Closest targets and strong monotonicity on the strongly efficient frontier in DEA

• We revise the literature on monotonicity and least distance measures.
• We highlight that strong monotonicity is not satisfied by Hölder norms.
• We give an explanation to why strong monotonicity fails.
• We provide a solution to this problem based on the extension of FDEFs.

The determination of closest efficient targets has attracted increasing interest of researchers in recent Data Envelopment Analysis (DEA) literature. Several methods have been introduced in this respect. However, only a few attempts exist that analyze the implications of using closest targets on the technical inefficiency measurement. In particular, least distance measures based on Hölder norms satisfy neither weak nor strong monotonicity on the strongly efficient frontier. In this paper, we study Hölder distance functions and show why strong monotonicity fails. Along this line, we provide a solution for output-oriented models that allows assuring strong monotonicity on the strongly efficient frontier. Our approach may also be extended to the most general case, i.e. non-oriented models, under some conditions of regularity.