Ratio-based data envelopment analysis: An interactive approach to identify benchmark

In the real world we are confronted with many cases where the ratio of input/output data is so important for managers, so in this regard we cannot use traditional Data Envelopment Analysis (DEA) models to evaluate the efficiency of decision-making units (DMU) and we should use DEA models based on ratio data. To get the corresponding benchmark for each inefficient decision-making unit, we need to reduce and increase the inputs and outputs, respectively, and get the unified projection of the decision maker unit on the efficiency frontier. In this paper we present a multi-objective linear programming (MOLP) model for evaluating efficiency based on defining the production possibility set in the presence of ratio data and to get the corresponding benchmark to each decision-making unit DMU. We use the Zionts and Wallenius (Z–W) interactive method to solve the MOLP model presented. Using the target setting by manager among the solutions resulting from the MOLP problem, we choose best solution according to the managers' preferences as benchmark and at the end we present the results of the research.