Enhanced bisection strategies for the maximin efficiency ratio model

The Maximum Efficiency Ratio (MER) model may be regarded as a new form of Data Envelopment Analysis (DEA) model, which is based on the Maximin Decisional Efficiency (MDE) estimation principle. The MER model involves a special class of generalized fractional programming problems. The paper proposes some improved computational algorithms as alternatives to the original Bolzano search and other general purpose algorithms for solving the MER model. One of these, which may be called a ‘cutting-wedges’ algorithm is similar to the algorithms of the ‘cutting planes’ type, but iteratively modifies coefficients of existing constraints rather than adding new constraints. A numerical illustration is presented for the new algorithm. A combination of the cutting-wedges and the general purpose Dinkelbach strategies leads to an enhanced bisection algorithm which improves either the upper or lower bound at all iterations.