Single Ideal Point Research Articles

A decentralized coordination algorithm for multi-objective linear programming with block angular structure

ABSTRACT This article considers linear multi-objective programming problems with block angular structure, which are analogous to multi-disciplinary optimization environments where disciplines must collaborate to achieve a common overall goal. In this decentralized environment, a mechanism to guide locally optimized decision makers’ solutions to a Pareto-optimal solution without sharing the entire local information is developed. The mechanism is based on an augmented Lagrangian approach to generate a solution and is separated into two phases: phase I determines an ideal point for each of the single objectives and phase II searches for a compromise solution starting from a single ideal point. Theoretical results show that the algorithm converges and the solution generated is Pareto optimal. The algorithm’s effectiveness is demonstrated via an illustrative example and a real-world bi-objective re-entrant flow-shop production planning problem. The real-world experimental results showed that the decentralized method had an average 50% better performance compared to other centralized methods.

Evaluating Change in Behavioral Preferences

The purpose of the article is to propose a multidimensional scaling single-ideal point model as a method to evaluate changes in individuals’ preferences under the explicit methodological framework of behavioral preference assessment. One example is used to illustrate the approach for a clear idea of what this approach can accomplish.

Evolutionary models in cash management policies with multiple assets

This work aimed to apply genetic algorithms (GA) and particle swarm optimization (PSO) in cash balance management using multiple asset investments. This problem consists of a stochastic model that does not define a single ideal point for cash balance, but an oscillation range between a lower bound, an ideal balance and an upper bound. Thus, this paper proposes the application of GA and PSO to minimize the total cost of cash maintenance, by obtaining the parameters of a cash management policy with three assets (cash and two investments), and using the assumptions presented in literature. Computational experiments were applied in the development and validation of the models. The results indicated that both the GA and PSO are applicable in determining the cash management policy, but with better results for the PSO model.

Multidimensional Perceptual Unfolding of Coping Behaviors: A Developmental Perspective on Preference Assessment

ABSTRACT The purpose of the current study was to study grade level and gender differences in coping behaviors among Chinese students using a multidimensional scaling (MDS) single-ideal point model. In contrast to approaches that utilize the aggregated scores such as average scores, the MDS single-ideal point model makes use of individual items in a well-constructed coping instrument to examine typical coping behaviors preferred by adolescents of different grade levels and gender. The results revealed that college students developed a set of more specific coping responses than the middle school students. Moreover, college male students used more coping responses than the college female students. The article discusses the processes and issues in analyzing developmental differences via MDS single-ideal point models from the developmental perspective.

Cash balance management: A comparison between genetic algorithms and particle swarm optimization

This work aimed to apply genetic algorithms (GA) and particle swarm optimization (PSO) in cash balance management using Miller-Orr model, which consists in a stochastic model that does not define a single ideal point for cash balance, but an oscillation range between a lower bound, an ideal balance and an upper bound. Thus, this paper proposes the application of GA and PSO to minimize the Total Cost of cash maintenance, obtaining the parameter of the lower bound of the Miller-Orr model, using for this the assumptions presented in literature. Computational experiments were applied in the development and validation of the models. The results indicated that both the GA and PSO are applicable in determining the cash level from the lower limit, with best results of PSO model, which had not yet been applied in this type of problem.

A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem

This paper focuses on a multiobjective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto-optimal solutions of a multiobjective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that a node in the search tree can be discarded if one can define a separating hypersurface in the objective space between the set of feasible solutions in the subtree and the set of points corresponding to potential Pareto-optimal solutions. Numerical experiments on the biobjective spanning tree problem are provided that show the efficiency of the approach in a biobjective setting.

Estimating Multiple Consumer Segment Ideal Points from Context-Dependent Survey Data

Previous research in marketing and consumer research has shown that consumers/households often possess multiple ideal points in a given product/service category. In such cases, traditional segmentation and positioning models that estimate a single ideal point per individual/segment may render an inaccurate portrayal of the true underlying utility functions of such consumers/segments and the resulting market structure. We propose a new clusterwise multiple-ideal-point spatial methodology that estimates multiple ideal points at the market segment level while simultaneously determining the market segments' composition of consumers, as well as the corresponding joint space.

