Management

We formalize an algorithm for solving the L1-norm best-fit hyperplane problem derived using first principles and geometric insights about L1 projection and L1 regression. The procedure follows from a new proof of global optimality and relies on the solution of a small number of linear programs. The procedure is implemented for validation and testing. This analysis of the L1-norm best-fit hyperplane problem makes the procedure accessible to applications in areas such as location theory, computer vision, and multivariate statistics.

1 Abstract The L1 norm has been applied in numerous variations of principal component analysis (PCA). L1-norm PCA is an attractive alternative to traditional L2-based PCA because it can impart robustness in the presence of outliers and is indicated for models where standard Gaussian assumptions about the noise may not apply. Of all the previously-proposed PCA schemes that recast PCA as an optimization problem involving the L1 norm, none provide globally optimal solutions in polynomial time.

Abstract We introduce a methodology for generalizing Data Envelopment Analysis (DEA) to incorporate the role and impact of constituencies in the classification of the model's attributes. Constituencies determine whether entities' attributes in a DEA study are treated as desirable or undesirable. This extension of DEA is the basis for a methodology to answer questions that arise such as: Which constituencies find what entities efficient? Which entities are in the efficient frontier for a specified constituency?

Consider a set, A of n points in m-dimensional space. The convex hull of these points is a polytope, P, in R m. The frame, F, of these points in the set of extreme points of teh polytope P with F⊆ A. The problem of identifying the frame plays a central role in optimization theory (redundancy in linear programming and stochastic programming), economics (data envelopment analysis), computational geometry (facial decomposition of polytopes) and statistics (Gastwirth estimators).

John R. Birge José H. Dulá Industrial and Operations Engineering Operations Research Program University of Michigan Southern Methodist University Ann Arbor, MI, USA 48109 Dallas, Texas, USA 75275 Keywords: integration, stochastic programming, moment problem, duality, approximation. Abbreviated title: Bounding separable recourse functions.

Tchebyscheff's Inequality is de rigueur in the first college course in statistics. This usually occurs by the second or third year in nearly all technically oriented undergraduate programs. This includes not just programs in mathematics, statistics, and engineering; but also business, economics, sociology, biology and many other areas. Tchebyscheff's Inequality is usually presented early in the course, soon after the concept of probability is introduced.

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Abstract: This paper considers bounds on the expectation of a convex function of a random variable when only limited information is available about the underlying distribution. The problem is presented as a generalized moment problem. A special class of functions is shown to have an easily computable solution to this problem with first and second moment constraints. Extensions are given for general convex functions on finite intervals or with finitely valued recession functions.

The job characteristics model has guided a great deal of research on the relationship between task characteristics and employee satisfaction and performance. Research in this area has indicated the necessity of incorporating nontask factors of jobs for further theory building in organizational behavior. Based upon the framework of organizational role theory, the dual attachment model is proposed for the integration of the job characteristic model and the leader-member exchange model. Questionnaire data from 101 employees in a federal agency is used to analyze the three models with respect to the prediction of job attitudes and performance. The results indicate the complementarity of task and interpersonal factors in the prediction of job outcomes. An additive model, as opposed to an interactive model, is supported for the combination of these factors. Findings from time lagged analysis of these models are generally consistent with those from concurrent analyses, but the findings from dynamic analysis are only partially consistent with those of the concurrent and time lagged analyses. Individual difference variables are found to be of little importance in these models.

There is an increasing interest in within-group agreement in organizations, in response to evidence that agreement is predictive of various organizational outcomes of interest. The model in this study suggests that within-group agreement on climate is predicted by the quality of exchange relationships, specifically team–member exchange (TMX), leader–member exchange (LMX), social interaction and work interdependence. Results suggest that average high quality LMX and TMX relationships are both predictive of within-group agreement on some measures of climate. The results also support the notion that differentiation in TMX relationships within a team is deleterious to within-group agreement on climate. Contrary to existing literature, social interaction and work interdependence were not significantly related to any of the other variables in the model.