Phillip E. Pfeifer

MODELING CUSTOMER RELATIONSHIPS AS MARKOV CHAINS

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-

A Three-Stage Iterative Procedure for Space-Time Modeling

A three-stage iterative procedure for building space-time models is presented. These models fall into the general class of STARIMA models and are characterized by autoregressive and moving average terms lagged in both time and space. This model class collapses into the ARIMA model class in the absence of spatial correlation. The theoretical properties of STARIMA models are presented and the model building procedure is described and illustrated by a substantive example.

A Three-Stage Iterative Procedure for Space-Time Modeling Phillip

A three-stage iterative procedure for building space-time models is presented. These models fall into the general class of STARIMA models and are characterized by autoregressive and moving average terms lagged in both time and space. This model class collapses into the ARIMA model class in the absence of spatial correlation. The theoretical properties of STARIMA models are presented and the model building procedure is described and illustrated by a substantive example.

Identification and Interpretation of First Order Space-Time ARMA Models

The effect of system size and shape on the theoretical space-time autocorrelation function is described for first order STARMA models. Figures and tables are presented to assist in identification considerations which include model interpretation, patterns of the theoretical spacetime autocorrelation and partial autocorrelation functions, and initial estimation for the STAR(11) and STMA(11) models.

Modeling the Customer Arrival Process and Comparing Decision Rules in Perishable Asset Revenue Management Situations

A model for customer arrivals is presented that allows evaluation of different decision rules in perishable asset revenue management (PARM) situations. The model is used to derive probabilities necessary to operationalize the implementation of an optimal decision rule for PARM problems with diversion and two price classes. Heuristic approaches are compared to the proper closing out of price classes to see how much of an improvement can be made in expected contribution. The sensitivity of the difference in expected contribution between these rules is tested relative to changes in the models input parameters. Managerial insights are presented.

Economic Selection of the Mean and Upper Limit for a Canning Problem with Limited Capacity

We consider the economic selection of both the process mean and the upper control limit in a two-level process-control scheme for a capacitated (bottleneck) production process. A closed-form expression for the optimal upper control limit is developed, a..

The economic value of using advance booking of orders

The advance booking of orders (ABO) is the practice of selling units of an item (either products or services) in advance of the actual availability of the item. We consider the question of whether or not advance bookings should be offered. Closed-form analytical results are derived for the expected profits for the classic single-period inventory (newsboy) problem both with and without advance bookings. These two profit expressions allow us to quantify the benefits of ABO. The benefits include both the yield-management benefits associated with the stimulation of demand and the planning and control benefits of using advance booking as a leading indicator of total demand.

Space-Time ARMA Modeling With Contemporaneously Correlated Innovations

A comprehensive model-building procedure is presented for the building of space-time ARMA models. This procedure explicitly considers the possibility that G, the covariance matrix of the innovations, might not be spherical (G = σ2 I). The cases of diagonal G, wherein the innovations are independent between sites but are allowed to have unequal variances, and genera1 G, wherein the innovations may in fact be contemporaneously correlated, are examined. Model identification, estimation, and diagnostic checking are described, and tests of the assumptions concerning the form of G are incorporated into the modeling procedure. The procedure is illustrated through two substantive examples.

An Economic Evaluation of Improvements in Process Capability for a Single-Level Canning Problem

Recent developments in quality improvement have emphasized variance reduction and created a need for methods to analyze the cost benefits that result from investments in increased conformance. In this paper we analyze the cost savings that result from a..

A General Piecewise Linear Canning Problem Model

This paper presents a general canning problem model consisting of a piecewise linear profit function with two breakpoints. The model is flexible enough to include several previous models as special cases. In addition, the model covers situations heretof..