資料包絡分析法機率形式之效率評估

Using Probability Form to Evaluate Efficiency in DEA

康秀芳(Shiu-Fang Kang)

指導教授 ： 魏乃捷

共同指導教授 ： 薄喬萍(Chiao-Pin Bao)

義守大學/管理學院/工業管理學系/博士(2016年)

摘要

以資料包絡分析(Data Envelopment Analysis, DEA)評估各受評單位之效率值，雖具有非常良好之功效，卻也常出現以下二種缺失：一者由於各受評單位之投入、產出變項值難以準確地獲得，因此當數據稍有變動時，則會影響效率值評估；二者假設受評單位A之效率優於受評單位B之效率，以傳統之效率評估，僅能給予第一層級之效率評比，受評單位A之效率優於受評單位B之效率。但在實際的情況下，受評單位A可能有某些部份會等於受評單位B之效率，甚至受評單位A也會有一些部份劣於受評單位B之效率。因此，改善上述二種傳統效率評估之缺失，即為本研究之主要目的。
針對上述缺失，本研究以交叉效率模式 之「強勢權重之效率評估」作為「效率值之上限」； 之「弱勢權重之效率評估」作為「效率值之下限」，以此求得該 之「區間效率」。本研究定義：假設 與 之區間效率，對於 小於 之機率，以 小於 表之；而，對於 大於 之機率，則以 大於 表之。由於〝小於〞與〝大於〞並非完全互斥，因此 小於 大於 ；為確定此定義之「完善性」，本研究以「資料包絡分析法之區間效率，進行各種機率形式效率評估，總和為〝1〞」之定理，證明此「機率形式之效率評估」完善性。如此的機率形式之效率評比，更可以解釋說明各受評單位之優劣，除了可用第一層級的效率評估，更可再做第二層級之效率評估。
將本研究之創新模式，應用於寺院服務品質績效之評估，針對20間寺院之服務品質（此時，投入變量均視為相等時，所求出的效率即為績效），發現以第一層級的CCR效率評估，績效為〝1〞的寺院有第16、第18及第19等三間；但經本研究「機率形式之區間效率評估」，由於第19間寺院之區間效率範圍〝最小〞，可認為其服務品質績效最佳，其次第18間寺院服務品質績效為第二名，第16間寺院服務品質績效為第三名。再針對「區間效率上限小於〝1〞者」，選取第12、第13、第14及第15等四間寺院，進行本研究四種機率形式之績效評估，結果發現，第15間寺院服務品質績效是優於第12間寺院的服務品質績效；第13間寺院服務品質績效是優於第12間寺院的服務品質績效；第12間寺院服務品質績效優於第14間；第15間寺院服務品質績效優於第13間寺院服務品質績效。

關鍵字

資料包絡分析法 ； 交叉效率 ； 區間效率 ； 機率形式之效率

並列摘要

The Charnes, Cooper, and Rhodes (CCR) model in Data Envelopment Analysis (DEA) is highly effective at measuring the efficiency of decision-making units (DMUs). However, it has two main limitations. One is that because accurately estimating the inputs and outputs of DMUs are difficult, slight changes in these data can affect the effectiveness of the model in estimating DMU efficiency. The other is that if DMU A is more efficient than DMU B, then only elementary efficiency ratings are obtained through the CCR; in reality, DMU A is as efficient as DMU B in certain aspects but less efficient in others. This study addressed both limitations.
To overcome these two limitations, this paper proposed DEA-PE model in which the strong weight and weak weight of the cross-efficiency, , were defined as the upper and lower limits of efficiency, respectively, to estimate the interval efficiency of the DMUs. In the interval efficiencies of and , was the probability that was lower than and was the probability that was larger than . “ < ” and “ > ” are not mutually repulsive of each other; thus, . One of the principles of DEA, where all probability interval will eventually sum up to 1 is utilized in this study, in order to establish the integrity of probability efficiency evaluation. Accordingly, this probability efficiency evaluation provided a more thorough explanation of the strengths and weaknesses of two DMUs and enabled the investigation of the respective efficiency evaluations of the DMUs at the in-depth meaning.
In the study, the innovation model which described earlier is applied to the assessment of the quality of service performance of targeted 20 monasteries. All input variables are treated equal, and the performances of monasteris will be treated as their effiency respectively. First, in the first level CCR evaluation of the study, there are 3 temples credited “1” for their service qualities. They are numbered as 16th, 18th and 19th. However, by the “efficiency interval evaluation in probability form” provided in the study, temple 19th finally took the first place since it has the lowest efficiency interval, thus 18th and 16th took second and third respectively.Second, the study focus on those who are credit less than 1. Four temples, the 12th, 13th, 14th, and 15th are selected for efficiency evaluation in 4 probability distributions. The results turn out to be the monastery porfermance of temple 15 th is greater than temple 12 th; temple 13 th is also greater than temple 12 th; and the temple 12 th is greated than temple 14 th and the temple 15 th is greater than temple 13 th. Knowing is greater than, indicating that when the temples obtained by the efficiency of the range is often not necessarily the absolute strength of the weak, the temples of the variable content although some strong, but some variables variable content is weak, through this method more objective understanding of each other Which is the second level of efficiency evaluation of the characteristics of this study.

並列關鍵字

Data Envelopment Analysis (DEA) ； CCR ； Cross Efficiency ； Interval Efficiency ； Probability Efficiency

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