A consensual peer-based DEA-model with optimized cross-efficiencies – Input allocation instead of radial reduction

Abstract

Data Envelopment Analysis DEA is a method for estimating (in-)efficiencies of Decision Making Units DMUs by means of weighted output – to input – ratios, being the weights optimal virtual prices of such ex-post activities for all units. The cross-efficiency matrix then evaluates these output – to input – relations with respect to all optimal price systems, and hence permits efficiency rankings for the DMUs by aggregating the matrix entries line – and/or columnwise. In this contribution the classical input oriented DEA approach is generalized twofold: its first aim is an optimal efficiency improving input allocation rather than a mere radial input reduction. The second aim is the choice of a peer-DMU, the price system of which is acceptable for the remaining units. As free input allocation permits substitutional effects and so rises productivities in view of possible peers and for all units, it supports such consensual choice. Numerical examples show the positive effects of the new concept.