Increasing the Discriminatory Power of DEA Using Shannon’s Entropy

Cross-efficiency evaluation, an extension of data envelopment analysis (DEA), can eliminate unrealistic weighing schemes and provide a ranking for decision making units (DMUs). In the literature, the determination of input and output weights uniquely receives more attentions. However, the problem of choosing the aggressive (minimal) or benevolent (maximal) formulation for decision-making might still remain. In this paper, we develop a procedure to perform cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into account the aggressive and benevolent formulations at the same time, and the choice of DEA weights can then be avoided. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The entropy, which is based on information theory, is an effective tool to measure the uncertainty. We then utilize the entropy to construct a numerical index for DMUs with cross-efficiency intervals. A mathematical program is proposed to find the optimal entropy values of DMUs for comparison. With the derived entropy value, we can rank DMUs accordingly. Two examples are illustrated to show the effectiveness of the idea proposed in this paper.

Section: Introductionmentioning

confidence: 99%

Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures

Liu

2016

“…Based on Soleimani-Damaneh and Zarepisheh's research, some other literature [25][26][27][28][29][30][31][32] can be found where the DEA method is also combined with Shannon's entropy. However, as there are a great many different DEA models, then the selection of DEA models would have a great effect on the results of the entropy DEA model.…”

Section: Dea With Shannon's Entropymentioning

confidence: 99%

“…Based on this first research, Bian and Yang [25] proposed an extension to the resource and environment efficiency analysis of the provinces in China. More recently, Xie et al [26] proposed an extension research of [24] in which different variable subsets were considered. Similarly, Wu et al [27] proposed a method for aggregating cross-efficiency with Shannon's entropy and they also extended their research in [28].…”

Section: Introductionmentioning

confidence: 99%

Determining Common Weights in Data Envelopment Analysis with Shannon’s Entropy

2014

Data Envelopment Analysis (DEA) is a non-parametric method for evaluating the efficiency of Decision Making Units (DMUs) with multiple inputs and outputs. In the traditional DEA models, the DMU is allowed to use its most favorable multiplier weights to maximize its efficiency. There is usually more than one efficient DMU which cannot be further discriminated. Evaluating DMUs with different multiplier weights would also be somewhat irrational in practice. The common weights DEA model is an effective method for solving these problems. In this paper, we propose a methodology combining the common weights DEA with Shannon's entropy. In our methodology, we propose a modified weight restricted DEA model for calculating non-zero optimal weights. Then these non-zero optimal weights would be aggregated to be the common weights using Shannon's entropy. Compared with the traditional models, our proposed method is more powerful in discriminating DMUs, especially when the inputs and outputs are numerous. Our proposed method also keeps in accordance with the basic DEA method considering the evaluation of the most efficient and inefficient DMUs. Numerical examples are provided to examine the validity and effectiveness of our proposed methodology.

“…Incorporating Shannon entropy into DEA has attracted the interests of a number of scholars [44][45][46]. In this section, Shannon entropy is utilized to calculate the weights of interval cross-efficiency.…”

Section: The Cross-efficiency Model Based On Shannon Entropymentioning

confidence: 99%

Entropy Cross-Efficiency Model for Decision Making Units with Interval Data

Wang

Hong

2016

Abstract:The cross-efficiency method, as a Data Envelopment Analysis (DEA) extension, calculates the cross efficiency of each decision making unit (DMU) using the weights of all decision making units (DMUs). The major advantage of the cross-efficiency method is that it can provide a complete ranking for all DMUs. In addition, the cross-efficiency method could eliminate unrealistic weight results. However, the existing cross-efficiency methods only evaluate the relative efficiencies of a set of DMUs with exact values of inputs and outputs. If the input or output data of DMUs are imprecise, such as the interval data, the existing methods fail to assess the efficiencies of these DMUs. To address this issue, we propose the introduction of Shannon entropy into the cross-efficiency method. In the proposed model, intervals of all cross-efficiency values are firstly obtained by the interval cross-efficiency method. Then, a distance entropy model is proposed to obtain the weights of interval efficiency. Finally, all alternatives are ranked by their relative Euclidean distance from the positive solution.