Finding efficient surfaces in DEA-R models

Abstract

• This paper focusses on finding efficient surfaces in DEA-R models. • The output-oriented, variable returns-to-scale assumption is analyzed. • Efficient hyperplanes were introduced for the 10 bank branches under study. Finding efficient surfaces is quite an important task in data envelopment analysis (DEA) because scale efficiency, returns to scale, and other characteristics of decision making units (DMUs) may easily be derived using them. Traditional DEA models assume that the inputs and outputs are given as non-ratio characteristics. In cases where only a ratio of inputs to outputs (or vice versa) is available for our DMUs, the decision maker is forced to make use of ratio data envelopment analysis (DEA-R) models for efficiency and performance evaluation. This paper deals with identification of efficient surfaces in DEA-R models. The axioms for specifying the production possibility set in constant returns to scale technology for DEA-R are discussed, and, finally an original algorithm for identification of efficient surfaces in this class of models is proposed. In the following, we will find the efficient hyper planes for the 10 bank branches under study. To expand the present study, a comparison was made between the BCC models in DEA and DEA-R, and DEA-R-efficient surfaces were calculated under CRS and VRS assumptions in a simple numerical example.