資料包絡分析模式創新應用之探討

An Innovative Research on Data Envelopment Analysis

蔡美英(Meei-Ing Tsai)

指導教授 ： 魏乃捷 ； 薄喬萍

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)模式做效率評估時，受評估單位(decision-making unit, DMU)有時會有增減，而其評估的投入、產出變項也會因實際情況而增減。因此，有許多學者針對效率評估時，受評單位數目之增減，與投入產出變項的改變，對評估結果的影響，做敏感度分析的研究。敏感度分析可讓決策者重新審視各個重要的決策變項。當我們對於決策問題中之資料不確定時，敏感度分析就變得相當的重要。
在敏感度分析的基礎上，本研究探討在其他條件不變的情況下，變動各受評單位之「投入」、「產出」的量，對該受評單位效率值之影響。首先，對此「穩定半徑」提出一明確定義，並在DEA-CCR模式與共同權重模式下，本研究以創新的見解，分別提出評估其「穩定半徑」的方法。
經由定理證明，並以台灣紡織產業16家上市、櫃公司的實際資料為例證，說明如何將所提出的方法，應用在實務的效率評估中。研究結果顯示，藉由穩定半徑的評估，不僅可以得出各受評單位之「敏感性」分析。對於在效率評估時，常有許多受評單位都是「有效率」的情形，也可以此「穩定半徑」之值，作為對各「有效率」受評單位，「再排序」之評估依據，可有效提高效率評估的鑑別度。

關鍵字

資料包絡分析 ； 穩定半徑 ； 敏感性分析

並列摘要

Data envelopment analysis (DEA) is used to evaluate the efficiency of decision-making units (DMUs), but sometimes the number of DMUs or the number of inputs and outputs may vary. Therefore, sensitivity analysis is often performed to investigate how these variations affect DEA outcomes. Sensitivity analysis allows decision-makers to re-examine all the important decision variables. When the data input to a DEA model are uncertain, sensitivity analysis becomes crucial.
Using sensitivity analysis, this study investigated how changes in the input or output of each DMU affected the assessment results if the other conditions were unchanged. First, the stability radius was clearly defined. Second, this study proposed innovative methods to assess the stability radii of DMUs in the DEA/Charnes–Cooper–Rhodes and DEA/common weights models.
Mathematical proof of the proposed methods is provided, and real data from 16 firms in the Taiwanese textile industry are used as a case study to explain how the methods can be applied in real situations. The study revealed that sensitivity analysis of each DMU can be performed by assessing the stability radius of the DMU. Additionally, the stability radius can be used as a criterion to re-rank multiple efficient DMUs and hence increase the subtlety of an efficiency evaluation.

並列關鍵字

Data Envelopment Analysis (DEA) ； Stability Radius (SR) ； Sensitivity Analysis (SA)

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