A Dynamic Model for Valuing Customers: A Case Study

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1 , pp A Dynamc Model for Valung Customers: A Case Study Hyun-Seok Hwang 1 1 Dvson of Busness, Hallym Unversty 1 Hallymdaehak-gl, Chuncheon, Gangwon-do, Korea hshwang@hallym.ac.kr Abstract. To support personalzed marketng, t s necessary to dentfy an ndvdual customer s true value. Varous researches on customer value have conducted under the name of Customer Lfetme Value (CLV), Customer Equty, Customer Proftablty, and Lfetme Value. In ths paper we present ssues of calculatng ndvdual customer s lfetme value to deploy more personalzed CRM actvtes. We propose a new method to calculate ndvdual customer s lfetme value dynamcally. The feasblty of the suggested model s llustrated through a case study of the wreless telecommuncaton ndustry n Korea. Data mnng technques are used to predct lfetme value of a customer. Marketng mplcatons wll be dscussed based on the result of ndvdual CLV. Keywords: Customer lfetme value, Customer relatonshp management, Dynamc model, Data mnng 1 Introducton The more a marketng paradgm evolves, the more a long-term relatonshp wth customers gans ts mportance. When evaluatng customer lfetme value, marketers are often remnded of the 80/20 rule (80% of the profts are produced by top 20% of proftable customers and 80% of the costs, by top 20% of unproftable customers, vce versa) [1]. It s requred to know ndvdual customer s value to a frm snce a frm has to foster proftable customers to optmze marketng efforts. Therefore we need a research foundaton for the recent but growng nterests n Customer Lfetme Value and ts marketng applcatons. Ths paper ams at proposng a new model for measurng customer lfetme value consderng both customer relatonshp dynamcs wth a frm and marketng potental. Customer relatonshp dynamcs denotes the change of customer relatonshps wth a frm such as customer retenton, customer churn, customer wnback, and customer loss. ISSN: ASTL Copyrght 2015 SERSC

2 2 Related Works CLV can be defned as the sum of the revenues ganed from a company s customers over the lfetme of transacton after the deducton of the total cost of attractng, sellng, and servcng customers, takng nto account of the tme value of money [2]. The lteratures n customer lfetme value research have taken multple drectons. However, the man drectons of prevous studes n CLV research are classfed nto four categores. The frst one s developng structural models to calculate CLV for a customer or customer group. The second drecton focuses on the strategc use of CLV n customer management [3-7]. The thrd drecton s normatve models used manly to understand the ssues concernng CLV [8]. The last area has been devoted to developng analytcal models whch help decson makng relevant to marketng management, such as promoton, campagn, prcng, and budget allocaton. If classfed n detal, the structural model can be dvded nto eght sub-models accordng to the classfcaton crtera shown n Table 1. Table 1. Classfcaton of the CLV researches Focus Category Model Customer Unt Indvdual model Segment (Customer base) model Retrospectve model Predcton data Structural Model Prospectve model Transacton Contractual model Non-Contractual model Purchase cycle Dscrete model Contnuous model Strategc Model Strategc use of CLV n management Normatve Model Relatonshp between Duraton and cost Analytc Model Resource allocaton (Budget allocaton) / Prcng 3 A Dynamc Model for Measurng Customer Lfetme Value To regard the tme varant characterstcs of customer relatonshp wth a frm, we adopt the Markov chan model to express the customer relatonshp dynamcs. Before expressng the customer relatonshp n terms of the Markov chan model, we should defne the states of the Markov chan. The relatonshp wth a customer can be classfed nto three states, P (potental customer state), D (defected customer state), and A (actve customer state). Fgure 1 shows the Customer Relatonshp Dynamcs (CRD) usng the Markov chan. CRD represents the changng relatonshp of a customer wth a frm durng a customer s lfetme. Customers are acqured from the potental customer (P) state and defect from the actve customer (A) state and become the defectng customer (D) state. Some of defected customers are wonback to an orgnal frm and move to the actve customer state but the others are lost and move to the potental customer state. Each Copyrght 2015 SERSC 57

3 state change s represented by the probablty of movement from one state to the other. Wthn the actve customer state, there are many substates representng possble states whle a customer served by a frm. Fg. 1. Customer Relatonshp Dynamcs 3.1 Indvdual CLV equaton The suggested ndvdual CLV model based on the Markov chan s as follows: CLV lm N T t N t 0 (1 d ) t R (1) T s the one-step transton matrx of customer. R s the reward vector of customer. The reward vector s a (mn+2)(mn+2) square matrx whose th column element represents the proftablty of a customer whle he or she remans at th rows state for one tme perod. To consder tme value of money, dscount rate d, converts future profts nto present one. All future profts changed nto Net Present Value (NPV) and then added. The suggested model, therefore, converts the future proft potentals composed of the probablty of customer stayng at a state and proft contrbuton to net present value. CLV 0 T (1 d ) 0 1 T (1 d ) 1 N T (1 d ) N R (2) 1 T CLV I R (3) (1 d ) 58 Copyrght 2015 SERSC

