Extended Pattern Search with Transformations for the Three-Parameter Weibull MLE Problem

The Weibull distribution has found extensive applications in a variety of engineering, science and business problems. A journal survey indicated that it is the third most often used distribution in the statistical literature. To use it, one must best estimate its parameters from a given sample. Maximum likelihood estimates (MLE) of the three Weibull parameters are usually desirable due to their nice asymptotic properties, but several computational difficulties arise during the solution of this bounded-variable nonlinear optimization problem. This paper extends a method (pattern search) which was successfully used by the author for obtaining joint MLE of all three Weibull parameters. Fifteen different transformations (to eliminate bounds) and three search direction approaches (derivative-free, exact and numerical gradient) of a revised unconstrained pattern search are evaluated on a set of randomly generated realistic test problems. Performance criteria include computation speed, accuracy of estimators (relatively to the true parameters and true MLEs), log-likelihood value achieved, and goodness of fit of the estimated distribution (to the sample or generating population). The results are analyzed statistically and successful (unsuccessful) transformation/direction options are identified for each criterion. User interest in different performance criteria and the flatness of the log-likelihood function prevent identification of a single "overall best" option. Simple percentile estimators, used as search starting points, proved to be superior to MLE in problems with a small shape parameter value. The search procedures examined in this paper may also be used for solving other types of nonlinear optimization problems with bounded variables. They are attractive to practitioners because they are easily programmed and understood; they run fast but they do not guarantee optimality.reliability: parameter estimation, optimization

Heuristic 0-1 Linear Programming: An Experimental Comparison of Three Methods

This paper examines the performance of three heuristic methods (Senju-Toyoda, Kochen-berger et al. and Hillier) when applied to the 0-1 linear programming problem with nonnegative coefficients. Their effectiveness, measured in terms of computing time, error and relative error, is evaluated on a set of problems from the literature and randomly generated 0-1 test problems with nonnegative coefficients. Analysis of variance and stepwise regressions are employed to study the effect of the number of variables, number of constraints and degree of constraint slackness. The methods exhibited some similarities bui also marked differences in their behavior. Interestingly enough, the larger the number of variables the belter the accuracy of each method. Error differences among the three methods were significant (1:0.8:0.2) yet small (less than 2% on the average) for many practical situations. Hillier's algorithm was the most accurate but much slower and more core demanding than the other two, which makes it difficult or impossible to use for solving large 0-1 problems. Kochenberger's et al. heuristic was the fastest (most accurate) of the three in tightly (loosely) constrained problems. In general the Senju-Toyoda algorithm was the fastest, but least accurate on small and medium size problems. Suggestions are made for selecting the "best" heuristic based on the problem characteristics.

A categorized bibliographic survey of goal programming

A total of 240 goal programming articles that have so far appeared in over 60 English journal publications are compiled and classified according to technique and application areas. Analysis of these data provides interesting insights regarding goal programming article characteristics, literature trends and future needs.

A value-satisfaction taxonomy of IS effectiveness (VSTISE): A case study of user satisfaction with IS and user-perceived value of IS

Information Systems (IS) effectiveness has been studied over the past three decades, with user satisfaction utilized as a key measure. However, very little attention has been given to the role of user-perceived cognitive value of IS in measuring the effectiveness of such systems. Therefore, this article defines and articulates user-perceived value of IS as an important construct for IS research, not from the financial or ‘net benefit’ perspective to the organization, rather from the cognitive perspective. Following literature review, a new taxonomy of IS effectiveness, Value-Satisfaction Taxonomy of IS Effectiveness (VSTISE), is presented. The VSTISE posits four quadrants to indicate level of user-perceived IS effectiveness: improvement, effective, misleading, and ineffective. A case study using the proposed VSTISE is discussed. Results based on the 192 responses identify several problematic system characteristics that warrant additional investigation for their limited IS effectiveness. Finally, recommendations for research and practice are provided