Abstract:
As we know, in evaluating of DMUs some of them might be efficient, so ranking of them have a high significant. One of the ranking methods is cross-efficiency. Cross efficiency evaluation in data envelopment analysis (DEA) is a commonly used skill for ranking decision making units (DMUs). Since, many studies ignore the intra-organizational communication and consider DMUs as a black box. For significant of this subject, we applied cross-efficiency for network DMUs. However, In view of the fact that precise input and output data may not always be available in real world due to the existence of uncertainty, we have developed the model with interval data. the existing classical interval DEA method is not able to rank the DMUs, but can only classify them as efficient or inefficient , so this paper improve that. The proposed method can be used for each network that includes DMUs with two stages in production process. However, this paper is the first study that examined cross efficiency of DMUs in structure framework with interval data. the new approach enables us to ranking of first stage for n DMU and second stages of them. DMUs with the best rank can be used as benchmark for improving efficiency of other DMUs. Finally, We present Illustrate example with two steps for proposed model that can be develop for more than two steps.
Machine summary:
Cross efficiency evaluation in data envelopment analysis (DEA) is a commonly used skill for ranking decision making units (DMUs).
Section 3presents the new model for the cross-efficiency evaluation method with interval data for tow stage DMUs. Illustrative example for proposed method are presented in section 4.
Material and methods Data envelopment analysis (DEA), originally proposed by Charnes, Cooper, and Rhodes (1978), is a non-parametric programming method for evaluating the efficiency of a group of homogenous decision making units (DMUs) with multiple inputs and multiple outputs [1, 2, 3, 4, 5] The main idea of DEA is to generate a set of optimal weights for each DMU in a set of DMUs to maximize the ratio of its sum of weighted outputs to its sum of weighted inputs while keeping all the DMU ratios at most 1.
Wu, Sun, Zha, and Liang (2011) and Contreras (2012) proposed weights selecting models in which the secondary goal is to optimize the ranking position of the DMU under evaluation[25, 26].
Maddahi, Jahanshahloo, Hosseinzadeh Lotfi, and Ebrahimnejad (2014) suggested optimizing proportional weights as a secondary goal in DEA cross-efficiency evaluation[28].
For example, Wu, Liang, and Yang (2009) considered the DMUs as players in a cooperative game, in which measure the efficiencies of the DMUs with uncertain inputs and outputs data, Despotis & Smirlis (2002) proposed a pair of linear problem models to generate the lower and upper bounds of the efficiency for each DMU.
A ranking method for DMUs with interval data based on dea cross-efficiency evaluation and TOPSIS.