Yiannis G. Smirlis

Data envelopment analysis with imprecise data

Abstract In original data envelopment analysis (DEA) models, inputs and outputs are measured by exact values on a ratio scale. Cooper et al. [Management Science, 45 (1999) 597–607] recently addressed the problem of imprecise data in DEA, in its general form. We develop in this paper an alternative approach for dealing with imprecise data in DEA. Our approach is to transform a non-linear DEA model to a linear programming equivalent, on the basis of the original data set, by applying transformations only on the variables. Upper and lower bounds for the efficiency scores of the units are then defined as natural outcomes of our formulations. It is our specific formulation that enables us to proceed further in discriminating among the efficient units by means of a post-DEA model and the endurance indices. We then proceed still further in formulating another post-DEA model for determining input thresholds that turn an inefficient unit to an efficient one.

Data envelopment analysis with nonlinear virtual inputs and outputs

An underlying assumption in DEA is that the weights coupled with the ratio scales of the inputs and outputs imply linear value functions. In this paper, we present a general modeling approach to deal with outputs and/or inputs that are characterized by nonlinear value functions. To this end, we represent the nonlinear virtual outputs and/or inputs in a piece-wise linear fashion. We give the CCR model that can assess the efficiency of the units in the presence of nonlinear virtual inputs and outputs. Further, we extend the models with the assurance region approach to deal with concave output and convex input value functions. Actually, our formulations indicate a transformation of the original data set to an augmented data set where standard DEA models can then be applied, remaining thus in the grounds of the standard DEA methodology. To underline the usefulness of such a new development, we revisit a previous work of one of the authors dealing with the assessment of the human development index on the light of DEA.

Assessing bids of Greek public organizations service providers using data envelopment analysis

The existing framework for the procurement of products and services for the Greek Public Organizations describes specific criteria structure and fixed-weighted formulas for the assessment of the provider’s bids. This assessment procedure suffers from specific shortcomings: it overestimates the price, it is very sensitive to small changes to performance indicators and especially for the services, is not able to incorporate variable price information. In this paper we develop a Data Envelopment Analysis model that overcomes the above mentioned shortcomings. It uses variable weights that are estimated in favor of each evaluated bid and are properly restricted to comply with the existing framework and to reflect criteria priorities. It also encounters ranges for prices that correspond to minimum and maximum expected number of service calls. For illustration purposes we provide a real case application for the assessment of courier service providers.

RELAXING THE IMPACT OF EXTREME UNITS IN DATA ENVELOPMENT ANALYSIS

Data envelopment analysis (DEA) is a nonparametric linear programming technique for measuring the relative efficiency of decision making units (DMUs) on the basis of multiple inputs and outputs. DEA assessments, however, are proved to be sensitive to extreme units that deviate substantially in their input/output patterns. In this paper we introduce an approach for handling extreme observations in DEA, i.e., observations that exhibit irregularly high values in some outputs and/or low values in some inputs. Unlike the usual practice of removing such observations, we retain them in the production possibility set reducing their impact on the other units. Our modeling approach is based on the concept of diminishing returns, assuming that the contribution of an output (input) to the efficiency score diminishes as the output increases beyond a pre-specified level, i.e., the level beyond which a value is characterized as extreme. According to our approach the original data set is transformed to an augmented data set, where standard DEA models can then be applied, remaining thus in the grounds of the standard DEA methodology. We illustrate our approach with a numerical example.

Piecewise Linear Virtual Inputs/Outputs in Interval DEA

A recent development in data envelopment analysis DEA concerns the introduction of a piece-wise linear representation of the virtual inputs and/or outputs as a means to model situations where the marginal value of an output input is assumed to diminish increase as the output input increases. Currently, this approach is limited to crisp data sets. In this paper, the authors extend the piece-wise linear approach to interval DEA, i.e. to cases where the input/output data are only known to lie within intervals with given bounds. The authors also define appropriate interval segmentations to implement the piece-wise linear forms in conjunction with the interval bounds of the input/output data and the authors propose a new models, compliant with the interval DEA methodology. They finally illustrate their developments with an artificial data set.