Cross Redundancy in the Modified Input-Oriented Variable-return-to-Scale DEA Models

Abstract: Data Envelopment Analysis (DEA) is a mathematical programming method for the assessment of relative efficiency of a set of Decision Making Units (DMUs) that use several inputs to produce several outputs. It measures the efficiency of each Decision Making Unit (DMU) by maximizing the ratio of virtual output to virtual input with the constraint that the ratio does not exceed one for each DMU. Standard DEA models (radial or non-radial) project under evaluation DMU onto efficient frontier, using decrease its inputs and/or increase its outputs. In the case that one output variable has a linear dependence (conic dependence, to be precise) with the other output variables, it can be hypothesized that the addition or deletion of such an output variable would not change the efficiency estimates. This is also the case for input variables. However, in the case that a certain set of input and output variables is linearly dependent, the effectless of such a dependency on DEA discussed by Lee and Choi, they called such a dependency a cross redundancy and examined the effect of a cross redundancy on DEA. They proved that the addition or deletion of a cross-redundant variable does not affect the efficiency estimates yielded by the CCR or BCC models [2]. In this paper, according to modifying the basic DEA models using facet analysis by Daneshvar [1], we examine the effect of a cross redundancy on the modified input-oriented BCC model using facet analysis. We prove that the addition or deletion of a cross-redundant variable does not affect the efficiency estimates yielded by the modified input-oriented BCC model.