Abstract:
Cross-efficiency evaluation, as an extension tool of data envelopment analysis (DEA), has been widely applied in evaluating and ranking decision making units (DMUs). Unfortunately, the cross-efficiency scores generated may not be Pareto optimal, which has reduced the effectiveness of this method. To solve this problem, we propose a cross-efficiency evaluation approach based on Pareto improvement, which contains two models (Pareto optimality estimation model and cross-efficiency Pareto improvement model) and an algorithm. The Pareto optimality estimation model is used to estimate whether the given set of cross-efficiency scores are Pareto-optimal solutions. If these cross-efficiency scores are not Pareto optimal, the Pareto improvement model is then used to make cross-efficiency Pareto improvement for all the DMUs. In contrast to other cross efficiency approaches, our approach always obtains a set of Pareto-optimal cross efficiencies under the predetermined weight selection principles for these DMUs.
Machine summary:
Improving Pareto Efficiency Using Cross-Efficiency in Data Envelopment Analysis Sara Fanati Rashidi Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran ------------------------------------------------------------ Abstract Cross-efficiency assessment, as an extensive tool for Data Envelopment Analysis, has wide applications in evaluating and ranking Decision Making Units (DMUs).
To solve this problem, in this article, we attempt to propose a cross-efficiency assessment approach based on Pareto improvement, which contains two models (the Pareto optimality estimation model and the cross-efficiency Pareto improvement model) and an algorithm.
Unlike other cross-efficiency approaches, our proposed approach always obtains a set of Pareto-optimal cross-efficiencies under predefined principles and foundations for selecting weights for these decision-making units.
In all cases, the proposed method creates Pareto-optimal cross-efficiencies for the DMUs. 2 CCR Model and Cross-Efficiency Assessment Method Suppose that n DMUs need to be evaluated and each DMUj (j=1,...
e. , provide a unique solution), in general, the results are not Pareto-optimal, which may not be acceptable by all DMUs. When creating improvements in the cross-efficiency scores for DMUs, DMUs need to select n sets of weights to re-evaluate the DMU for better cross-efficiency scores.
(Refer to page image) By averaging the self-evaluation and pairwise evaluation scores for each DMUd, we can obtain the corresponding Pareto-improved cross-efficiency for the DMU as will be defined in relation (8).
Consider {ω*dT, μ*dT} as an optimal solution for model (7) with respect to DMUd. For each (Refer to page image) Pareto-improved cross-efficiency is defined.
To solve this problem, we first proposed a Pareto optimality estimation model to determine whether a hypothetical set of cross-efficiency scores, under weight selection principles, are Pareto-optimal solutions or not.
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