顧客價值分析之隨機模型建立及實證

Stochastic Modeling and Validation of Customer Value Analysis

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

《管理學報》 21卷5期 (2004/10) Pp. 675-692

https://doi.org/10.6504/JOM.2004.21.05.07

摘要

消費者對於產品屬性的偏好是具變異性的。遊客對於主題樂園產品屬性的偏好則至少存有三種變異的情形。首先，是因個別差異所造成的「分歧性變異」，另外則是隨其年齡或遊園經驗之不同而產生的「年齡性變異」與「經驗性變異」。本研究除了以市場區隔分析方法探討主題樂園遊客偏好的分歧性變異外，也以Pearce (1993) 所提出的休閒階梯理論為基礎，驗證該理論所假設支持的年齡性與經驗性變異。本研究採便利抽樣，於六福村的遊客中取得265個有效抽樣單位。研究結果指出，該主題樂園之產品屬性可歸納成：「主要利益」、「餐旅娛樂」、「驚險刺激」、「化外風情」與「異國幻境」等五個基本要素。本研究進而在此實證的分析基礎上明確指出「主題樂園」與「遊樂園」的區別所在。基於遊客偏好的分歧性變異，該樂園之市場可劃分為：「漫不經心型」、「積極狂熱型」、「情境陶醉型」、與「冒險犯難型」等四種區隔的遊客。研究結果同時提供各區隔中遊客的辨識特徵與有效的媒體通路。最後，因不同年齡層遊客的偏好在「感官刺激」與「增進關係」此兩動機階層中具有顯著差異，而且隨著階層的提升，最被驅動遊客的年齡層也由低往高移轉。因此遊客偏好的年齡性變異獲得一定程度的證實。然而其經驗性變異則未能獲得證實。

關鍵字

顧客價值分析 ； 馬可夫鏈 ； 貝氏統計

並列摘要

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.

並列關鍵字

Customer's value analysis ； Markov chain ； Bayesian statistics

參考文獻

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.