Data envelopment analysis based on maximin relative efficiency criterion

While gauging the performances of operating entities using imprecise information on the input and output importance weights, an entity is considered Farrell efficient as long as it outperforms its peers for at least one feasible combination of the weights for inputs and outputs. This paper argues that Farrell efficiency computations are based on an optimistic perspective and a Farrell-efficient entity may perform rather poorly when weights corresponding to realistic considerations are assigned to inputs and outputs. An entity is defined as robust efficient if its relative efficiency score reaches 1 in all feasible combinations of the input and output weights. A linear programming based approach is proposed to perform what is referred to as robust efficiency analysis to identify robust efficient entities. In contrast to Farrell efficiency analysis, robust efficiency analysis involves the computation of the lowest efficiency score that can be assigned to an entity relative to the highest score among all the entities where an identical combination of weights for inputs and outputs is applied. The production possibility set underlying the proposed approach is also defined and interpreted. An experimental study illustrates that when compared with Farrell efficiency analysis robust efficiency analysis has sharper discrimination capability and the entity it identifies as efficient has superior average performance.

► The traditional DEA models can mislead policy makers because they consider only the best-case scenario.
► We have proposed a robust efficiency analysis framework that uses the maximin relative efficiency criterion.
► The robust efficiency analysis identifies the DMUs with the best guaranteed level of performance possible for all feasible scenarios.
► Our computational experiment suggests that a robust efficient DMU performs quite well on average.
► The robust efficiency analysis is more effective than the traditional DEA models in discriminating the efficiencies of DMUs.