Mathematical analysis of the optimizing acquisition and retention over time problem

Adi Ditkowski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)119-137
Number of pages19
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number1
StatePublished - Jan 2009


  • Boundedness
  • Comparison of solutions
  • Numerical methods ODE boundary value problems
  • ODE applications
  • ODE asymptotic expansions
  • ODE growth
  • ODE nonlinear boundary value problems
  • Optimal control


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