engleski

Evaluation of robustness of decision making unit using dual multipliers

Sensitivity analysis is a topic of great importance in DEA, either because data can be erroneous, or we can use procedures of sensitivity analysis to assess robustness of chosen DMU, i. e. how much data can change before an efficient DMU become inefficient. In the present paper we are interested in proportional changes of inputs and outputs of all DMUs, such that we increase inputs and decrease outputs of DMU under evaluation, and decrease inputs and increase outputs of remaining DMUs. In this approach we use dual multipliers obtained via extended, or superefficient DEA model. We also compare results with the approach of Thompson et al., where primal-dual interior-point method was used to obtain solution of dual program which is centrally positioned and satisfies strong complementarity slackness condition. Using superefficint DEA model, and obtaining dual multipliers from optimal simplex tableau for primal (envelopment) program we can assess percentage of possible changes which do not alter efficiency of DMU. Next, using parametric programming we can obtain set of dual multipliers with the property that DMU is efficient, after increasing its inputs and decreasing its outputs, if and only if at least one of the obtained dual multipliers is optimal for DMU. Numerical examples illustrating the results are provided.

Data envelopment analysis; efficiency; robustness; sensitivity analysis; linear programming; parametric programming

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