Treating Scale-Efficiency Gaps in Peer-Based DEA

Data envelopment analysis (DEA) is a method for calculating relative efficiency as a ratio of weighted outputs to weighted inputs of decision making units (DMUs). It is well-known that DEA can be done under the assumption of constant returns to scale (CRS) or variable returns to scale (VRS). One major disadvantage of the classical approach is that each DMU optimizes its individual weighting scheme–often called self-appraisal. To overcome this flaw cross-efficiency evaluation has been developed as an alternative way of efficiency evaluation and ranking of DMUs. Here all individual weighting schemes–called price systems–are applied to the activities of all DMUs. The derived cross-efficiency matrix can form the basis for seeking a consensual price system–a peer–, and hence this price system can be used for a peer-based activity planning. The present contribution shows that a scale-efficiency gap can occur when peer-based activity planning under VRS is applied, i.e. there is no feasible point in which self-appraisal efficiency under CRS, VRS and peer-appraisal efficiency under VRS coincide. As a consequence, we propose a mixed integer linear problem to avoid this drawback.