Piecewise Linear Virtual Inputs/Outputs in Interval DEA

Data envelopment analysis (DEA) is the leading technique for assessing the efficiency of decision 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 performance 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. Efficiency 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