# Mathematical analysis of the optimizing acquisition and retention over time problem

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

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## Abstract

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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

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Ditkowski, Adi. "Mathematical analysis of the optimizing acquisition and retention over time problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 43.1 (2009): 119-137. <http://eudml.org/doc/245193>.

@article{Ditkowski2009,
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.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
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},
language = {eng},
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/245193},
volume = {43},
year = {2009},
}

TY - JOUR
TI - Mathematical analysis of the optimizing acquisition and retention over time problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2009
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
UR - http://eudml.org/doc/245193
ER -

## References

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