“…Unlike previous studies, the particular features of UK banking data require additional types of DEA models. Therefore, we shall use both input-and output-oriented CCR models (Charnes et al 1978); both inputand output-oriented BCC models (Banker et al 1984); BCC models without explicit inputs, BCC-WEI, or without explicit outputs, BCC-WEO (Lovell and Pastor 1999); input-oriented, output-oriented, and non-oriented SBM models (Tone 2001); and SBM-WEI model (Liu et al 2011) and SBM-WEO model that we propose. CCR and BCC models are described in Table 1, BCC models without explicit inputs or outputs are described in Table 2, SBM models are described in Table 3, and SBM models without explicit inputs or outputs are described in Table 4, where θ k denotes the technical efficiency of DMU k and measures the efficiency with which DMU k transforms inputs into outputs, which reflects the quality of its management decisions, λ j denotes the weight assigned to DMU j in constructing the "ideal" benchmark of DMU k ; that is, its projection on the efficiency frontier, and s − i,k and s + r,k denote the slacks in input i and output r , respectively, which represent input excess and output shortfall.…”