Continuous Optimization Data envelopment analysis with imprecise data Dimitris K. Despotis a, * , Yiannis G. Smirlis b a Department of Informatics, University of Piraeus, 80 Karaoli & Dimitriou Str., 18534 Piraeus, Greece b Department of Statistics and Actuarial Science, University of Piraeus, 80 Karaoli & Dimitriou Str., 18534 Piraeus, Greece Received 19 September 2000; accepted 4 June 2001 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. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Data envelopment analysis; Interval data; Ordinal data; Imprecise data 1. Introduction Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and outputs. The original DEA models [2] assume that inputs and outputs are measured by exact values on a ratio scale. Recently, Cooper et al. [6] addressed the problem of imprecise data in DEA, in its general form. The term ‘‘imprecise data’’ reflects the situation where some of the input and output data are only known to lie within bounded intervals (interval numbers) while other data are known only up to an order. Imprecise DEA (IDEA), proposed in that work, is the first unified approach for dealing directly with imprecise data in DEA (bounds and/or rankings imposed directly on input/output data). In the same work, IDEA was extended to AR-IDEA to include the assurance region approach (fixed or ratio bounds and/or ordinal relations imposed on the weights) European Journal of Operational Research 140 (2002) 24–36 www.elsevier.com/locate/dsw * Corresponding author. Tel.: +30-1-4142315; fax: +30-1-4142357. E-mail address: despotis@unipi.gr (D.K. Despotis). 0377-2217/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S0377-2217(01)00200-4