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.