In the standard Data Envelopment Analysis (DEA), the strong disposability and convexity axioms along with the variable/constant return to scale assumption provide a good estimation of the production possibility set and the efficient frontier. However, when data contains some or all measures represented by ratios, the standard DEA fails to generate an accurate efficient frontier. This problem has been addressed by a number of researchers and models have been proposed to solve the problem. This thesis proposes a “Maximized Slack Model” as a second stage to an existing model. This work implements a two phase modified model in MATLAB (since no existing DEA software can handle ratios) and with this new tool, compares the results of our proposed model against the results from two other standard DEA models for a real example with ratio and non-ratio measures. Then we propose different approaches to get a close approximation of the convex hull of the production possibility set as well as the frontier when ratio variables are present on the side of the desired orientation.

In the standard Data Envelopment Analysis (DEA), the strong disposability and convexity axioms along with the variable/constant return to scale assumption provide a good estimation of the production possibility set and the efficient frontier. However, when data contains some or all measures represented by ratios, the standard DEA fails to generate an accurate efficient frontier. This problem has been addressed by a number of researchers and models have been proposed to solve the problem. This thesis proposes a “Maximized Slack Model” as a second stage to an existing model. This work implements a two phase modified model in MATLAB (since no existing DEA software can handle ratios) and with this new tool, compares the results of our proposed model against the results from two other standard DEA models for a real example with ratio and non-ratio measures. Then we propose different approaches to get a close approximation of the convex hull of the production possibility set as well as the frontier when ratio variables are present on the side of the desired orientation.