Extended secondary goal models for weights selection in DEA cross-efficiency evaluation

Desirable targets and undesirable targets for each DMU are identified.The targets are reachable and more reasonable for the DMUs.Several secondary goal models are proposed considering both kinds of targets.Strong ability of discriminating the DMUs are shown in application examples. Data Envelopment Analysis (DEA) has been extended to cross-efficiency evaluation for ranking decision making units (DMUs) and eliminating unrealistic weighting schemes. Unfortunately, the non-unique optimal weights problem in DEA has reduced the usefulness of this extended method. Aiming at solving this problem, we first incorporate a target identification model to get reachable targets for all DMUs. Then, several secondary goal models are proposed for weights selection considering both desirable and undesirable cross-efficiency targets of all the DMUs. Compared with the traditional secondary goal models, the cross-efficiency targets are improved in that all targets are always reachable for the DMUs. In addition, the proposed models considered the DMUs' willingness to get close to their desirable cross-efficiency targets and to avoid their undesirable cross-efficiency targets simultaneously while the traditional secondary goal models considered only the ideal targets of the DMUs. Finally, the calculation results of our proposed models are compared with those of some other traditional methods for two published examples: an efficiency evaluation of six nursing homes and an R&D project selection.

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