Mathematical analysis of the optimizing acquisition and retention over time problem

Adi Ditkowski

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 43, Issue: 1, page 119-137
  • ISSN: 0764-583X

Abstract

top
While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer 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 innovative numerical method was developed for solving ODE systems with initial/final value problems.


How to cite

top

Ditkowski, Adi. "Mathematical analysis of the optimizing acquisition and retention over time problem." ESAIM: Mathematical Modelling and Numerical Analysis 43.1 (2008): 119-137. <http://eudml.org/doc/194440>.

@article{Ditkowski2008,
abstract = { While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer 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 innovative numerical method was developed for solving ODE systems with initial/final value problems.
},
author = {Ditkowski, Adi},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {ODE nonlinear boundary value problems; ODE applications; ODE growth; boundedness; comparison of solutions; ODE asymptotic expansions; optimal control; numerical methods ODE boundary value problems.; ODE nonlinear boundary value problems; ODE applications; ODE growth; comparison of solutions; ODE asymptotic expansions; optimal control; numerical methods ODE boundary value problems},
language = {eng},
month = {11},
number = {1},
pages = {119-137},
publisher = {EDP Sciences},
title = {Mathematical analysis of the optimizing acquisition and retention over time problem},
url = {http://eudml.org/doc/194440},
volume = {43},
year = {2008},
}

TY - JOUR
AU - Ditkowski, Adi
TI - Mathematical analysis of the optimizing acquisition and retention over time problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/11//
PB - EDP Sciences
VL - 43
IS - 1
SP - 119
EP - 137
AB - While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer 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 innovative numerical method was developed for solving ODE systems with initial/final value problems.

LA - eng
KW - ODE nonlinear boundary value problems; ODE applications; ODE growth; boundedness; comparison of solutions; ODE asymptotic expansions; optimal control; numerical methods ODE boundary value problems.; ODE nonlinear boundary value problems; ODE applications; ODE growth; comparison of solutions; ODE asymptotic expansions; optimal control; numerical methods ODE boundary value problems
UR - http://eudml.org/doc/194440
ER -

References

top
  1. T. Ambler, Abandon lifetime value theories and take care of customers now. Marketing12 (2001) 18.  
  2. 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).  
  3. R.C. Blattberg and J. Deighton, Managing marketing by the customer equity test. Harvard Business Rev.74 (1996) 136–144.  
  4. 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).  
  5. H.-C. Chang, D. Gottlieb, M. Marion and B.W. Sheldon, Mathematical analysis and optimization of infiltration processes. J. Scientific Computing13 (1998) 303–321.  
  6. A. Ditkowski, Numerical method for solving non-contiguous initial/final-value problems. J. Scientific Computing (to appear).  
  7. A. Ditkowski, D. Gottlieb and B.W. Sheldon, On the mathematical analysis and optimization of chemical vapor infiltration in materials science. ESAIM: M2AN34 (2000) 337–351.  
  8. A. Ditkowski, B. Libai and E. Muller, Optimizing acquisition and retention over time. Marketing Lett. (submitted).  
  9. C. Fornell and B. Wernerfelt, Defensive marketing strategy by customer complaint management: A theoretical analysis. J. Marketing Research24 (1987) 337–346.  
  10. S. Gupta and D.R. Lehmann, Customers as assets. J. Interactive Marketing17 (2003) 9–24.  
  11. S. Gupta, D.R. Lehmann and J.A. Stuart, Valuing customers. J. Marketing Research41 (2004) 7–18.  
  12. 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).  
  13. J.E. Hogan, K.N. Lemon and R.T. Rust, Customer equity management: Charting new directions for the future of marketing. J. Service Research5 (2002) 4–12.  
  14. D. Jain and S.S. Singh, Customer lifetime value research in marketing: A review and future directions. J. Interactive Marketing16 (2002) 34–46.  
  15. M. Kamien and N.L. Schwartz, Dynamic Optimization. Second edition, New York: North Holland (1991).  
  16. L.Y. Lester, CRM meets Wall Street. Target Marketing26 (2003) 50–54.  
  17. R.J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics ETH Zürich. Second edition, Birkhäuser Verlag (1992).  
  18. 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).  
  19. W.J. Reinartz and V. Kumar, On the profitability of long-life customers in a non-contractual setting: An empirical investigation and implications for marketing. J. Marketing64 (2000) 17–35.  
  20. W.J. Reinartz, J. Thomas and V. Kumar, Balancing acquisition and retention resources to maximize customer profitability. J. Marketing69 (2005) 63–79.  
  21. R.T. Rust, K.N. Lemon and V.A. Zeithaml, Return on marketing: Using customer equity to focus marketing strategy. J. Marketing68 (2004) 109–127.  
  22. L. Selden and G. Colvin, How to measure the profitability of your customers. Harvard Business Rev. (2003) 74–81.  
  23. J.S. Thomas, A methodology for linking customer acquisition to customer retention. J. Marketing Research38 (2001) 262–268.  
  24. B. Vatanasombut, A.C. Stylianou and M. Igbaria, How to retain online customers. Communication of the ACM47 (2004) 65–78.  
  25. R. Venkatesan and V. Kumar, A customer lifetime value framework for customer selection and optimal resource allocation strategy. J. Marketing68 (2004) 106–125.  
  26. R. Weinstock, Calculus of Variations. Dover Punlications, Inc., NY (1974).  
  27. V.A. Zeithaml, 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.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.