Input–output substitutability and strongly monotonic p-norm least distance DEA measures

• There does not exist any least distance p-norm DEA measure satisfying strong monotonicity.
• We introduce least distance p-norm DEA measures satisfying strong monotonicity.
• We introduce a tradeoff set that represents substitutable inputs and outputs.

In DEA, there are two frameworks for efficiency assessment and targeting: the greatest and the least distance framework. The greatest distance framework provides us with the efficient targets that are determined by the farthest projections to the assessed decision making unit via maximization of the p-norm relative to either the strongly efficient frontier or the weakly efficient frontier. Non-radial measures belonging to the class of greatest distance measures are the slacks-based measure (SBM) and the range-adjusted measure (RAM). Whereas these greatest distance measures have traditionally been utilized because of their computational ease, least distance projections are quite often more appropriate than greatest distance projections from the perspective of managers of decision-making units because closer efficient targets may be attained with less effort. In spite of this desirable feature of the least distance framework, the least distance (in) efficiency versions of the additive measure, SBM and RAM do not even satisfy weak monotonicity. In this study, therefore, we introduce and investigate least distance p-norm inefficiency measures that satisfy strong monotonicity over the strongly efficient frontier. In order to develop these measures, we extend a free disposable set and introduce a tradeoff set that implements input–output substitutability.