On the product line selection problem under attraction choice models of consumer behavior

Product line design (PLD) involves important decisions at the interface of operations and marketing that are very costly to implement and change, and, simultaneously, determinant for market success. To evaluate the financial performance of a product line, a number of mathematical programming approaches have been proposed. Problem formulations are typically mixed or pure integer non-linear optimization models that are intractable for exact solution - in particular when empirically supported consumer choice models are incorporated.     

Evaluation of choice set generation algorithms for route choice models

This paper discusses choice set generation and route choice model estimation for large-scale urban networks. Evaluating the effectiveness of Advanced Traveler Information Systems (ATIS) requires accurate models of how drivers choose routes based on their awareness of the roadway network and their perceptions of travel time. Many of the route choice models presented in the literature pay little attention to empirical estimation and validation procedures. In this paper, a route choice data set collected in Boston is described and the ability of several different route generation algorithms to produce paths similar to those observed in the survey is analyzed. The paper also presents estimation results of some route choice models recently developed using the data set collected.     

Stochastic models of consumer behaviour

During the past thirty years much research has been carried out in order to produce decision aids for managers. Considerable efforts have been dedicated to models that describe how consumers make purchase decisions. Within this vast area of research we review stochastic approaches to consumer behaviour, i.e. probabilistic laws relating the observed strings of consecutive purchases to explanator variables. We start out by discussing the basic concepts underlying this field. Then we deal with models concentrating on brand choice, whereby we trace the development from the early ideas in the Fifties to today's sophisticated models. Subsequently we turn to the Negative Binomial Distribution, the ‘classical’ purchase incidence model, and its extensions. Then we describe combined purchase timing-brand selection models and introduce models of store choice and purchase quantity selection. After briefing on estimation and validation methods for stochastic models we finally critically review the state-of-the-art in this field. Special emphasis is placed on empirical applications throughout the review.     

Structural models in consumer credit

We propose a structural credit risk model for consumer lending using option theory and the concept of the value of the consumer’s reputation. Using Brazilian empirical data and a credit bureau score as proxy for creditworthiness we compare a number of alternative models before suggesting one that leads to a simple analytical solution for the probability of default. We apply the proposed model to portfolios of consumer loans introducing a factor to account for the mean influence of systemic economic factors on individuals. This results in a hybrid structural-reduced-form model. And comparisons are made with the Basel II approach. Our conclusions partially support that approach for modelling the credit risk of portfolios of retail credit.     

Forecasting accuracy of behavioural models for participation in the arts

This paper assesses the forecasting performance of count data models applied to arts attendance. We estimate participation models for two artistic activities that differ in their degree of popularity – museums and jazz concerts – with data derived from the 2002 release of the Survey of Public Participation in the Arts for the United States. We estimate a finite mixture model – a zero-inflated negative binomial model – that allows us to distinguish between “true” non-attendants and “goers” and their respective behaviour regarding participation in the arts. We evaluate the predictive (in-sample) and forecasting (out-of-sample) accuracy of the estimated model using bootstrapping techniques to compute the Brier score. Overall, the results indicate the model performs well in terms of forecasting. Finally, we draw certain policy implications from the model’s forecasting capacity, thereby allowing the identification of target populations.     

Mathematical programming models for revenue management under customer choice

We study a network airline revenue management problem with discrete customer choice behavior. We discuss a choice model based on the concept of preference orders, in which customers can be grouped according to a list of options in decreasing order of preference. If a customer’s preferred option is not available, the customer moves to the next choice on the list with some probability. If that option is not available, the customer moves to the third choice on the list with some probability, and so forth until either the customer has no other choice but to leave or his/her request is accepted. Using this choice model as an input, we propose some mathematical programs to determine seat allocations. We also propose a post-optimization heuristic to refine the allocation suggested by the optimization model. Simulation results are presented to illustrate the effectiveness of our method, including comparisons with other models.     

The optimal resource portfolio under consumer choice and demand risk for vertically differentiated products

We study the optimal resource portfolio of a firm that sells two vertically differentiated products and utilizes resource flexibility and responsive pricing. We model this decision problem as a two-stage stochastic programming problem with recourse: In the first stage, the firm determines its resource mix and capacities so as to maximize the expected profit under demand uncertainty; in the second stage, uncertainty is resolved and the firm determines its production and pricing decision, constrained by its investment decision. We show that the objective function of this decision problem is not well-behaved (ie, it may have multiple local maxima). Using the concept of Pareto dominance, we reduce the feasible investment region, without loss of optimality, to one in which the objective function is well-behaved everywhere. This reduction allows us to derive the necessary and sufficient conditions for the optimal capacity decision and to gain insights.     

Mixture models for ordinal responses to account for uncertainty of choice

In CUB models the uncertainty of choice is explicitly modelled as a Combination of discrete Uniform and shifted Binomial random variables. The basic concept to model the response as a mixture of a deliberate choice of a response category and an uncertainty component that is represented by a uniform distribution on the response categories is extended to a much wider class of models. The deliberate choice can in particular be determined by classical ordinal response models as the cumulative and adjacent categories model. Then one obtains the traditional and flexible models as special cases when the uncertainty component is irrelevant. It is shown that the effect of explanatory variables is underestimated if the uncertainty component is neglected in a cumulative type mixture model. Visualization tools for the effects of variables are proposed and the modelling strategies are evaluated by use of real data sets. It is demonstrated that the extended class of models frequently yields better fit than classical ordinal response models without an uncertainty component.     

