M.Sc Thesis
M.Sc Student Nelly Wainberg Analysis of Input Output Data for the Case of Quasi Concave Production Function Department of Industrial Engineering and Management Full Professor Passy Ury

Abstract

Data Envelopment Analysis (DEA) is linear programming, based technique used for measuring the relative performance of organizational and production units, with multiple inputs and outputs. Since the introduction of DEA approach in1978 (Charnes, Cooper and Rhodes-1978), it became a popular method for determining the efficiency of production systems and general method, in decision analysis, for comparing, sorting and ranking different alternatives.

In order to adopt the efficiency concept to economic and managerial systems, while the ratio of output to input represents efficiency, the physical concept of efficiency was generalized to include multi-input multi -output systems by using weights or trade off coefficient. This generalization induces the classical formulation of DEA. The method can successfully be applied to non profit organizations mainly, but can be adopted also to profit organizations.

In the case of the single output the classical DEA model implicitly assumes that the Production Function is Concave. In the present approach we assume that the technology is Well Behaved Technology, thus the induced level sets are convex but the Production Function is merely Quasi concave.

In the first part of this dissertation a linear programming for input efficiency and two models for output efficiency were developed. One output efficiency model is defined by linear programming with binary variables, while the second is essential a linear programming procedure.

The second part of this dissertation is an experimental one. In this part we formulated the output efficiency and evaluated the output efficiency of various data sets.

The data set contained of 448 DMU`s. and were generated 17000 efficiency scores in order to compare the Quasi concave output efficiency result versus Concave formulation (DEA). Similar to the Classical DEA models the Quasi concave models are essentially given by a linear program. Thus large system can easily be solved. Moreover, as was expected, the Quasi concave formulation is less restrictive as the DEA. Moreover, as also was expected, the number of inefficient DMUs increases with the model type and with the sample size.

The experiments show that Quasi concave models can be applied for efficiency analysis.