engleski

Projection points of inefficient DMU in DEA model with VRS

Data envelopment analysis is a set of methods and models used for assessment of relative efficieny of DMUs, each using m inputs to produce s outputs. Using this data production possibility set is defined. Based on obtained data, and model applied, each DMU is classified as efficient or inefficient, where efficiency is defined as Pareto-Koopmans efficiency. If DMU is inefficient, the applied model as an outcome gives measure of inefficiency and one efficient point, as a reference point which Pareto dominates the inefficient point under observation. This point, called projection point, is on the efficient part of the production possibility set. The decision maker is also interested in obtaining all, or part of the efficient points which can be considered as a reference point for the inefficient DMU. In this case we are interested in equation of the frontier of the production possibility set. Under the assumption of the variable returns of scale, the frontier is composed of hyperplanes defined with efficient points. Using modified DEA model with VRS, an LP model, we obtain one projection point, along chosen input or output, of inefficient DMU under evaluation on the frontier. Applying parametric programming and relationship between primal and dual LP, we move projection point along the frontier obtaining equations of the facet spanning the frontier. We can also obtain some other characteristics of the frontier, i. e. is it efficient or not, or does it shows increasing or decreasing returns to scale.

Data envelopment analysis (DEA); efficiency; decision making unit (DMU); variable returns to scale (VRS); projection

nije evidentirano