Markov Chain Model

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MODELING CUSTOMER RELATIONSHIPS
AS MARKOV CHAINS
Phillip E. Pfeifer
Robert L. Carraway
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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 strategic competitive advantage.

Dwyer (1989) helped to popularize the lifetime value (LTV)
concept by illustrating the calculation of LTV for both a customer retention and a customer migration situation. Customer retention refers to situations in which customers who are not retained are considered lost for good. In a customer retention situation, nonresponse signals the end of the firm’s relationship with the customer. In contrast, customer migration situations are those in which nonresponse does not necessarily signal the end of the relationship. Besides articulating this distinction between customer retention and migration, Dwyer listed several impediments to the use of LTV.

More recently, Berger and Nasr (1998) argue for the impor© 2000 John Wiley & Sons, Inc. and Direct Marketing Educational Foundation, Inc.
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JOURNAL OF INTERACTIVE MARKETING
VOLUME 14 / NUMBER 2 / SPRING 2000

43

PHILLIP E. PFEIFER AND
ROBERT L. CARRAWAY are with
the Darden School of Business,
Charlottesville, Virginia.

JOURNAL OF INTERACTIVE MARKETING

between an individual customer and a marketing firm.
In addition to its flexibility, the MCM offers
other advantages. Because it is a probabilistic
model, it explicitly accounts for the uncertainty
surrounding customer relationships. It uses the
language of probability and expected value—
language that allows one to talk about the firm’s
future relationship with an individual customer.
As direct marketers move toward true one-toone marketing, we suggest that their language will also change. Rather than talking about
groups or cohorts of customers, direct marketers will talk about Jane Doe. Rather than talking about retention rates, they will talk about the
probability Jane Doe will be retained. Rather
than talking about average profits from a segment
of customers, they will talk about the expected
profit from their relationship with Jane Doe.
Because the MCM incorporates this language of
probability and expected value, it is ideally
suited for facilitating true one-to-one marketing.
Another advantage of the MCM is that it is
supported by a well-developed theory about
how these models can be used for decision making (see, e.g., Puterman, 1994). We will introduce the theory surrounding Markov decision processes, and illustrate how this theory can
help direct marketers manage and optimize
their relationships with individual customers.
The MCM also works quite nicely with the
popular Recency, Frequency, Monetary value
(RFM) framework (see, e.g., David Shepard Associates, Inc., 1995), which direct marketers use to categorize customers and manage customer
relationships. We will illustrate the relationship
between the MCM and the RFM framework.
This paper is organized as follows. After this
introduction, we present the fundamentals of
the MCM. The section following that will illustrate the use of the MCM for a variety of customer relationship assumptions. For these illustrations, we will choose customer situations similar to those addressed previously in the literature. A final section will illustrate the use of MCM and Markov decision processes to help a

firm optimize a customer relationship. For this
illustration, we look at a catalog company...
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