DEA-R模式之發展、驗證與比較

Abstract

資料包絡分析法(Data Envelopment Analysis, DEA)是效率評估方法中很重要的一種，而權重是資料包絡分析法的主要議題之一。近來發展出DEA-R這種以比率為概念的新模式以解決多餘權重限制所造的無法表達特定投入產出關係之問題。可是關於這種新模式的相關議題並沒有被深入的探討，因此本文首先發展了投入導向DEA-R，接著以效率前緣的概念證明了DEA-R模式的正確性。除此之外，本文藉由CCR與DEA-R的比較，發現多餘權重限制除了無法表達特定投入產出關係，還會造成低估效率值甚至更嚴重的假低效問題。最後，本文將權重作轉換以評估多餘權重限制造成低估的程度，評估的結果顯示，多餘的權重限制是造成效率值低估的原因之一，且高效DMU低估的幅度較大。因為投入導向DEA-R是一個受驗證模式且不包含多餘權重限制，所以可以安穩地採用投入導向DEA-R代替投入導向CCR以避免多餘權重限制造成的問題。

DEA is one of the most representative methods of efficiency evaluation and weight is a popular issue in DEA field. A new DEA model, DEA-R, had been developed for avoiding needless weight restriction, which causes the expression problem of specific input-output relationship. But some issue about DEA-R need to be discussed. So this article developed the input-oriented DEA-R and proved the validity of DEA-R through new defined efficient frontier. In addition, this article found that needless weight restriction causes not only the expression problem but also underestimation of efficiency and pseudo-inefficiency. Finally, this article converts the optimal weight to analyze the influences of needless weight restrictions. The result showed that the underestimations of efficient DMUs are bigger than in-efficient DMUs and the needless weight restriction really causes underestimation. Because input-oriented DEA-R is a valid model and excludes needless weight restriction, input-oriented DEA-R is a good substitued model for input-oriented CCR.