Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T00:57:29.379Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical analysis of the optimizing acquisitionand retention over time problem

Published online by Cambridge University Press:  14 November 2008

Adi Ditkowski
Adi Ditkowski*
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel. adid@post.tau.ac.il
Get access

Abstract

While making informed decisions regardinginvestments in customer retention and acquisition becomes apressing managerial issue, formal models and analysis, which mayprovide insight into this topic, are still scarce. In this studywe examine two dynamic models for optimal acquisition andretention models of a monopoly, the total cost and the cost percustomer models.These models are analytically analyzed using classical, direct,methods and asymptotic expansions (for the total cost model).In order to numerically simulated the models, an innovativenumerical method was developed for solving ODE systems withinitial/final value problems.


Keywords

ODE nonlinear boundary value problems; ODE applications; ODE growthboundednesscomparison of solutions; ODE asymptotic expansions; optimal control; numerical methods ODE boundary value problems.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 1 , January 2009 , pp. 119 - 137
Copyright
© EDP Sciences, SMAI, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ambler, T., Abandon lifetime value theories and take care of customers now. Marketing 12 (2001) 18.
C.M. Bender and S.A. Orszag, Advanced mathematical methods for scientists and engineers, McGraw-Hill International Series in Pure and Applied Mathematics. McGraw-Hill, New York (1978).
Blattberg, R.C. and Deighton, J., Managing marketing by the customer equity test. Harvard Business Rev. 74 (1996) 136–144.
R.C. Blattberg, G. Getz and J.S. Thomas, Customer Equity: Building and Managing Relationships as Valuable Assets. Harvard Business School Press, Boston, MA, USA (2001).
Chang, H.-C., Gottlieb, D., Marion, M. and Sheldon, B.W., Mathematical analysis and optimization of infiltration processes. J. Scientific Computing 13 (1998) 303–321. CrossRef
A. Ditkowski, Numerical method for solving non-contiguous initial/final-value problems. J. Scientific Computing (to appear).
Ditkowski, A., Gottlieb, D. and Sheldon, B.W., On the mathematical analysis and optimization of chemical vapor infiltration in materials science. ESAIM: M2AN 34 (2000) 337–351. CrossRef
A. Ditkowski, B. Libai and E. Muller, Optimizing acquisition and retention over time. Marketing Lett. (submitted).
Fornell, C. and Wernerfelt, B., Defensive marketing strategy by customer complaint management: A theoretical analysis. J. Marketing Research 24 (1987) 337–346. CrossRef
Gupta, S. and Lehmann, D.R., Customers as assets. J. Interactive Marketing 17 (2003) 9–24. CrossRef
Gupta, S., Lehmann, D.R. and Stuart, J.A., Valuing customers. J. Marketing Research 41 (2004) 7–18. CrossRef
D. Hanssens, Allocating marketing communication expenditures: A long run view, in Measuring and Allocating Marcom Budgets: Seven Expert Points of View, Marketing Science Institute, Cambridge, MA, USA (2003).
Hogan, J.E., Lemon, K.N. and Rust, R.T., Customer equity management: Charting new directions for the future of marketing. J. Service Research 5 (2002) 4–12. CrossRef
Jain, D. and Singh, S.S., Customer lifetime value research in marketing: A review and future directions. J. Interactive Marketing 16 (2002) 34–46. CrossRef
M. Kamien and N.L. Schwartz, Dynamic Optimization. Second edition, New York: North Holland (1991).
Lester, L.Y., CRM meets Wall Street. Target Marketing 26 (2003) 50–54.
R.J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics ETH Zürich. Second edition, Birkhäuser Verlag (1992).
W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in C, The Art of Scientific Computing. Second edition, Cambridge University Press (1992).
Reinartz, W.J. and Kumar, V., On the profitability of long-life customers in a non-contractual setting: An empirical investigation and implications for marketing. J. Marketing 64 (2000) 17–35. CrossRef
Reinartz, W.J., Thomas, J. and Kumar, V., Balancing acquisition and retention resources to maximize customer profitability. J. Marketing 69 (2005) 63–79. CrossRef
Rust, R.T., Lemon, K.N. and Zeithaml, V.A., Return on marketing: Using customer equity to focus marketing strategy. J. Marketing 68 (2004) 109–127. CrossRef
L. Selden and G. Colvin, How to measure the profitability of your customers. Harvard Business Rev. (2003) 74–81.
Thomas, J.S., A methodology for linking customer acquisition to customer retention. J. Marketing Research 38 (2001) 262–268. CrossRef
Vatanasombut, B., Stylianou, A.C. and Igbaria, M., How to retain online customers. Communication of the ACM 47 (2004) 65–78.
Venkatesan, R. and Kumar, V., A customer lifetime value framework for customer selection and optimal resource allocation strategy. J. Marketing 68 (2004) 106–125. CrossRef
R. Weinstock, Calculus of Variations. Dover Punlications, Inc., NY (1974).
Zeithaml, V.A., Service quality, profitability, and the economic worth of customers: What we know and what we need to learn. J. Acad. Mark. Sci. 28 (2000) 67–85. CrossRef