Permanence of general stage-structured consumer–resource models

Much of the existing stage-structured consumer–resource models ignore the permanence. In this paper, we consider the permanence for a series of staged-structured consumer–resource models with the function response of so-called “prey-dependence”(resource-dependence) type. We show that the systems are permanent, if and only if the adult consumer's recruitment rate at the peak of resource abundance is more than its death rate. Our results indicate that the large consumer's maturation time delay will directly lead to its extinction. Furthermore, our arguments for the main results give a light for permanence in the general stage-structured consumer–resource systems.     

Time will tell: behavioural scoring and the dynamics of consumer credit assessment

This paper discusses the use of dynamic modelling in consumercredit risk assessment. It surveys the approaches and objectivesof behavioural scoring, customer scoring and profit scoring.It then investigates how Markov chain stochastic processes canbe used to model the dynamics of the delinquency status andbehavioural scores of consumers. It discusses the use of segmentation,mover–stayer models and the use of second- and third-ordermodels to improve the fit of such models. The alternative survivalanalysis proportional hazards approach to estimating when defaultoccurs is considered. Comparisons are made between the wayscredit risk is modelled in consumer lending and corporate lending.     

Mathematical-economic models of regional production planning of consumer commodities

Presented at the seminar of the Department of Economic Cybernetics, February 4, 1983.     

Determining the effects of observed and unobserved heterogeneity on consumer brand choice

This paper investigates the effects of heterogeneity in consumer choice behaviour. Omitted consumer heterogeneity may lead to badly biased results, and wrong inferences concerning marketing strategies to follow. In this research we study the extent and the cause of this bias. We distinguish between observed and unobserved heterogeneity, by partialing out the effects of unmeasured heterogeneity and modelling it explicitly. The following questions will be addressed: What is unobserved heterogeneity and how much of it can be explained? How should heterogeneity be incorporated in consumer choice models? A hazard model is used for the analysis. The hazard model will yield patterns of switching among brands, as well as, the effect of marketing mix variables on brand choice and purchase timing. Differences between switchers and repeat purchasers are studied and the extent to which brand choice can be explained. Our model is estimated using scanner panel data. We find that it is important to include both observed and unobserved heterogeneity in order to obtain a better fit of the model. Our results show that it may be sufficient to only include observed heterogeneity to obtain unbiased parameter estimates. Including observed heterogeneity also reduces the aggregation or heterogeneity bias in the hazard function. © 1998 John Wiley & Sons, Ltd.     

The role of processing-by-attribute noncompensatory choice models

Research work on modeling consumer multiple choice problems using logit, regression, and probit is gaining more attention. However, in their work, Russ (1971), Tversky (1972), Newell and Simon (1972), Tversky and Sattath (1979), and Gensch and Svestka (1979; 1984) indicate that for many problems, choice behavior appears to be context dependent and hierarchical. With this specific issue in mind, this paper discusses a mathematical model which estimates threshold tolerances, eliminates nonchosen alternatives, provides choice probabilities and finally offers diagnostic information regarding the key attributes that are responsible for making a final decision. The use of other individual specific models such as: lexicographic, conjunctive, etc., have been briefly explicated.     

Some selection criteria for nested binary choice models: a comparative study

This paper deals with the problem of choosing the optimum criterion to select the best of a set of nested binary choice models. Special attention is given to the procedures which are derived in a decision-theoretic framework, called model selection criteria (MSC). We propose a new criterion, which we call C ₂, whose theoretical behaviour is compared with that of the AIC and SBIC criteria. The result of the theoretical study shows that the SBIC is the best criterion whatever the situation we consider, while the AIC and C ₂ are only adequate in some cases. The Monte Carlo experiment that is carried out corroborates the theoretical results and adds others: finite sample behaviour and robustness to changes in some aspects of the data generating process. The classical hypothesis testing procedures LR and LM are included and compared with the three criteria of the MSC category. The authors wish to thank the financial support provided by the Spanish Department of Education under project BEC 2003-01757.     

Approximation algorithms for the transportation problem with market choice and related models

Given facilities with capacities and clients with penalties and demands, the transportation problem with market choice consists in finding the minimum-cost way to partition the clients into unserved clients, paying the penalties, and into served clients, paying the transportation cost to serve them.     

On substitutability and complementarity in discrete choice models

In this paper, we propose the concepts of substitutability and complementarity in discrete choice models. These concepts concern whether the choice probability of one alternative in a choice model increases or decreases with the utility of another alternative, and they play important roles in capturing certain practical choice patterns, such as the halo effect. We study conditions on discrete choice models that will lead to substitutability and complementarity. We also present ways of constructing choice models that exhibit complementary property.     

Approximations of choice probabilities in mixed logit models

This paper is concerned with the approximate computation of choice probabilities in mixed logit models. The relevant approximations are based on the Taylor expansion of the classical logit function and on the high order moments of the random coefficients. The approximate choice probabilities and their derivatives are used in conjunction with log likelihood maximization for parameter estimation. The resulting method avoids the assumption of an apriori distribution for the random tastes. Moreover experiments with simulation data show that it compares well with the simulation based methods in terms of computational cost.