A New Bi-Objective Generalized DEA Model

Data envelopment analysis (DEA for short), originally formulated by A. Charnes, Cooper and Rhodes, measures the relative efficiencies among the decision making units (DMUs) with multiple-input and multiple-output as a linear programming formulation. It is a new cross-subject that covers mathematics, operational research, economics as well as management science. It has been successfully employed to study the comparative performance of units by using mathematical programming (including linear programming, multiple objective programming, generalized optimization with cone-structure, Semi-infinite Multi-criteria Programming, chance programming, etc.).The performance of a DMU depends only on the identified efficient frontier characterized by the DMUs with a unity efficiency score. If the DMU is efficient then it lies on the efficient frontier. Using the data envelopment analysis, we can determine the structure, feature of the efficient frontier so as to know how to construct it. The nonparametric mathematical programming approach is one of the most popular techniques used in efficiency analysis. For its " natural " economic background, DEA method has attracted many researchers to study on it and they have done a lot of works during the course of data envelopment analysis being developed into a new research field. However, there exists some shortcomings in previous DEA studies. In measurements of technical efficiency of DMUs,for example,there exists difference between input-based and output-based version in value. As a result, it brings in more difficulties in analyzing actually technical efficiency of a DMU and ranking appropriately DMUs being assessed as inefficient.This paper is mainly divided into two parts. Firstly, a new bi-objective generalized data envelopment analysis (Nbi-GDEA) model is proposed. This model's objective is to minimize the radio of input efficiency k₁θto output efficiency k₂z. After defining its efficientcy, we show the equivalence between the Nbi-GDEA efficiency and the non-dominated solutions of the multi-objective programming problem defined on the production possibility set. Then, we discuss the returns to scale under the Nbi-GDEA model. Secondly, we introduce a ranking system for efficient DMUs based on the change of production surface. The DMU that makes the original efficient frontier to get farther from the inefficient DMUs is more efficient.