Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis

 In the last decade, ranking units in data envelopment analysis (DEA) has become the interests of many DEA researchers and a variety of models were developed to rank units with multiple inputs and multiple outputs. These performance factors (inputs and outputs) are classified into two groups: desirable and undesirable. Obviously, undesirable factors in production process should be reduced to improve the performance. Also, some of these data may be known only in terms of ordinal relations. While the models developed in the past are interesting and meaningful, they didn't consider both undesirable and ordinal factors at the same time. In this research, we develop an evaluating model and a ranking model to overcome some deficiencies in the earlier models. This paper incorporates undesirable and ordinal data in DEA and discusses the efficiency evaluation and ranking of decision making units (DMUs) with undesirable and ordinal data. For this purpose, we transform the ordinal data into definite data, and then we consider each undesirable input and output as desirable output and input, respectively. Finally, an application that shows the capability of the proposed method is illustrated.