Appendix

SBM algorithms for matrix-type organizations

As the SBM algorithms presented by Tone (2001, 2002) are described in Cooper et al (2007), we omit their explanations. The SBM algorithm for matrix-type organizations is the same as the network DEA algorithms using SBM presented by Tone and Tsutsui (2009). This algorithm is obtained by replacing Equation (3) with the following equation:

Super efficiency of matrix-type organizations is measured using the following equation, which is obtained modifying the SBM algorithm presented by Tone (2002):

subject to