5 Matching Results

Search Results

Advanced search parameters have been applied.

Mathematical Programming Approaches to the Three-Group Classification Problem

Description: In the last twelve years there has been considerable research interest in mathematical programming approaches to the statistical classification problem, primarily because they are not based on the assumptions of the parametric methods (Fisher's linear discriminant function, Smith's quadratic discriminant function) for optimality. This dissertation focuses on the development of mathematical programming models for the three-group classification problem and examines the computational efficiency and classificatory performance of proposed and existing models. The classificatory performance of these models is compared with that of Fisher's linear discriminant function and Smith's quadratic discriminant function. Additionally, this dissertation investigates theoretical characteristics of mathematical programming models for the classification problem with three or more groups. A computationally efficient model for the three-group classification problem is developed. This model minimizes directly the number of misclassifications in the training sample. Furthermore, the classificatory performance of the proposed model is enhanced by the introduction of a two-phase algorithm. The same algorithm can be used to improve the classificatory performance of any interval-based mathematical programming model for the classification problem with three or more groups. A modification to improve the computational efficiency of an existing model is also proposed. In addition, a multiple-group extension of a mathematical programming model for the two-group classification problem is introduced. A simulation study on classificatory performance reveals that the proposed models yield lower misclassification rates than Fisher's linear discriminant function and Smith's quadratic discriminant function under certain data configurations. Data configurations, where the parametric methods outperform the proposed models, are also identified. A number of theoretical characteristics of mathematical programming models for the classification problem are identified. These include conditions for the existence of feasible solutions, as well as conditions for the avoidance of degenerate solutions. Additionally, conditions are identified that guarantee the classificatory non-inferiority of one model over another in the training ...
Date: August 1993
Creator: Loucopoulos, Constantine
Partner: UNT Libraries

The Effect of Certain Modifications to Mathematical Programming Models for the Two-Group Classification Problem

Description: This research examines certain modifications of the mathematical programming models to improve their classificatory performance. These modifications involve the inclusion of second-order terms and secondary goals in mathematical programming models. A Monte Carlo simulation study is conducted to investigate the performance of two standard parametric models and various mathematical programming models, including the MSD (minimize sum of deviations) model, the MIP (mixed integer programming) model and the hybrid linear programming model.
Date: May 1994
Creator: Wanarat, Pradit
Partner: UNT Libraries

A Goal Programming Safety and Health Standards Compliance Model

Description: The purpose of this dissertation was to create a safety compliance model which would advance the state of the art of safety compliance models and provide management with a practical tool which can be used in making safety decisions in an environment where multiple objectives exist. A goal programming safety compliance model (OSHA Model) was developed to fulfill this purpose. The objective function of the OSHA Model was designed to minimize the total deviation from the established goals of the model. These model goals were expressed in terms of 1) level of compliance to OSHA safety and health regulations, 2) company accident frequency rate, 3) company accident cost per worker, and 4) a company budgetary restriction. This particular set of goals was selected to facilitate management's fulfillment of its responsibilities to OSHA, the employees, and to ownership. This study concludes that all the research objectives have been accomplished. The OSHA Model formulated not only advances the state of the art of safety compliance models, but also provides a practical tool which facilitates management's safety and health decisions. The insight into the relationships existing in a safety compliance decision system provided by the OSHA Model and its accompanying sensitivity analysis was demonstrated by the empirical application during the research. The optimal solution values showed what could be accomplished with a given objective structure and the existing safety and health functional relationships. The optimal solution values obtained during the sensitivity analysis showed how sensitive the model is to the uncertainties relating to goal structures and the specific exogenous and endogenous parameter values. This new insight available to management can provide a scientific base upon which the total system decisions can be made.
Date: August 1976
Creator: Ryan, Lanny J.
Partner: UNT Libraries