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

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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 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

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