An improved non-convex model for discriminating efficient units in free disposal hull

• MAJ-FDH is used to discriminate among efficient units in non-convex DEA.
• We show that the MAJ-FDH model is not always feasible.
• We propose a modified MAJ-FDH model and show that it is always feasible.
• Modified MAJ-FDH produces optimal solution without solving the integer programming problem.
• We use two numerical examples to show the efficacy of the proposed method.

A number of methods, including data envelopment analysis (DEA), have been proposed for evaluating the performance of decision making units (DMUs) converting multiple inputs into multiple outputs. The free disposal hull (FDH) is an alternative non-parametric, deterministic production method useful to evaluate the technical efficiency of DMUs. Unlike DEA, the FDH imposes minimal assumptions on the production technology and it does not require convexity. The conventional FDH model assigns an efficiency score less than one to inefficient DMUs, from which a ranking can be derived. However, all efficient DMUs have an efficiency score of 1 and, hence, equal ranking. Several ranking methods have been proposed to discriminate among the efficient DMUs. These ranking methods are sometimes either break down or produce infeasible solution(s). The Mehrabian, Alirezae, Jahanshahloo (MAJ) (1999) method is usually used to discriminate among the efficient DMUs in convex DEA problems, while the MAJ-FDH method proposed by Sun and Hu (2009) has been used to discriminate among the efficient DMUs in non-convex DEA problems. In this paper: (1) we show that the MAJ-FDH model is not always feasible; (2) we propose a modified MAJ-FDH model, both input and output oriented, and mathematically prove that this model is always feasible; (3) we show that the proposed method can produce an optimal solution without the need to solve the integer programming problem; (4) we prove the validity of the proposed method through theorems; and (5) we provide two numerical examples to demonstrate the applicability and show the efficacy of the proposed method.