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Customer lifetime value in service contracts (christoph heitz)
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Customer lifetime value in service contracts (christoph heitz)

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  • 1. Customer Lifetime Value in service contracts The world is not Markovian! Christoph Heitz, Andreas Ruckstuhl, Marcel Dettling Zurich University of Applied Sciences Swiss Institute of Service Science
  • 2. Content Customer lifetime value (CLV) – What is CLV? – Contractual vs noncontractual settings – Classical models for calculating CLV CLV in contractual settings – Modeling customer dynamics: Why the Markov assumption does not hold, and why this matters Semi-markov model Application: Swiss newspaper subscription Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 3. Measuring customer value Concept of customer lifetime value (CLV) – sum of future revenue – discounting net present value – well known concept in marketing ∞ CLVk = ∑ ck (t ) α t t =1 Future revenue - stochastic process CLV depends on what the customer will do in the future: ck(t)=? Needed: Modeling of future customer behavior Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 4. Contractual vs noncontractual settings Main question: What will customer do? Non-contractual setting acquisition – Start business – Stop vs. continue business retention – Increase business Customer development Contractual setting – Subscribe new contract acquisition – Keep contract vs. cancel retention – Change contract (e.g. upgrade) Customer development Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 5. Modeling customer dynamics Model 1: Lost-for-good (Dwyer 1989) – Two-state model: customer / no customer – Customer who has left never returns – Modeling issue: lifetime analysis 5 5 5 5 5 Model 2: Always-a-share – multi-state model 4 4 4 4 4 – More complete dynamics (includes Lost- for-good dynamics) 3 3 3 3 3 – Modeling issues: describe state changes – Classical model: Markov Chains 2 2 2 2 2 (Pfeiffer/Carraway (2000), Piersma/Jonker (2000), Tirenni (2005)) 1 1 1 1 1 – Basic assumption: the probability of a state change („hazard rate“) does not depend on the past, in particular not on the sojourn time! Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 6. Specifics of contractual settings observability Contract impacts behavior of customer – e.g. minimum duration: customer might want to cancel but is not allowed to! – Fixed renewal periods allow cancelling only at specific times – Contradiction to Markov assumption! Contract design is an important driver for customer lifetime value Is it important to account for „contract mechanics“ when determining CLV?? Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 7. Typical hazard functions for contractual settings h(t) h(t) Contract cancellation after minimum Markovian dynamics contract duration t t h(t) Minimum contract duration without h(t) cancelling Periodic withdrawal dates t t h(t) Long-time customers are more loyal t Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 8. Empirical example: contract durations for newspaper subscription Lebensdauer Festabo in Wochen 4000 3000 Häufigkeit 2000 1000 0 0 50 100 150 Lebensdauer in Wochen Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 9. A simple example Contract with minimum duration period Assumed customer behavior: – 50% cancellation after one year, expected lifetime if not cancelled: additional 5 years – This results in average lifetime of 3 years – Constant revenue stream during contract duration h(t) t Calculation of CLV with – Markov model (reflecting correct avg. fifetime) – Correct formula Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 10. CLV under non-markovian dynamics h(t) CLV(t) True CLV t 40% difference CLV calculated with best Markov model 1 yr t Markov model results in wrong CLV at any given time! Deviation can be substantial Taking contract into consideration can be crucial for any marketing decision Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 11. Modeling of dynamics with Semi-Markov models Semi-Markov models are 5 5 5 5 5 generalization of Markov models 4 4 4 4 4 – Dynamics consist of two steps • Sojourn in a state 3 3 3 3 3 • Jump to another state 2 2 2 2 2 – Lifetime in state may be arbitrarily distributed 1 1 1 1 1 • Hazard rate: Rate of leaving state • Hazard rate may depend on sojourn time – Jump to another state may depend on sojourn time as well Modeling elements: – Hazard function for each state: hi(t) = probability of leaving state i at sojourn time t – Matrix of jump probabilities pij(t) Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 12. Applying SMM to customer dynamics Semi-Markov models allow incorporating many important contract rules, e.g. – Minimum contract duration – Specific renewal dates – Upgrading possible at each time, but downgrading restricted At the same time, Semi-markov models allow modeling known effects such increasing loyalty of customers – Churn rate tends to decrease with contract duration Additional modeling elements: – hazard functions hi(t) for each state – Jump probabilities pij(t) Integrating in CLV calculation framework – CLV can be calculated analytically with simple operations ∞ CLVk = ∑ ck (t ) α t t =1 Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 13. Analytical calculation of CLV, discrete time version Discrete lifetime distribution, calculated from hazard function ∞ xi = ∑ f i (T ) α T T =1 Monthly discount factor ∞ y ij = ∑ pij (T ) f i (T ) α T T =1 Jump matrix elements ( ) r r J = Ι− y −1 (Ι − x )⋅ 1 − α c Monthly revenue in states Current sojourn time ci in state i CLVi (T0 ) = ⋅ (1 − xi ) + ∑ yij ⋅ J j % % 1−α j Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 14. Estimation of model parameters hazard function hi(t) of leaving state i at sojourn time t data CLV Individual matrix of jump probabilities pij Individual jump probabilities pk,ij: – Estimated by (multinomial) logistic regression models based on the recent past Individual hazard function hk(t) : – Estimated by forward continuation ratio model with proportional hazard properties (discretized version of proportional hazard model) Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 15. Application Subscription of national newspaper of Switzerland Data: Contract history of 450k customers in 2002-2008 Modelling with SMM, and estimation of CLV for each customer Probeabo Aktionsabo evtl. Kein Abo Festabo Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 16. Average empirical hazard function for standard subscription Empirical Hazard Festabo 0.015 Hazard Rate pro Woche 0.010 0.005 0 50 100 150 200 250 300 Wochen Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 17. Results of case study Clear non-markovian dynamics in nearly all states – Validated with empirical data Parameters of Semi-markov model could be estimated on individual customer basis with high accuracy – Validation with repeatedly simulated data for 450k customers – Average statistical error in individual CLV estimate less than 1% Approach seems viable for marketing optimization, in particular for direct marketing SAS and R/MATLAB implementations available (idp, SAS Switzerland) Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 18. Conclusion Markov chain models not suited for many contractual settings – Risk of substantially wrong CLVs for individual customers Framework for Semi-Markov modeling developed – parameter estimation on individual customer level – Formulas for CLV calculation, given model parameters Use of model: – Operational marketing planning: Optimum selection of customers for marketing campaigns – Strategic and tactical marketing planning Frontiers in Service Conference, Karlstad, June 10-13, 2010
  • 19. Thank you for your attention! Frontiers in Service Conference, Karlstad, June 10-13, 2010

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