36 International Journal of Operations Research and Information Systems, 4(2), 36-49, April-June 2013 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Piecewise Linear Virtual Inputs/ Outputs in Interval DEA Yiannis G. Smirlis, IT & Infrastructure Division, University of Piraeus, Piraeus, Greece Dimitris K. Despotis, Department of Informatics, University of Piraeus, Piraeus, Greece Keywords: Crisp Data Sets, Data Envelopment Analysis (DEA), Interval DEA, Marginal Value, Piece- Wise Linear Approach, Piecewise Linear Virtual Inputs/Outputs INTRODUCTION Data envelopment analysis (DEA) is the leading technique for assessing the efficiency of deci- sion making units (DMU) in the presence of multiple inputs and outputs. The two milestone DEA models, namely the CCR (Charnes et al., 1978) and the BCC (Banker et al., 1984) models have become standards in the literature of per- formance measurement. Recent applications of DEA include, among others, those of Mahdavi et al. (2008), Martin and Roman (2010), Pramodth et al. (2008) and Sufian (2010). The underlying mathematical instrument for performing the analysis is linear programming. Performing a typical DEA analysis means solving a series of linear programs, one for each DMU. Ef- ficiency is measured in a bounded ratio scale by the fraction ‘weighted output’ to ‘weighted input’. The inputs and outputs are assumed to be continuous positive variables and the weights are estimated through the associated linear program in favor of the evaluated unit so as to maximize its efficiency. Focusing on the outputs, an output measure multiplied by the associated weight is called virtual output. The summation of the virtual outputs over all the output dimensions, called ABSTRACT 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 defne 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 fnally illustrate their developments with an artifcial data set. DOI: 10.4018/joris.2013040103