A data envelopment analysis model for performance evaluation and ranking of DMUs with alternative scenarios

Abstract

Data envelopment analysis (DEA) is a general tool for measuring the relative efficiency ofhomogeneous decision-making units (DMUs). DEA models usually deal with crisp data and do not consider the conditions in which the inputs and outputs are uncertain. Many researchers have focused their research on these types of conditions, in which they assumed fuzzy data, interval data, and probabilistic data, as well as other expressions of uncertainty in the dataset. Various models, such as mean value and variance, robust DEA, multiple criteria decision-making (MCDM) models, and several other models, have been proposed. This paper deals withinstances in which uncertainty in the dataset is expressed by several alternative scenarios. The first presented model for problems with several alternative scenarios in their inputs and outputs is derived directly from the definition of the relative efficiency formula similar as those in traditional DEA models. This model is not linear and cannot be linearized. Due to this, we modify this model and derive a new model that is linear and can be solved easily. The proposed models have none of the common drawbacks attending other methods commonly applied to this set of issues. They are always feasible; moreover, they are able to generate a complete ranking of all DMUs using a computationally efficient procedure. Bothmodels are illustrated using a numerical example with 10 DMUs and three scenarios for input and output values, and their results are compared and discussed.