A new method based on finding the weak and strong defining supporting hyperplanes to recognize the anchor points

Abstract

One of the main important issues in Data Envelopment Analysis (DEA) is to recognize the set of anchor points which is the subset of the extreme efficient points of the production possibility set (PPS). An anchor point is an extreme efficient point which is located on the intersection of the strong efficient frontier and the weak efficient frontier. In the other word, each anchor point delineate the strong efficient frontier from the weak efficient frontier. So, if a decision making unit (DMU) is an anchor point, then there is at least one supporting hyperplane whose the gradient vector has some of zero components, and so some input\output factor does not play any role in the performance of the unit under evaluation. The concept of anchor point was used in DEA for the generation of unobserved DMUs in order to extend the DEA efficient frontier and so, this concept plays a critical role in the DEA theory and its applications. Given the importance of the anchor pints in the DEA literature, this study focuses on finding the anchor points and presents a new method to search the anchor points of the PPS under the variable returns to scale (VRS) assumption. For this purpose, we use the definition of the anchor points and present an approach to find the anchor points of the PPS. The proposed method is based on finding the weak and strong defining supporting hyperplanes passing through the unit under evaluation. The main advantage of the proposed method is that it exactly uses the definition of the anchor points to provide the approach and it is very simple to use and the anchor points can be easily identified by solving two simple models. In addition, the proposed approach is such that in addition to determining the anchor points, it also finds two important defining supporting hyperplanes on the PPS, which can be used in many problems in DEA. The potentially of the proposed method is illustrated by some numerical examples, reported in the literature to compare the proposed method with the existing methods.