Expected efficiency based on directional distance function in data envelopment analysis

Directional distance function (DDF), an evaluation technique that estimates relative efficiency of a decision making unit (DMU) along a pre-determined direction vector that is not restricted by the radial direction, has been widespread in productive efficiency research over the past two decades. A key challenge in DDF applications, however, is to decide on an appropriate (or the best) direction along which to measure efficiency. To circumvent this issue, we build on the DDF model and propose expected efficiency in efficiency estimation. Expected efficiency is defined as the mean value of all relative efficiency scores of a DMU along all directions. When calculating the overall relative efficiency score of a DMU, the expected efficiency model incorporates all possible directions rather than choosing a particular direction. As such, the expected efficiency approach extends DDF from a single direction to all directions. Some benefits of the expected efficiency approach include (1) relieving a decision maker of the burden of determining a particular directional vector among many choices; (2) overcoming a decision maker's subjectivity in the direction selection; (3) resolving the sensitivity issue caused by choosing different directions; and (4) ensuring that all DMUs are estimated in a consistent and equitable manner. Our study contributes to productive efficiency research and data envelopment analysis by introducing a new efficiency estimate that does not need to rely on one specific direction. Using two examples, we demonstrate the validity and the robustness of expected efficiency as an alternative efficiency estimate.