4 3.2 Lmtng probablty of CRD Generally speakng, the one-step transton matrx has the lmtng probablty on condton that the Markov chan s rreducble and ergodc,.e., postve recurrent and aperodc. The CLV transton matrx, T, communcates among all states and the expected tme, startng at state, untl the process returns to state s fnte. Furthermore, all states have the perod 1. Therefore the matrx T has the lmtng probablty. P, where P s the transton probablt y from state to state (4) 4 A Case Study of a Wreless Telecommuncaton Company Churn s the one of the most serous problems n the wreless telecommuncaton ndustry where customers on a cellular servce for an ntroductory offer and then on a dfferent company when the ntroductory offer of the orgnal frm expres. To decde several probabltes for the one-step transton matrx of a customer, the probabltes of the customer denoted n Fgure 3 should be calculated. We use data mnng technques to predct these probabltes One-step transton matrx of customer The one-step transton matrx conssts of the probabltes lsted n Table 2. Fgure 8 represents the one-step transton probabltes of customer after normalzng the probabltes. Fg. 2. One-step transton matrx of customer Copyrght 2015 SERSC 59

5 4.2 Reward vector of customer The reward vector of customer, the contrbuted proft whle he or she stays at a certan state, s derved from an ntervew as shown n table 3. Table 2. Cost drvers of a telecommuncaton company ID Proft/Cost Drvers Proft/cost (KRW) D1 Monthly Proft from Charge wthout optonal servce (+)15,000 D2 Proft from a cross-sellng servce (+)1,000 D3 Marketng cost for a cross-sellng promoton (-)3,000 D4 Marketng cost for a defected customer (-)2,000 D5 Subsdy for a wonback customer (-)20,000 D6 Marketng cost for acqurng a potental customer (-)2,000 D7 Subsdy for an acqured customer (-)20, Lfetme value of customer Lfetme value of customer can be derved through Equaton 4 as shown above. Monthly nterest rate are used for the dscount rate, d, and t s set as 0.3 (%/month). The result of Equaton 3 s shown n Fgure 10. As mentoned before, the dagonal elements are the lfetme value and, therefore, Fgure 10 can be summarzed as Fgure 11. A 1 A 2 A 3 A 4 D P A 1 2,2 4 4, ,2 4 4, ,2 4 4, ,2 4 7, ,4 3 6, ,4 3 6,5 3 3 A 2 2,2 6 2, ,2 6 2, ,2 6 2, ,2 6 5, ,4 2 0, ,4 2 0,1 7 3 C L V = A 3 A 4 2,2 8 2, ,2 9 3, ,2 8 2, ,2 9 3, ,2 8 2, ,2 9 3, ,2 8 5, ,2 9 6, ,4 0 0, ,3 8 6, ,4 0 0, ,3 8 6,3 1 9 D 1,9 2 8, ,9 2 8, ,9 2 8, ,9 3 1, ,3 6 1, ,3 6 1,9 5 0 P 1,1 6 1, ,1 6 1, ,1 6 1, ,1 6 4, ,1 8 0, ,1 8 0,5 7 7 Fg. 3. CLV matrx of customer 60 Copyrght 2015 SERSC

6 6 Concluson and Further Research Drectons Ths paper focused on the mplementaton of an ndvdualzed Customer Lfetme Value model. Customer relatonshp wth a frm s emboded by a state of the Markov chan. The suggested CLV model provdes not only the lfetme value of a customer but the fractonzed lfetme value of a customer accordng to the state. The model also covers the long-run proporton of tme for a state where he or she stays. The suggested model s llustrated by an ndustral case study on the wreless telecommuncaton ndustry n Korea. In future, we expect ths work to spur further research on personalzed stochastc CLV model, whch ncludes the Markov chan model and other structural CLV models based on probablstc revenue estmaton. Another further research ssue s to develop a personalzed marketng strategy based on ndvdual CLV. Indvdual CLV s expected to vary wth changes of busness envronment. Therefore, marketng strateges should be bult based on the result of senstvty analyss. A senstvty analyss can help the strategy development by decdng optmal budget allocaton, forecastng proftablty change, and measurng marketng effectveness. References 1. Duboff, R.S.: Marketng to maxmze proftablty, J. Busness Strategy. 13, (1992) 2. Hwang, H., Jung, T., Suh, E.: An LTV model and customer segmentaton based on customer value: a case study on the wreless telecommuncaton ndustry. Expert systems wth applcatons. 6, (2004) 3. Ptt, L.F., Ewng, M.T., Berthon, P.: Turnng compettve advantage nto customer equty. Busness Horzons. 43, (2000) 4. Ruyter, K., Wetzels, M.: Customer equty consderatons n servce recovery: a crossndustry perspectve. Int l J. Servce Industry Management. 11, (2000) 5. Shapro, B.P., Rangan, V.K., Morarty, R.T., Ross, E.B.: Manage customers for profts (not ust sales). Harvard Busness Revew. 65, (1987) 6. Stahl, H.K., Matzler, K., Hnterhuber, H.H.: Lnkng customer lfetme value wth shareholder value. Industral Marketng Management. 32, (2003) 7. Kumar, V., Lemon, K. N., Parasuraman, A.: Managng Customers for Value An Overvew and Research Agenda. J. Servce Research. 9, (2006) 8. Jan, D., Sngh, S.S.: Customer lfetme value research n marketng: A revew and future drectons. J. nteractve marketng. 16, (2002) Copyrght 2015 SERSC 61