A Method for Ranking All Efficient DMUs in Tv
Farhad Hosseinzadeh Lotfi, Reza Fallahnejad · 2011
Introduction: In the evaluation of Decision Making Units (DMUs) using Data Envelopment Analysis (DEA) models, more than one DMU may be identified as efficient. So ranking them is necessary for Decision Makers (DM). One of the main problems in ranking DMUs, by using Data Envelopment Analysis, is the ranking of non-extreme efficient DMUs. Most of the existing methods can only rank extreme DMUs. Aim: In this paper, we propose a method to rank non-extreme DMUs in Tv. Materials and Methods: We rank non-extreme DMUs by finding a positive convex combination (with the best score) of extreme efficient DMUs located on the minimum face containing the non-extreme DMU. Results: Our proposed method can rank all efficient DMUs in 3 steps: at first, extreme and non-extreme efficient DMUs must be identified (It can be done by AP model). Ranking related score for each extreme DMU can be attained by one of the existing ranking methods that can rank extreme DMUs. Then for obtaining ranking related score for non-extreme DMU, we consider the face with minimum dimension, containing the non-extreme DMU. At last, by solving a model or its dual, and based on the ranking related scores of extreme efficient DMUs located on the minimum face containing the non-extreme DMU, a ranking related score for non-extreme DMUs can be obtained. Conclusion: Although, we rarely have got observed non-extreme efficient DMUs, we must theoretically be able to rank them, because, all virtual efficient DMUs are almost nonextreme. Our method can rank non-extreme efficient DMUs as same as extreme efficient DMUs.