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

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The directional distance function and the translation invariance property (2016, background): “Specifically, the satisfaction of the translation invariance property should be studied in more recent contexts, as for example (1) centralized resource allocation [13], (2) the determination of least distance measures [2], (3) network DEA [19] and (4) bounded models [25].”
Performance evaluation through DEA benchmarking adjusted to goals (2018, background): “…frontier has also been investigated for purposes of developing efficiency measures that satisfy some desirable properties (see Ando et al. (2017), Aparicio and Pastor (2014), Fukuyama et al. (2014a, 2014b) and Fukuyama et al. (2016)). j jX ,Y , j 1,...,n, where j 1j mj mX x ,..., x 0 , j…”