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/
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