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Mathematical analysis of the optimizing acquisitionand 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 regardinginvestments in customer retention and acquisition becomes apressing managerial issue, formal models and analysis, which mayprovide insight into this topic, are still scarce. In this studywe examine two dynamic models for optimal acquisition andretention models of a monopoly, the total cost and the cost percustomer 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 innovativenumerical method was developed for solving ODE systems withinitial/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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