A New MIP Approach on the Least Distance Problem in DEA

In this paper, we deal with the least distance problem (LDP) in Data Envelopment Analysis (DEA), which is to find a closest efficient target over the whole efficient frontier. To this end, we define the efficient frontier by a linear complementarity system and propose a mixed integer programming (MIP) approach to solve the LDP. Our proposed MIP approach: (1) can solve the LDP based on ⪙p-norm (p ≥ 1) by using a state-of-the-art solver and obtain the closest efficient target over the whole efficient frontier instead of a subset of it; (2) can be applied for computing the least distance DEA models satisfying the monotonicity; (3) is more user-friendly, because it allows a decision maker to improve the efficiency of a decision making unit (DMU) by setting the affordable input/output level under his/her circumstance. Thus, the efficient target provided by our approach may be more appropriate from the perspective of the decision makers of DMUs.