Some aspects of primal–dual relationship in sensitivity analysis in data envelopment analysis

In the present paper sensitivity analysis, or robustness, of extreme efficient decision making unit DMU(0) is considered. We are interested in absolute changes of inputs and outputs, where inputs are increased and outputs are decreased, of DMU(0) which do not alter its efficiency status, i.e. DMU(0) remains efficient. In the first part of the paper we show how to obtain equation of a hyperplane defined with m + s points obtained using method proposed by Zhu. This hyperplane, under some assumptions, i.e. nondominance, serves as a boundary to the possible changes of inputs and outputs of DMU(0) which leave DMU(0) efficient. In the second part we introduce dual of proposed linear program for extended DEA model of Zhu, and based on relationship between primal and dual program and using sensitivity analysis and parametric programming we obtain equation of the above-mentioned hyperplane.