Knowledge that Transforms

The multi-attribute utility model serves as a basis for many marketing decisions such as new product planning and advertising message selection. The estimation of individuals' attribute weights can be performed using several data types and estimation techniques. There is evidence to suggest that the estimates derived from ordinal preference data through linear programming show greater stability and predictive validity. In this paper we address two fundamental issues which have not been addressed in the context of this latter type estimation: the theoretical foundations for estimating cardinal utility functions from ordinal preference data and the properties of the linear programming estimators. First, we establish the theoretical foundations from economics, mathematical psychology, and decision analysis of obtaining a cardinal (interval scaled) multi-attribute function from ordinal data. This leads us to recommend that in addition to the collection of paired preference comparisons, also comparisons of pairs of pairs be collected. We then describe the type of errors which are likely to arise in the measurement stage, and their relationship to the phenomenon of intransitivities. We formulate a linear program, LINPAC, for the estimation of attribute weights from the above preference data. The previously proposed LINMAP procedure is a special case of this formulation when only the information on the paired preferences is utilized. Next, the statistical properties of the estimators, such as uniqueness, unbiasedness, consistency and efficiency, are examined. Then, through a simulation study we examine the rate of convergence of the estimated weights to the true weights as a function of the number of brands. In the simulation study we also examine the conditions under which the estimators outperform equal weights and compare the estimates derived from LINPAC with those derived from LINMAP. Finally, the estimation procedures are examined with actual data while the simulation results, an equal weights model, and a stated weights model serve as benchmarks.

A reappraisal of previously suggested strategies for betting on football games using results of the period 1975–1981 casts considerable doubt on the profitability of relying on the past history of games for guidance in placing bets.

Risk attitude and time preference are well-known and distinct concepts in the study of individuals' preferences for goods such as money. This paper reviews and explores the application of these concepts to the field of health. A mathematical model is presented, both in a general form and in an exponential form, which relates an individual's risk attitude in health to three effects—a quantity effect, a gambling effect and a time preference effect. It is shown that the overall risk attitude, as measured by its direction and magnitude, is merely the sum of the individual effects, as measured by their directions and magnitudes. Measurement methods are presented which can be used in a given situation to determine which effects are operating, in what directions and with what magnitudes. A new measurement procedure based on the temporary palliation of a chronic condition is described as a method of obtaining an individual's time preference pattern for health.

This note develops properties of quasi-efficient solutions and explores interrelationships to the classical concept of efficiency. In particular, a point is a quasi-efficient solution to a multiple objective mathematical program if and only if it is an optimal solution to a scalar maximum problem for some set of nonnegative weights on the objectives. This result is then used to characterize the set of quasi-efficient solutions as the union of efficient solutions to a multiple objective problem over all nonempty subsets of the objectives.

This paper presents several new concepts for portfolio problems with independently distributed asset prices. A criterion is developed for including or excluding assets in an optimal portfolio for an investor maximizing the expected value of a von Neumann–Morgenstern utility function. The central concept of the generalized harmonic mean is introduced: it is shown to be the analogue of the riskless rate of return for problems without a riskless asset. A new ordering theorem is proven, showing that an optimal portfolio always consists of positive amounts of the assets with the largest mean values. Next, the concept of independence from irrelevant alternatives is introduced for portfolio problems; this is a property of utility functions and is proven to be true for most of the commonly used utility functions. Altogether, the results provide new insights and tools for portfolio problems with independent assets and extend earlier results by Samuelson, and Fishburn and Porter.

A number of proposals have been put forth regarding the proper way to model the societal impact of fatal accidents. Most of these proposals are based on some form of utility function asserting that the social cost (or disutility) of N lives lost in a single accident is a function of N α . A common view is that a single large accident is more serious than many small accidents producing the same number of fatalities, hence α > 1. Drawing upon a number of empirical studies, we argue that there is insufficient justification for using any function of N fatalities to model societal impacts. The inadequacy of such models is attributed, in part, to the fact that accidents are signals of future trouble. The societal impact of an accident is determined to an important degree by what it signifies or portends. An accident that causes little direct harm may have immense consequences if it increases the judged probability and seriousness of future accidents. We propose that models based solely on functions of N be abandoned in favor of models that elaborate in detail the significant events and consequences likely to result from an accident.

In a companion paper we developed a unified scheme for using poststratified sampling and control variables to improve the efficiency of regenerative queueing simulations. We adapted these variance reduction techniques to the estimation methods of replication analysis and regenerative analysis by exploiting the asymptotic joint normality of certain standardized concomitant variables that are defined on each input process sampled during a queueing simulation. In this paper we present an experimental evaluation of the reductions in point-estimator variance and confidence-interval width that can be achieved with each procedure in several closed and mixed machine-repair systems. For the analytically tractable model, nominal and actual confidence-interval coverage probabilities are also compared. Poststratification generally produced variance reductions ranging from 10% to 40% and confidence-interval reductions between 1% and 20%. The control-variates schemes yielded variance reductions ranging from 20% to 90% and confidence-interval reductions between 10% and 70%. In some instances where small sample sizes were used, the poststratification schemes produced confidence-interval width increases between 1% and 10%. With a small number of regenerative cycles, some loss of confidence-interval coverage was observed with both post-stratified and controlled regenerative analysis. When larger sample sizes were used, all of the estimation schemes yielded fairly consistent efficiency gains.

How many patrol cars staffed with a single police officer are needed to provide equivalent police service to an existing system with n two-officer patrol cars? This question is explored for New York City using a multiple patrol car per call priority queueing model. It is shown that a one-officer patrol program is feasible, yet pitfalls exist which could adversely affect its performance. The paper details the process of data analysis and model building and emphasizes the subjective elements that remain in a highly technical OR study. Speed of response to emergency calls from the public was the key performance characteristic considered. The analysis also raised issues related to the safety of police officers in one-officer cars.

A recurring problem in managing project activity involves the allocation of scarce resources to the individual activities comprising the project Resource conflict resolution decisions must be made whenever the concurrent demand for resources by the competing activities of a project exceeds resource availability. When these resource conflict resolution decisions arise, project managers seek direction on which activities to schedule and which to delay in order that the resulting increase in project duration is the minimum that can be achieved with the given resource availabilities. The procedures examined in this paper are all designed to provide for this type of decision support. Each procedure examined is enumerative based, methodically searching the set of possible solutions in such a way that not all possibilities need be considered individually. The methods differ in the manner in which the tree representing partial schedules is generated and is saved, and differ in the methods which are used to identify and discard inferior partial schedules. Each procedure was found to be generally superior on a specific class of problems, and these classes are identified.

In this paper the theory and estimation procedures for several consumer preference models are discussed. Predictive accuracy in the form of internal consistency of these models is compared in an empirical application. Consumer decision situations are classified into two classes: decisions under certainty and decisions under uncertainty. For each of the two classes of decision situations two modeling strategies have been used: statistical estimation and algebraic solution. An additive conjoint, an additive and a multiplicative measurable value, and an additive and a multiplicative utility model are considered. Our main finding is that the statistical estimation procedures outperform their algebraic counterparts on the criterion of predictive accuracy. The utility model provides better predictions for decisions under uncertainty than the widely used conjoint models. The relationship between models for decisions under certainty and decisions under uncertainty is discussed. It is shown how a conjoint or a measurable value function model can be transformed into a utility model with minimum additional information from the subjects. A concept of relative risk attitude is proposed to segment consumers by the degree of their risk aversion or risk seeking propensities.