Finding the strong efficient frontier and strong defining hyperplanes of production possibility set using multiple objective linear programming

Data envelopment analysis (DEA) models use the frontier of the production possibility set (PPS) to evaluate decision making units (DMUs). However, the explicit-form equations of the frontier cannot be obtained using the traditional DEA models. To fill this gap, the current paper proposes an algorithm to generate all strong-efficient DMUs and the explicit-form equations of the strong-efficient frontier and the strong defining hyperplanes for the PPS with the variable returns to scale (VRS) technology. The algorithm is based on a multiple objective linear programming (MOLP) problem in the DEA methodology, which is solved through the multicriteria simplex method. Also, Isermann’s test is employed to specify strong-efficient nonbasic variables in each strong-efficient multicriteria simplex table. Before presenting the algorithm, a theoretical framework is introduced to characterize the relationships between the feasible region in the decision space of the MOLP problem and the PPS with the VRS technology. It is shown that the algorithm which has four phases is finitely convergent and has less computational complexity than other algorithms in the related literature. Finally, two examples are used to illustrate the algorithm.