engleski

Sensitivity Analysis of Efficient DMU in DEA MOdel wirh VRS

Data envelopment analysis, DEA, is a set of methods and models used for assessment of relative efficiency of n DMUs, each using m inputs to produce s outputs. In this paper we consider DEA model with VRS. Each DMU, according to the results od applied LP programm is classified as efficient or inefficient, where efficiency is defined as Pareto-Koopmans efficiency. If DMU is efficient then we are interested in how much its data can change, where we consider increase of inputs and decrease of outputs, so that it remains efficient. Such changes form region of efficiency for the observed DMU. In obtaining characterization of the region of efficiency we apply extended, or superefficient, DEA model. It is a model where DMU under observation is excluded from the reference set and reduced production possibility set, RPPS, is defined with remaining n-1 DMUs. Using LP for the primal DEA model we obtain projection point along single input or output of the chosen DMU, i e. maximaly increasing the input or decreasing the output, on the RPPS. Using data from optimal tableau we also obtain equation of a facet which is part of the frontier of RPPS and contains the projection point. The obtained facet is a border to the possible changes of inputs and outputs of choosen DMU so that it remains efficient. Using parametric programming, where changes of the inputs and outputs are applied only to RHS, and using relationship between primal and dual LP, we move along the frontier of RPPS thus obtaining equations of the adjacent facets and in this way we characterize the region of efficiency. The obtained results do not serve only as a way to characterize region of efficiency, but also give us better insight in the structure of the production possibility set. Namely, using standard DEA model inefficient DMUs, which could be very close to the DMU under observation, are excluded from the representation of the PPS.

DEA; VRS; Additive model; LP; Parametric programming

nije evidentirano