運用資料包絡分析法與集群分析做績效評估

Performance Evaluation with DEA and Cluster Analysis

張原彰(Yuan-Chang Chang)

指導教授 ： 蔡榮發

國立臺北科技大學/管理學院/商業自動化與管理研究所/碩士(2005年)

https://doi.org/10.6841/NTUT.2005.00019

摘要

資料包絡分析法(Data Envelopment Analysis, DEA)是一個可處理多重投入及多重產出的績效評估工具，自從Charnes、Cooper與Rhodes三位學者於1978年提出後，這套方法已廣泛被應用在現實生活中。當使用DEA演算法求受評單位的效率分數時，已存在一個非常根本的問題，即各受評單位，或稱為決策單位元(Decision Making Unit,DMU)透過演算法所求得的各組權重可能差異過大，導致所求得的績效評估或排名資料可能被扭曲，這引發一連串的相關問題，例如：受評單位之間的鑑別度不高、不一致的次序關係過多。
本研究針對已知的投入產出值代入DEA演算法所獲得的權重，進行二階段的集群分析，依照不同的群組來做績效評估。其基本精神是，同樣重視某一評價指標的受評單位去做DEA的績效排名，所得的排名結果將更不會有爭議。且研究的結果確實能改善鑑別度，且當受評單位增多，效果將更為明顯。又雖然透過分群，可提高一些鑑別度，但各群還是有鑑別不出來的受評單位，我們針對各群有效率的DMU，使用正規化權重向量的槪念，使各有效率的DMU能區分高下。對於各群無效率的DMU，我們也使用差額變數分析(Slack Variable Analysis)，指引各無效率的DMU改善的方向。
最後，我們亦舉了二個實際的例子，來比較原始DEA方法的評估結果與本研究所提出之方法的評估結果有何差別，並希望未來能應用到其他不同領域、不同層面的績效評估。

關鍵字

資料包絡分析法 ； 二階段集群分析 ； 正規化權重向量 ； 差額變數分析

並列摘要

Data Envelopment Analysis (DEA) is a tool of performance assessment handling multiple input and output production correspondences. Since Charnes, Cooper and Rhodes (1978) presented this methodology, it has broadly been applied in real life. Nevertheless, DEA has an extremely fundamental problem that each set of favorable weights maximizing each DMU under consideration could be diverse when we use DEA to obtain relatively efficient score of each DMU. This problem may cause performance assessment or ranking acquired through mathematical programming technique of DEA to be twisted seriously. Furthermore, a series of related issues such as lack of discrimination and inconsistent orders among DMUs are involved in this basis problem.
This study proposes a novel algorithm to rank DMUs that have similar weights. The algorithm performs two-stage cluster analysis with weights obtained by DEA algorithm, and ranks DMUs of each group generated by cluster analysis. The outcome proves that the proposed method can improve the discrimination because of removing outliers. Although discrimination advances through cluster analysis, there are still indiscriminable DMUs in each group. We focus on efficient DMUs in each group and make them differentiable by the concept of normalizing the weight vectors. On the other aspect, we provide inefficient DMUs in each group with improvable directions by the method of slack variable analysis.
Practical examples are also presented to compare the original DEA method with the proposed method and illustrate that it is applicable and useful to other applications of different fields.

並列關鍵字

Data Envelopment Analysis ； Two-stage Cluster Analysis ； Normalized Weight Vectors ； Slack Variable Analysis

參考文獻

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