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Mathematical analysis of the optimizing acquisition and retention over time problem

Published online by Cambridge University Press:  14 November 2008

Adi Ditkowski
Adi Ditkowski*
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel. adid@post.tau.ac.il
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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.


Keywords

ODE nonlinear boundary value problems; ODE applications; ODE growthboundednesscomparison of solutions; ODE asymptotic expansions; optimal control; numerical methods ODE boundary value problems.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 1 , January 2009 , pp. 119 - 137
Copyright
© EDP Sciences, SMAI, 2008

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