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Sensitivity analysis of the proportionate change of a subset of inputs or/and outputs in data envelopment analysis

Sensitivity analysis in Data Envelopment Analysis (DEA) for the case of the proportionate change of all inputs or/and of all outputs of an efficient Decision Making Unit (DMU) can be considered as a special case of additive change of all inputs or/and of all outputs. Sufficient conditions for an efficient DMU according to the Charnes-Cooper-Rhodes (CCR) model to preserve its efficiency under proportionate change of all inputs (or outputs) are given in (A. Charnes and L. Neralić, Glas. Mat. 27(47) (1992), 393-405). Similar results for the CCR model with simultaneous proportionate change of all inputs and of all outputs of an efficient DMU are obtained in (A. Charnes and L. Neralić, Res. Rep. CCS 667, Center for Cybernetic Studies, The Univ. of Texas at Austin, 1991). The case of the proportionate change of all inputs or/and of all outputs of an efficient DMU accoriding to the Additive model is considered in (L. Neralić, Proc. of the Int. Conf. "Restructuring Transitional Economies", S. Sharma and P. Sikavica (eds.), Book I, Fac. of Economics, Zagreb, 1995, 221-233). For all these cases two coefficients of proportionality are considered, one for outputs and the other for inputs. Sensitivity analysis for the case of different coefficients of proportionality for all inputs or/and all outputs of an efficient DMU is studied in (L. Neralić and T. Sexton, In: J. Guddat et al. (eds.), Parametric Optimization and Related Topics IV, Peter Lang, Frankfurt am Main, 1996, pp. 261-280). In this paper we consider sensitivity analysis in DEA for the case of the proportionate change of a subset of inputs or/and of a subset of outputs of an efficient DMU according to the CCR model. Sufficient conditions for an efficient DMU to treserve its efficiency under the proportionate change of a subset of inputs or/and of a subset of outputs are obtained. An illustrative numerical example is provided.

Data envelopment analysis; proportionate change of inputs or/and outputs; sensitivity analysis; linear programming

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