Data Envelopment Analysis Of A Number Of Theories And Methods Of Research

Data Envelopment Analysis (DEA) is believed to be a leading approach to execute performance analysis in most industries in literature since it provides a better way to organize and analyze data which allows efficiency to change over time and requires no prior assumption on the specification of the best practice frontier. Anyway, classical DEA models encounter many hurdles when applied to real-world problems where uncertainty, environmental factors and competition are of importance. This thesis aims to solve the above problems by introducing game theory, fuzzy set theory and machine learning theory to develop new aggregation models with DEA.This thesis studies State-Of-the-Art Topics in DEA theory and approach. Its main contents and innovations are as follows:â… . DEA game is discussed through max-min DEA Nash Bargaining model. The model applies the idea that combines self-rated and other-rated scheme. Thus, to some extent, two inter-related problems that are weak discriminating power and unrealistic weight distribution occurred in classical DEA are solved.â…¡. An aggregated ratio analysis model is proposed for evaluating relative efficiency of decision making units (DMUs). It is shown that this proposed ratio model is equivalent to the CCR DEA model. This equivalence property offers a great deal of opportunities for DEA to be interpreted and applied in different ways. This model also offers an insight into the frontier analysis. Whether a DMU is on the frontier or efficient frontier it can be informed by using the aggregated ratio analysis. Several results developed in the paper are coincident with that in the literature. Formulars regarding how to achieve ARA efficient are presented and proofed. The effect of changing the number of DMUs over ARA efficiency is carefully examed. Theorems about how to term the frontier DMUs greatly facilitate the DEA Monte Carlo simulation so that in our paper we can implement the algorithm of DEA Monte Carlo simulation in Excel for 5000 and 10000 iterations respectively.