Setting closer targets based on non-dominated convex combinations of Pareto-efficient units: A bi-level linear programming approach in Data Envelopment Analysis

Data Envelopment Analysis (DEA) very often sets unrealistic targets, which require from the decision-making units (DMUs) a huge amount effort, perhaps non-assumable, for their achievement. For the identification of best practices in the benchmarking, this paper proposes considering as peers not only DEA efficient DMUs but also those that are Pareto efficient, and allowing for reference sets spanning convex combinations that are not dominated by observed DMUs. It is therefore an approach that somehow relaxes the convexity in DEA, and sets targets representing best practices in the sense that they define a course of action leading to results that are not worse than those of the real plans. A bi-level linear programming (BLP) DEA model is developed which finds the closest targets from a convex combination of the DMUs in a reference set satisfying such non-dominance requirement. This approach has proven to be successful in setting targets that require an effort significantly smaller than that needed to achieve the closest targets on the strong efficient frontier of both the DEA and the free disposal hull (FDH) technologies. In the empirical illustration, we have observed reductions in the order of 40 percentage points on average in the total effort required for their achievement, thus setting more realistically implementable directions for improving performance towards best practices than those provided by conventional DEA and FDH.