Qualitative and quantitative data envelopment analysis with interval data

In this paper, we investigate DEA with interval input‐output data. First we show various extensions of efficiency and that 25 of them are essential. Second we formulate the efficiency test problems as mixed integer programming problems. We prove that 14 among 25 problems can be reduced to linear programming problems and that the other 11 efficiencies can be tested by solving a finite sequence of linear programming problems. Third, in order to obtain efficiency scores, we extend SBM model to interval input‐output data. Fourth, to moderate a possible positive overassessment by DEA, we introduce the inverted DEA model with interval input‐output data. Using efficiency and inefficiency scores, we propose a classification of DMUs. Finally, we apply the proposed approach to Japanese Bank Data and demonstrate its advantages.