اندازه گیری وزن برای بهره وری متقابل نهایی با استفاده از آنتروپی شانون
|کد مقاله||سال انتشار||تعداد صفحات مقاله انگلیسی||ترجمه فارسی|
|4367||2011||4 صفحه PDF||سفارش دهید|
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Expert Systems with Applications, Volume 38, Issue 5, May 2011, Pages 5162–5165
This paper firstly reviews the cross efficiency evaluation method which is an extension tool of data envelopment analysis (DEA), then we describe the main shortcomings when the ultimate average cross efficiency scores are used to evaluate and rank the decision making units (DMUs). In this paper, we eliminate the assumption of average and utilize the Shannon entropy to determine the weights for ultimate cross efficiency scores, and the procedures are introduced in detail. In the end, an empirical example is illustrated to examine the validity of the proposed method. Some future research directions are also pointed out.
Data envelopment analysis (DEA) is a non-parametric programming technique for evaluating efficiency of a set of homogenous decision making units (DMUs) with multiple inputs and multiple outputs. It has been proven to be an effective approach in identifying the best practice frontiers and ranking the DMUs. DEA has been extensively applied in performance evaluation and benchmarking of schools, hospitals, bank branches, production plants, and so on (Charnes, Cooper, Lewin, & Seiford, 1994). However, traditional DEA models, such as CCR model in Charnes, Cooper, and Rhodes (1978) can simply classify the DMUs into two groups, namely efficient DMUs and inefficient DMUs. Moreover, it is often possible in traditional DEA models that some inefficient DMUs are in fact better overall performers than some efficient ones. This is because of the unrestricted weight flexibility problem in DEA by being involved in an unreasonable self-rated scheme (Dyson and Thannassoulis, 1988 and Wong and Beasley, 1990). The DMU under evaluation heavily weighs few favorable measures and ignores other inputs and outputs in order to maximize its own DEA efficiency. The cross efficiency method was developed as a DEA extension technique that could be utilized to identify efficient DMUs and to rank DMUs using cross efficiency scores that are linked to all DMUs (Sexton, Silkman, & Hogan, 1986). The main idea of the cross evaluation method is to use DEA in a peer evaluation instead of a self evaluation. There are at least three main advantages for cross-evaluation method. Firstly, it provides a unique ordering among the DMUs (Sexton et al., 1986). Secondly, it eliminates unrealistic weight schemes without requiring the elicitation of weight restrictions from application area experts (Anderson, Hollingsworth, & Inman, 2002). Finally, the cross evaluation method can effectively differentiate between good and poor performers (Boussofiane, Dyson, & Thanassoulis, 1991). Therefore the cross-evaluation method has been widely used for ranking performance of DMUs, for example, efficiency evaluations of nursing homes (Sexton et al., 1986), selection of a flexible manufacturing system (Shang & Sueyoshi, 1995), justification of advanced manufacturing technology (Talluri & Yoon, 2000), diagnosing best intelligent mailer (Kabassi, Virvou, & Despotis, 2003), and so on. Although average cross efficiency has been widely used, there are still several disadvantages for utilizing the final average cross efficiency to evaluate and rank DMUs, like the losing association with the weights by averaging among the cross efficiencies (Despotis, 2002), which means that this method cannot clearly provide the weights to help decision makers improve their performance, especially, the average cross efficiency measure is not good enough since it is not a Pareto solution. Considering the shortcomings above, Wu, Liang, and Yang (2009) eliminate the average assumption for determining the ultimate cross efficiency scores, and DMUs are considered as the players in a cooperative game, in which the characteristic function values of coalitions are defined to compute the Shapley value of each DMU, and the common weights associate with the imputation of the Shapley values are used to determine the ultimate cross efficiency scores. In the current paper, we will propose an approach based on information entropy theory instead of calculating the average cross efficiency scores. This approach has several advantages, for example, in this method, the most productive scale size (MPSS) units (Cooper, Seiford, & Tone, 2000) get the best rank and the interior points of the smallest production possibility sets (PPSs) which are inefficient in all models lie at the end of the ranking list (Soleimani & Zarepisheh, 2009). The rest of this paper is organized as follows: Section 2 introduces the cross efficiency evaluation method. The new method using Shannon entropy is proposed in Section 3. Section 4 gives an illustrative example, and conclusion and remarks are shown in Section 5.
نتیجه گیری انگلیسی
Aiming at the flaws when the ultimate average cross efficiency scores are used to evaluate DMUs, we eliminate the assumption of average and utilize the concept of Shannon entropy to determine the ultimate cross efficiency scores for each DMU. Finally, a numerical example is illustrated to prove the effectiveness of the proposed approach. We should point out that the numerical example in this paper is chosen only for illustrative purposes and for better understanding of the main principles of the proposed approach, so how the proposed approach can be used in the real-world application case is obvious an interesting research in the future.