Masters Theses

Date of Award

8-1999

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Yueh-er Kuo

Committee Members

Julius Smith, Chanaka P. Edirisinghe

Abstract

Data Envelopment Analysis (DEA) is motivated in chapter one. DEA mod els are nonlinear / linear programming based nonparametric models. DEA models optimize methods, systems, and machines compared to best estimates of average and variation from parametric statistical models. CCR, BCC, and Additive models are discussed in chapter two. With Charnes and Cooper linear transformation, CCR, and BCC linear models follow from CCR, and BCC nonlinear (ratio) models, respectively. Primal problem, multiplier problem optimizes the input and output multipliers of the decision making units (data) and categorizes the units into managerially efficient and managerially inefficient units. Additionally, dual problem, envelopment problem provides information on how to make inefficient decision making units efficient. Four extensions to DEA models are discussed in chapter three; inclusion of dis cretionary, and nondiscretionary variables, inclusion of categorical variables, incorporation of managerial insight, and judgement, in the models, and analysis of multiple time period data.

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