Sensitivity and stability of efficiency classifications in Data Envelopment Analysis

Abstract

A new technique for assessing the sensitivity and stability of efficiency classifications in Data Envelopment Analysis (DEA) is presented. Here developed for the ratio (CCR) model, this technique extends easily to other DEA variants. An organization's input-outut vector serves as the center for a cell within which the organization's classification remains unchanged under perturbations of the data. For the ll, l~. and generalized l~. norms, the radius of the maximal cell can be computed using linear programming formulations. This radius can be interpreted as a measure of the classifications stability, especially with respect to errors in the data.

Generalized tolerance sensitivity and DEA metric sensitivity

“…This corresponds to an observation in [8] that τ* in Theorems 4 and 5 can be interpreted as a ratio relative to the positive weights used for each constraint. Also, in a similar analysis for the Ratio (CCR) model, Charnes et al [5] observe that τ* denotes "the minimum percentage change necessary in every input and output to bring the test unit to its nearest unstable point". Note that the interpretations of the perturbations are identical to those in Tolerance sensitivity.…”

“…This was followed by Charnes and Neralić [4], Neralić [13], Neralić and Wendell [14] and others. One of the approaches to DEA sensitivity, proposed by Charnes et al [3,5], was to apply metric concepts in a way to make it possible to determine allowable variations in all inputs and outputs for one DMU in a DEA model. In particular, using an l p norm to characterize distance, these papers propose optimization models to determine a maximum radius, called a "radius of stability", within which variations of the inputs and outputs in a selected DMU would remain efficient, if the selected DMU was originally efficient, and would remain inefficient, if it was originally inefficient.…”

Finding stability regions for preserving efficiency classification of variable returns to scale technology in data envelopment analysis

“…A new avenue for sensitivity analysis was opened by Charnes et al (1992Charnes et al ( , 1996. They determined ''radii of stability'' within which data variations will not alter a DMU's classification from efficient to inefficient status (or vice versa).…”

“…They determined ''radii of stability'' within which data variations will not alter a DMU's classification from efficient to inefficient status (or vice versa). Then, Cooper et al (2001) modified the models in Charnes et al (1996) for sensitivity analysis of inefficient DMUs. Their model have yielded a radius of stability within which all inputs and outputs for an inefficient DMU p can be improved without producing a change from inefficient to efficient status.…”

“…This means that no reclassification to efficient status will occur within the symmetric region defined by them. However, for sensitivity analysis of efficient DMUs, they used the proposed model by Charnes et al (1996). Jahanshahloo et al (2005b) presented a modified version of the proposed models in Cooper et al (2001) to determine stability radius for inputs and outputs of efficient and inefficient DMUs by one-model approach.…”