Cross Efficiencies

The cross efficiency of a DMU (j) is computed as the ratio of the sum of its weighted outputs to the sum of its weighted inputs using the weights that are optimal for some other DMU (k). Doyle and Green (1994) introduced the concept of cross efficiency grounding it on the intuitive concept of peer-appraisal, DMU k appraising DMU j in the above example as opposed to self-appraisal represented by the traditional DEA efficiency rating.

In the illustration above H01 weights yield efficiencies of 64.25%, 100%, 100%, 71.26%, 47.33% and 64.58% to DMUs H01 to H06 respectively. Thus note how H02 is efficient under the weights optimal for all other DMUs whereas H03 is very inefficient under the optimal weights for H02. (However, as noted elsewhere the optimal weights of a DMU, especially so for an efficient one such as H02 may not be unique.)