Fair efficiency decomposition in network DEA: A compromise programming approach

We introduce in this paper a novel network DEA approach to determine a single and fair efficiency decomposition for series multi-stage processes. We provide direct comparisons with the bargaining approach of Zhou et al. (2013) [1]. First, we prove the equivalence of the proposed approach with the bargaining approach for series two-stage processes in which only the intermediate products are the outputs of the first stage and the inputs to the second one. Next, we reveal the inadequacy of the bargaining approach to be applied in series processes with more than two stages, as it yields multiple non-extreme efficiency decompositions instead of one. On the contrary, we show that our approach provides a single non-extreme efficiency decomposition. In addition to these contributions, our approach is novel in the sense that the obtained efficiency decomposition represents a fair compromise between the stages, as it is as close as possible to the maximum efficiency score and as far away as possible to the minimum efficiency score attained by each stage. To reach such a fair compromise among the stages we employ the weighted min-max method in a multi-objective programming framework, and we guide the search direction on the line that connects the ideal point with the nadir point. We provide graphical illustrations and comparisons based on data drawn from the literature as well as on synthetic data.