Geodesic
Mathematical analysis of the optimizing acquisition and retention over time problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 1, pp. 119-137

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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.

DOI : 10.1051/m2an:2008043
Classification : 34B15, 34B60, 34B93, 34C11, 34E05, 49N05, 65L10
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 
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     author = {Ditkowski, Adi},
     title = {Mathematical analysis of the optimizing acquisition and retention over time problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {119--137},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {1},
     year = {2009},
     doi = {10.1051/m2an:2008043},
     mrnumber = {2494796},
     zbl = {1156.91432},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008043/}
}
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Ditkowski, Adi. Mathematical analysis of the optimizing acquisition and retention over time problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 1, pp. 119-137. doi: 10.1051/m2an:2008043

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