A Multiple Ideal Point Model: Capturing Multiple Preference Effects from within an Ideal Point Framework

Previous research has suggested that households and individuals may possess multiple preferences for a given product category. These multiple preferences may be the result of multiple individuals in a household, different uses and usage occasions, and/or variety seeking. As such, single ideal point models that assume a single invariant ideal point may be operating from a false and misleading assumption. We propose a multiple ideal point model to capture these multiple preference effects. The basic premise of the model is that consumers may possess a set of ideal points, each of which represents a distinct preference. At any given purchase occasion, one of these points is “activated” with some probability, and choices are made with respect to its characteristics. In this article, the authors assess the multiple ideal point model and an associated estimation procedure with respect to the model's ability to recover a true choice structure. The authors then empirically test the model on Information Resources Inc. panel data from the powdered soft drink category. The authors discuss the results and introduce directions for further research.

A Multiple Ideal Point Model: Capturing Multiple Preference Effects From Within an Ideal Point Framework

Previous research has suggested that households and individuals may possess multiple preferences for a given product category. These multiple preferences may be the result of multiple individuals, different uses and usage occasions, and/or variety seeking. As such, single ideal point models that assume a single invariant ideal point may be operating from a false and misleading assumption. We propose a Multiple Ideal Point Model to capture these multiple preference effects. The basic premise of the model is that consumers may possess a set of ideal points, each of which represents a distinct preference. At any given purchase occasion, one of these points is activated with some probability and choices are made with respect to its characteristics. In this paper, the Multiple Ideal Point Model and an associated estimation procedure are assessed with respect to its ability to recover a true choice structure. We then empirically test the model on IRI panel data from the powdered soft drink category. The results are discussed and directions for future research are introduced.

Spatial extrapolation of agrometeorological variables

Agrometeorological variables are especially subject to variations in space – a fact that makes calculations of areal mean values for e.g. evaporation extremely elusive. Wind, temperature, and humidity cannot be measured continuously in space. In this paper we present simple methods to determine values of those variables for non-ideal positions from measurements at a single ideal point and test these spatial functions by measurements at three non-ideal points in a catchment. For wind, we were able to obtain a relatively good fit by taking the sheltering effects of the catchment rims into account. Temperature was not regionalizable with simple approaches, but needs to be regionalized with spatially and temporally differentiated models. Specific humidity can be assumed to be homogeneously distributed even though there were sinks and sources for water vapor in the study area.

A Single Ideal Point Model for Market Structure Analysis

A Single Ideal Point Model for Market Structure Analysis

A Single Ideal Point Model for Market Structure Analysis

Computing unsegmented product maps from preference data by means of single ideal point models is commonly thought to be impossible because of indeterminacy problems. The authors show that this mathematical indeterminacy can be overcome by incorporating dependent sampling assumptions into a probabilistic multidimensional scaling (MDS) model. As a result, product space maps can be estimated for single markets from preference data alone. If desired, dissimilarity data can be combined with preference data to produce jointly estimated product space maps. The authors illustrate the advantages of the proposed approach with real and simulated data. They also make comparisons to both internal and external deterministic models. The results are favorable.

A latent class unfolding model for analyzing single stimulus preference ratings

A multidimensional unfolding model is developed that assumes that the subjects can be clustered into a small number of homogeneous groups or classes. The subjects that belong to the same group are represented by a single ideal point. Since it is not known in advance to which group of class a subject belongs, a mixture distribution model is formulated that can be considered as a latent class model for continuous single stimulus preference ratings. A GEM algorithm is described for estimating the parameters in the model. The M-step of the algorithm is based on a majorization procedure for updating the estimates of the spatial model parameters. A strategy for selecting the appropriate number of classes and the appropriate number of dimensions is proposed and fully illustrated on some artificial data. The latent class unfolding model is applied to political science data concerning party preferences from members of the Dutch Parliament. Finally, some possible extensions of the model are discussed.

An Ideal-Point Probabilistic Choice Model for Heterogeneous Preferences

This paper presents a new ideal point probabilistic choice model. Unlike the model suggested by Cooper and Nakanishi (Cooper, L. G., M. Nakanishi. 1983. Two logit models for external analysis of preferences. Psychometrika 48 (4) 607–619.) which attempts to capture choices via a single ideal point, the proposed model, though based on aggregate data, allows for heterogeneity in preferences by estimating a distribution of ideal points. The model accounts for substitutability among choice alternatives and alleviates one of the major sources for the violation of the “Independence from Irrelevant Alternatives” property. It is demonstrated that the final form of the model is a Multinomial Probit, with a covariance matrix that depends on the relative position of the choice alternatives. An empirical application is provided and the resulting parameters are compared to the distributions of ideal points and attribute weights obtained via LINMAP (at the individual level) and via both the Logit and Probit versions of the model proposed by Cooper and Nakanishi (at the aggregate level).