An algorithm for the anchor points of the PPS of the FRH models

Akbarian, Dariush

doi:10.1051/ro/2020086

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…They presented two approaches to recognize whether a given feasible point is an anchor point or not. Akbarian 25 used a variant of super-efficiency model to characterize all extreme efficient decision making units and anchor points of the PPS with the free disposability postulate. Shadab et al 26 developed an algorithm to show the connection between the anchor points and the concept of congestion by using the S-shape form of the production function and the geometric features of the anchor points.…”

Section: Introductionmentioning

confidence: 99%

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

Khazaeyan

Sohraiee

Mostafaee

et al. 2022

Measurement and Control

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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.

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Section: Introductionmentioning

confidence: 99%

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

Khazaeyan

Sohraiee

Mostafaee

et al. 2022

Measurement and Control

View full text Add to dashboard Cite

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An algorithm for the anchor points of the PPS of the BCC model

et al. 2022

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Anchor points play an important role in data envelopment analysis theory and applications; they delineate the efficient part of the production possibility set (PPS) frontier. In this paper, we propose an approach for finding the anchor points of the PPS of the Banker, Charnes and Cooper (BCC) model. This approach is based on a variant of super-efficiency models and their duals. The necessary and sufficient conditions for the characterization of the anchor points are also provided. Finally, the applicability of the proposed model is illustrated with some numerical examples.

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An algorithm for the anchor points of the PPS of the FRH models

Cited by 2 publications

References 21 publications

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

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

An algorithm for the anchor points of the PPS of the BCC model

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