7679 Words31 Pages

MODELING CUSTOMER RELATIONSHIPS
AS MARKOV CHAINS
Phillip E. Pfeifer
Robert L. Carraway f INTRODUCTION
The lifetime value of a customer is an important and useful concept in interactive marketing. Courtheaux (1986) illustrates its usefulness for a number of managerial problems—the most obvious if not the most important being the budgeting of marketing expenditures for customer acquisition. It can also be used to help allocate spending across media (mail vs. telephone vs. television), vehicles (list A vs. list B), and programs (free gift vs. special price), as well as to inform decisions with respect to retaining existing customers (see, e.g., Hughes, 1997). Jackson
(1996) even argues that its use helps ﬁrms to achieve a*…show more content…*

They offer ﬁve such mathematical models, couched in the Dwyer customer retention/migration classiﬁcation scheme. While Dwyer illustrates the calculation of LTV using two extensive numerical examples, Berger and Nasr provide mathematical equations for LTV for ﬁve situations—four involving customer retention and one involving customer migration. Blattberg and Deighton (1996) also formulate a mathematical model for LTV, for the purpose of helping managers decide the optimal balance between customer acquisition spending (investments to convince prospects to become customers) and customer retention spending (investments to convince current customers to continue purchasing from the ﬁrm). Whereas the Berger and Nasr models apply only to customers (people or organizations who have already purchased from the ﬁrm), the Blattberg and Deighton model applies speciﬁcally to prospects (people or organizations who have yet to purchase from the ﬁrm). Because the Blattberg and Deighton model uses an inﬁnite horizon, their resulting equation for LTV is quite simple and easy to evaluate, and involves none of the summation operators on which the Berger and Nasr ﬁnite-horizon models rely. This paper builds directly on the work of Berger and Nasr (1998) and Blattberg and Deighton (1996) in that it introduces a general class of mathematical models, Markov Chain Models, which are appropriate for modeling customer relationships

They offer ﬁve such mathematical models, couched in the Dwyer customer retention/migration classiﬁcation scheme. While Dwyer illustrates the calculation of LTV using two extensive numerical examples, Berger and Nasr provide mathematical equations for LTV for ﬁve situations—four involving customer retention and one involving customer migration. Blattberg and Deighton (1996) also formulate a mathematical model for LTV, for the purpose of helping managers decide the optimal balance between customer acquisition spending (investments to convince prospects to become customers) and customer retention spending (investments to convince current customers to continue purchasing from the ﬁrm). Whereas the Berger and Nasr models apply only to customers (people or organizations who have already purchased from the ﬁrm), the Blattberg and Deighton model applies speciﬁcally to prospects (people or organizations who have yet to purchase from the ﬁrm). Because the Blattberg and Deighton model uses an inﬁnite horizon, their resulting equation for LTV is quite simple and easy to evaluate, and involves none of the summation operators on which the Berger and Nasr ﬁnite-horizon models rely. This paper builds directly on the work of Berger and Nasr (1998) and Blattberg and Deighton (1996) in that it introduces a general class of mathematical models, Markov Chain Models, which are appropriate for modeling customer relationships

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