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.
Mots clés : ODE nonlinear boundary value problems, ODE applications, ODE growth, boundedness, comparison of solutions, ODE asymptotic expansions, optimal control, numerical methods ODE boundary value problems
@article{M2AN_2009__43_1_119_0,
author = {Ditkowski, Adi},
title = {Mathematical analysis of the optimizing acquisition and retention over time problem},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {119--137},
publisher = {EDP-Sciences},
volume = {43},
number = {1},
year = {2009},
doi = {10.1051/m2an:2008043},
mrnumber = {2494796},
zbl = {1156.91432},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2008043/}
}
TY - JOUR AU - Ditkowski, Adi TI - Mathematical analysis of the optimizing acquisition and retention over time problem JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 119 EP - 137 VL - 43 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008043/ DO - 10.1051/m2an:2008043 LA - en ID - M2AN_2009__43_1_119_0 ER -
%0 Journal Article %A Ditkowski, Adi %T Mathematical analysis of the optimizing acquisition and retention over time problem %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 119-137 %V 43 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008043/ %R 10.1051/m2an:2008043 %G en %F M2AN_2009__43_1_119_0
Ditkowski, Adi. Mathematical analysis of the optimizing acquisition and retention over time problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 1, pp. 119-137. doi : 10.1051/m2an:2008043. http://www.numdam.org/articles/10.1051/m2an:2008043/
[1] , Abandon lifetime value theories and take care of customers now. Marketing 12 (2001) 18.
[2] and , Advanced mathematical methods for scientists and engineers, McGraw-Hill International Series in Pure and Applied Mathematics. McGraw-Hill, New York (1978). | MR | Zbl
[3] and , Managing marketing by the customer equity test. Harvard Business Rev. 74 (1996) 136-144.
[4] , and , Customer Equity: Building and Managing Relationships as Valuable Assets. Harvard Business School Press, Boston, MA, USA (2001).
[5] , , and , Mathematical analysis and optimization of infiltration processes. J. Scientific Computing 13 (1998) 303-321. | MR | Zbl
[6] , Numerical method for solving non-contiguous initial/final-value problems. J. Scientific Computing (to appear).
[7] , and , On the mathematical analysis and optimization of chemical vapor infiltration in materials science. ESAIM: M2AN 34 (2000) 337-351. | Numdam | MR | Zbl
[8] , and , Optimizing acquisition and retention over time. Marketing Lett. (submitted).
[9] and , Defensive marketing strategy by customer complaint management: A theoretical analysis. J. Marketing Research 24 (1987) 337-346.
[10] and , Customers as assets. J. Interactive Marketing 17 (2003) 9-24.
[11] , and , Valuing customers. J. Marketing Research 41 (2004) 7-18.
[12] , 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] , and , Customer equity management: Charting new directions for the future of marketing. J. Service Research 5 (2002) 4-12.
[14] and , Customer lifetime value research in marketing: A review and future directions. J. Interactive Marketing 16 (2002) 34-46.
[15] and , Dynamic Optimization. Second edition, New York: North Holland (1991). | MR | Zbl
[16] , CRM meets Wall Street. Target Marketing 26 (2003) 50-54.
[17] , Numerical Methods for Conservation Laws, Lectures in Mathematics ETH Zürich. Second edition, Birkhäuser Verlag (1992). | MR | Zbl
[18] , , and , Numerical Recipes in C, The Art of Scientific Computing. Second edition, Cambridge University Press (1992). | MR | Zbl
[19] and , 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.
[20] , and , Balancing acquisition and retention resources to maximize customer profitability. J. Marketing 69 (2005) 63-79.
[21] , and , Return on marketing: Using customer equity to focus marketing strategy. J. Marketing 68 (2004) 109-127.
[22] and , How to measure the profitability of your customers. Harvard Business Rev. (2003) 74-81.
[23] , A methodology for linking customer acquisition to customer retention. J. Marketing Research 38 (2001) 262-268.
[24] , and , How to retain online customers. Communication of the ACM 47 (2004) 65-78.
[25] and , A customer lifetime value framework for customer selection and optimal resource allocation strategy. J. Marketing 68 (2004) 106-125.
[26] , Calculus of Variations. Dover Punlications, Inc., NY (1974). | MR | Zbl
[27] , 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.
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