model. Here, R refers recency and has states between 1 and r, F refers frequency and has states between 1 and f, and M refers Monetary and has states between 1 and m. With the defined states, a transition matrix with  columns and   rows can be constructed.
Step 3: Use Bayesian theorem to derive transition state probabilities. Since the distribution of purchasing frequency and money amount are assumed independent, the transition probability can be obtained by multiplying two independent probabilities. For a transition probability from state (R,F,M)=（r1,f1,a1＜m1＜b1）to state (R,F,M)=(r1+1,f1,a1＜m1＜b1)we have f(subscript r,f,m)(r1+1,f1, a1＜m1＜b1׀r1,f1, a1＜m1＜b1)=f(subscript f) (0׀f1,r1).For a transition probability from state (R,F,M)=(r1,f1,a1＜m1＜b1) to state (R,F,M)=(0,f2, a2＜m2＜b2)we have f(subscript r,f,m)
(1,f2, a2＜m2＜b2׀r1,f1,a1＜m1＜b1)=f(subscript f)(f2׀f1,r1)f(subscript m)( a2＜m2＜b2׀a1＜m1＜b1).
Step 4: Construct customers’ transition and reward matrices and calculate customers’ lifetime value.
The proposed method has been validated using the sales data of a computer company. In this empirical study, sales data of 30 months were split into 24 months of training data and 6 months of testing data. A cluster analysis was also used to cluster the customers into two more homogeneous groups, one group of high-value customers and another one of low-value customers. Customers' lifetime value analysis were then performed with two individual groups. The results were then compared with those by a traditional method as proposed by Hughes (1994). Several conclusions can be made: (1) The Hughes’s RFM model underestimates the customers’ value and can’t capture the stochastic behavior of customers; (2) a cluster analysis should be performed before applying the proposed method since a homogeneous population is assumed within the same group; (c) the proposed model outperforms the current methods and achieves a very accurate estimation of customers' value.

参考文献 ( 21 ) 〈TOP〉

Berger, Paul D.,Nada I. Nasr(1998).Customer Lifetime Value: Marketing Models and Applications.Journal of Interactive Marketing,12,17-29.
Brockett, Patrick L.,Linda L. Golden,Harry H. Panjer(1996).Flexible Purchase Frequency Modeling.Journal of Marketing Research,33,94-107.
Colombo, Richard,Weina Jiang(1999).A Stochastic RPM Model.Journal of Interactive Marketing,13,2-12.
Dwyer, F. Robert(1989).Customer Lifetime Valuation to Support Marketing Decision Making.Journal of Direct Marketing,3,8-15.
Ehrenberg, A.S.C(1959).The Pattern of Consumer Purchases.Applied Statistics,8(1),26-41.

被引用文献 ( 4 ) 〈TOP〉

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