| Issue |
ESAIM: M2AN
Volume 43, Number 1, January-February 2009
|
|
|---|---|---|
| Page(s) | 119 - 137 | |
| DOI | https://doi.org/10.1051/m2an:2008043 | |
| Published online | 14 November 2008 | |
Mathematical analysis of the optimizing acquisition and retention over time problem
School of Mathematical Sciences,
Tel Aviv University, Tel Aviv 69978, Israel. adid@post.tau.ac.il
Received:
21
December
2007
Revised:
3
July
2008
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.
Mathematics Subject Classification: 34B15 / 34B60 / 34B93 / 34C11 / 34E05 / 49N05 / 65L10
Key words: ODE nonlinear boundary value problems; ODE applications; ODE growth / boundedness / comparison of solutions; ODE asymptotic expansions; optimal control; numerical methods ODE boundary value problems.
© EDP Sciences, SMAI, 2008
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.