Some results concerning the quality of vertex solutions found by a method for multiple-objective linear programming

The Zionts-Wallenius algorithm for multiple-objective linear programming terminates with an extreme point solution that is locally but not necessary globally optimal. To find the globally optimal solution, a search along the facets of the solution space polyhedron may be required. In this paper we report the results of an experiment to determine how close the local and global optima are. We discuss the concept of closeness and propose one measure. Computer simulation is used to determine, in general, the quality of the solution found by the Zionts-Wallenius method for two types of non-linear utility functions. The merits of a search procedure are discussed in the context of the results.     

The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability

In theory, the greatest lower bound (g.l.b.) to reliability is the best possible lower bound to the reliability based on single test administration. Yet the practical use of the g.l.b. has been severely hindered by sampling bias problems. It is well known that the g.l.b. based on small samples (even a sample of one thousand subjects is not generally enough) may severely overestimate the population value, and statistical treatment of the bias has been badly missing. The only results obtained so far are concerned with the asymptotic variance of the g.l.b. and of its numerator (the maximum possible error variance of a test), based on first order derivatives and the asumption of multivariate normality. The present paper extends these results by offering explicit expressions for the second order derivatives. This yields a closed form expression for the asymptotic bias of both the g.l.b. and its numerator, under the assumptions that the rank of the reduced covariance matrix is at or above the Ledermann bound, and that the nonnegativity constraints on the diagonal elements of the matrix of unique variances are inactive. It is also shown that, when the reduced rank is at its highest possible value (i.e., the number of variables minus one), the numerator of the g.l.b. is asymptotically unbiased, and the asymptotic bias of the g.l.b. is negative. The latter results are contrary to common belief, but apply only to cases where the number of variables is small. The asymptotic results are illustrated by numerical examples.This research was supported by grant DMI-9713878 from the National Science Foundation.     

Joint production model: A note on a connection between market prices and CP anchor values

This paper focuses on a justification of the assumption ‘In a joint production competitive industry, market prices are inversely proportional to anchor values’. This assumption is important to underpin the property ‘In a competitive industry the maximum profit mix and the best technological mix coincide’.     

Teaching help‐seeking when lost to individuals with autism spectrum disorder

Deficits in safety skills and communication deficits place individuals with autism spectrum disorder (ASD) at an increased risk of danger. We used a multiple‐probe across‐participants design to evaluate the effects of video modeling and programming common stimuli to teach low‐ and high‐tech help‐seeking responses to children with ASD when lost. Participants acquired answering or making a FaceTime^® call and exchanging an identification card in contrived and natural settings. Responses generalized to novel community settings and maintained during a one‐ and two‐week follow‐up. Social validity measures showed that the procedures and outcomes of the study were acceptable to indirect and direct consumers, and immediate and extended community members. Implications are that children with ASD can effectively be taught both low‐ and high‐tech help‐seeking responses when lost.     

A Recourse Stochastic Goal Programming Approach for the Multi‐objective Stochastic Vehicle Routing Problem

This paper addresses a multi‐objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic nature. In order to build a certainty equivalent program to the multi‐objective stochastic vehicle routing problem, we propose a solution strategy based on a recourse approach, a chance‐constrained approach and a goal‐programming approach. The resulting certainty equivalent program is solved to optimality using CPLEX. Copyright © 2016 John Wiley & Sons, Ltd.     

An interactive multiobjective programming approach to combinatorial data analysis

Combinatorial optimization problems in the social and behavioral sciences are frequently associated with a variety of alternative objective criteria. Multiobjective programming is an operations research methodology that enables the quantitative analyst to investigate tradeoffs among relevant objective criteria. In this paper, we describe an interactive procedure for multiobjective asymmetric unidimensional seriation problems. This procedure uses a dynamic-programming algorithm to partially generate the efficient set of sequences for small to medium-sized problems, and a multioperation heuristic to estimate the efficient set for larger problems. The interactive multiobjective procedure is applied to an empirical data set from the psychometric literature. We conclude with a discussion of other potential areas of application in combinatorial data analysis.Stephanie Stahl is a freelance writer and editor. She can be reached via e-mail at s-stahl@worldnet.att.net.     

A review of multiobjective programming and its application in quantitative psychology

Multiobjective programming, a technique for solving mathematical optimization problems with multiple conflicting objectives, has received increasing attention among researchers in various academic disciplines. A summary of multiobjective programming techniques and a review of their applications in quantitative psychology are provided.     

Reaction Time Analysis of Two Types of Motor Preparation for Speech Articulation: Action as a Sequence of Chunks

Reaction time (RT) prior to speech articulation increased as a function of response complexity. The RT findings formed 2 patterns, each of which was a different Response Complexity × Paradigm (choice RT vs. simple RT) interaction. That result extends previous findings from manual button-pressing tasks (S. T. Klapp, 1995) to a different action modality. Two different types of response programming, INT and SEQ, are assumed in the interpretation. Whereas INT can be identified with response programming within a word, SEQ fits a different interpretation related to timing of onsets of speech units. A critical assumption is that a long response is represented as a sequence of chunks; that organization is subject to manipulation. New findings suggest some modifications of the previous theory.     

Differential Method of Characterizing Gait Strategies From Step Lengths and Frequencies: Strategy of Velocity Modulation

The differential method consists of the analysis of the variation of gait parameters length, frequency, and velocity with respect to their mean values, respectively, ΔL = L — L_m , Δf = f — f_m , and Δv = v – v_m , where L_m , f_m , and v_m represent the mean values of those parameters. Assuming that the strategy of modulation of velocity implies that L and f are functions of v and that statistical analyses of ratios ΔL/Δv and Δf/Δv have established that there is a very significant linear correlation, close to 1, between those ratios, the mathematical procedure allows one to determine the equation of step length, L = a · f + b · v + K, where a and b are the slope and the intercept of the linear regression and K is close to L_m . The equation was experimentally tested on 140 gait sequences performed by 6 participants and for gait velocities ranging from 0.6 to 2.2 m/s and was found to be very representative of all individual values. The differential method provides another way of using the derivative of velocity, v = L·f, to characterize the strategy of velocity modulation, which then permits one to determine the linear equation of velocity, v = f · L_m + L · f_m — L_m · f_m , and to show that the respective parts played by each parameter in the progression velocity are approximately equal. The author establishes the uniqueness of the different linear adjustments and discusses the differential method's own modes of use, that is, interindividually or globally.     

Spiritual Need Four: Opportunities to Be Served and to Share with Others

SUMMARY

Older adults have unique opportunities to be served and to share with others through groups and individual relationships and programs in religious congregations. Where programs and senior centers with public funding can provide only for physical, emotional, and social needs, religious congregations can be more wholistic and provide for the spiritual needs as well. This chapter offers further discussion of planning that will facilitate program development for the whole person.