engleski

Efficient frontier for inefficient DMU in DEA model with CRS

Data Envelopment Analysis is a set of methods and models used for assessment of relative efficiency of DMUs. Each DMU uses m inputs to produce s outputs. Based on this data the production possibility set is defined via supporting hyperplanes to the set of DMUs. Each DMU is classified as efficient or inefficient. Efficiency is considered as Pareto efficiency, i. e. DMU is efficient if it is not dominated with some (frontier) point from production possibility set with less or equal inputs or more or equal outputs. In this work we are interested in efficient frontier of production possibility set which dominates inefficient DMU under evaluation. In general situation this part of the frontier is composed of subsets of different hyperplanes. Using LP we obtain projection point along chosen input or output of inefficient DMU to the frontier of production possibility set. Dual variables in optimal simplex tableau can be interpreted as coefficients of the hyperplane which contains the obtained projection point. Using parametric programming, where only RHS is changed with parameters representing decrease in inputs and increase in outputs of ineffcient DMU under evaluation, we obtain subset of this hyperplane which dominats DMU under evaluation. Using dual pivot step we obtain neighboring hyperplanes. Proposed procedure is repeted, resulting with equations, and subsets, of all hyperplanes which dominate DMU under evaluation. Numerical example is provided.

DEA; inefficient DMU; efficient projection point

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