Advanced X-efficiencies for CCR- and BCC-models – towards Peer-based DEA controlling

Classical CCR and BCC DEA-models follow a general concept: they allow each DMU to evaluate its (in-) efficiency in the most favorable way, and then propose input reduction and/or output raise so as to follow its best practice units. A first step beyond this ‘self-appraisal’ is the consideration of X-efficiencies thus evaluating DMUs with optimal weights of a peer. Doing this for all possible peers yields a cross-efficiency matrix, either for CCR or for BCC models. This matrix might help to find a fair peer for the remaining DMUs. In a second step recent contributions analyze for CCR-models how such X-evaluated DMUs might improve their efficiency with respect to a peer’s weight system. In these models even free variation of inputs/outputs is possible rather than reduction and/or raise. Such models will be portrayed here and generalized for variable returns to scale. The remaining discomfort which a DMU might feel with the choice for peer among business rivals, leads to the concept of a ‘virtual peer’ VP. This paper proposes such a peer as a consensual option for all DMUs. Now for either return to scale – CCR and BCC – for an input or output oriented focus and by free variation of inputs and outputs they can meet the requirements of VP. The DMUs pay a heavy price, however: the peer controls their respective weights and even their activities; he is a dictator.

► Away from self-appraisal and towards peer-appraisal is here the new credo.
► The objective for such a choice is a consensual improvement of the DMUs’ performances, improvement in the light of a peer.
► We show the calculation of cross-efficiencies for either return to scales, CCR and BCC.
► Some ideas how to tackle the problem of negative X-efficiencies are sketched.
► We illustrate the concept of a so called “virtual peer”.