Robert L. Carraway

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-

Generalized dynamic programming for multicriteria optimization

Abstract Applications of dynamic programming (DP) to multicriteria sequential decision problems involving the optimization of a multicriteria preference function have been rare. This is due to the ease with which DPs monotonicity assumption can be violated in such situations. Generalized DP avoids the potential pitfalls created by this absence of monotonicity, thereby guaranteeing optimality. The methodology is applied to a prototypical multicriteria DP problem, namely a multicriteria version of the shortest path problem.

Generalized Dynamic Programming for Stochastic Combinatorial Optimization

In stochastic versions of combinatorial optimization problems, the objective is to maximize or minimize a function of random variables. For many problems of this type, conventionally applied dynamic programming DP may fail to generate an optimal solution due to the potential violation of the monotonicity assumption of DP. We develop a generalization of DP that guarantees optimality even in the absence of monotonicity. We illustrate the methodology on a version of the stochastic traveling salesman problem for which a previously proposed DP algorithm E. Kao is potentially suboptimal due to the violation of monotonicity M. Sniedovich. Using Generalized DP, we are able to modify the algorithm to guarantee optimality.

Dominance and decomposition heuristics for single machine scheduling

New heuristic dominance rules and a flexible decomposition heuristic are developed for the problem of minimizing weighted tardiness on a single processor. Extensive computational experience demonstrates that, when our new heuristic dominance rules were incorporated into an optimal algorithm, optimal or nearly optimal solutions were obtained quickly. In fact, solution times were orders of magnitude faster than those using the optimal algorithm alone. On larger problems, our decomposition heuristic obtained better solutions than previous heuristics. Furthermore, on 50-job problems our decomposition heuristic obtained an optimal solution over ten times more often on the average than the best competing heuristic (22% versus 2% of the time). Since both our approaches are basically relaxations of optimal solution algorithms, they could easily be adapted for use in the solution of other scheduling problems.

Multiobjective, preference-based search in acyclic OR-graphs☆

We consider the problem of determining a most preferred path from a start node to a goal node set in an acyclic OR-graph, given a multiattribute preference function, a multiobjective reward structure, and heuristic information about this reward structure. We present an algorithm which is shown to terminate with a most preferred path, given an admissible heuristic set. The algorithm illustrates how Artificial Intelligence techniques can be productively employed to solve multiobjective problems.

Single machine sequencing with nonlinear multicriteria cost functions: an application of generalized dynamic programming

Scope and P lupose--A task frequently encounter in operations management is the ~h~uling of tasks or jobs where the attractiveness of the schedule is evaluated relative to multiple performance measures. If there exists a linear multicriteria cost (or penalty) function of these performance measures, then dynamic programming (DP) may be used to find an optimal schedule. However, in the more general case of a nonlinear multicriteria cost function, conventional DP may fail to produce an optimal schedule due to the potential violation of monotonicity. Furthermore, the alternative of first generating the entire efficient set (over which the multicriteria cost function can subsequently be minimized) often requires a prohibitive computational effort. We present an alternative generalized DP approach to this class of problems that guarantees optimaIity, notwithstanding the nonlinearity of the cost function. An example demonstrates that our approach can represent a significant computational improvement over first generating the entire efficient set, and is only slightly more expensive computationally than applying conventional DP, which in this case is only a heuristic.

Buckeye Power & Light Company

This case describes the coal-procurement process of a small electric utility. The manager of the production-fuel department must decide how much coal to purchase from each vendor and how to allocate the purchased coal among the utilitys three coal-burning plants. The situation can be modeled and solved as a linear program. Sensitivity analysis can be used to help formulate a strategy for negotiating with the vendors and to address other special issues.