Data envelopment analysis based on maximin relative efficiency criterion

Abstract

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.