Data envelopment analysis (DEA) is a non‐parametric analytical methodology widely used in efficiency measurement of decision making units (DMUs). Conventionally, after identifying the efficient frontier, each DMU is compared to this frontier and classified as efficient or inefficient. This paper first introduces the strongly efficient frontier (SEF) and strongly inefficient frontier (SIF), and then proposes several models to calculate various distances between DMUs and both frontiers. Specifically, the distances considered in this paper include: (1) both the distance to SEF and the distance to SIF, where the former reveals a unit’s potential opportunity to become a best performer while the latter reveals its potential risk to become a worst performer, and (2) both the closest distance and the farthest distance to frontiers, which may provide different valuable benchmarking information for units. Subsequently, based on these distances, eight efficiency indices are suggested to rank DMUs. Due to different distances adopted in these indices, the efficiency of units can be evaluated from diverse perspectives with different indices employed. In addition, all units can be fully ranked by these indices. The efficiency of 24 major Asian container ports is analyzed with our study, where the potential opportunities and potential crises of these ports are revealed and some new insights about their efficiency are provided.
