Abstract
It is very important for a company to determine spending for acquisition and retention of customers which affect the Customer lifetime value of the company. In this paper, we formulate the Customer lifetime value model as an optimal control problem. The obtained problem is to find an acquisition policy which maximizes the present value of all future profits generated from a customer. Here the state variable is the average margin for each customer about how much each customer contributes to the company and the control variable is the cost of acquisition. We use the maximum principle for optimality to solve the problem, estimate some parameters of the problem using statistical data for Mobile service sector of Mongolia and calculate the optimal Customer lifetime values of the sector for some values of parameters.
Highlights
IntroductionA number of applications of optimal control theory have been made to the field of marketing
Over the years, a number of applications of optimal control theory have been made to the field of marketing
The obtained problem is to find an acquisition policy which maximizes the present value of all future profits generated from a customer
Summary
A number of applications of optimal control theory have been made to the field of marketing Many of these applications deal with the problem of finding or characterizing an optimal advertising price over time (Singh & Jain, 2013). While some companies followed this basic economic principle, others apparently did not (Nerlove & Arrow, 1962). It is very important for a company to determine spending for acquisition and retention of customers. In order to find an optimal acquisition cost, we formulated the Customer lifetime value model as an optimal control problem.
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