DEA based multiple criteria evaluation and the cross efficiency method for units ranking

Data envelopment analysis (DEA) method was originally designed to evaluate the efficiency of decision making units (DMUs), and it classifies the units merely into two dichotomic groups: efficient and inefficient ones. The purpose of the paper is to combine the multiple criteria evaluation problem with DEA and to fully rank the evaluation units from the most efficient to the least efficient ones as classified by DEA. In this paper we propose a new cross efficiency DEA based model for multiple criteria evaluation. The method could solve multiple criteria evaluation problem, which includes three types of index (cost, benefit, and fixed), and provide a full ranking of the efficient and inefficient units based on the cross efficiency score. Two types of secondary goal formulations (aggressive and benevolent) are introduced in this cross efficiency method in order to deal with the non uniqueness of the optimal solution issue. We compare the performances of aggressive, benevolent, and arbitrary cross efficiency models with that of the simple efficiency model and come to a conclusion that the cross efficiency model is a good surrogate for the simple efficiency model in multiple criteria evaluation, and the aggressive cross efficiency model is better than the arbitrary one. We also demonstrate these methods for evaluation and full ranking through an example.