以資料包絡分析法評量兩階段流程績效時中間指標之屬性解析

Abstract

針對多個相同的決策單位(Decision-making Unit, DMU)將多項投入指標經一內部之處理流程轉換成多項產出指標的評量，Charnes, Cooper和Rhodes三人提出資料包絡分析法(Data Envelopment Analysis, DEA-CCR)，分析各DMU的相對最高績效值，換言之即為訂定主觀之各項投入及各項產出之權重。DEA利用效率前緣(Efficiency frontier)的概念，將所有DMU區分成高效群與非高效群兩群。本研究的問題所不同的是此內部流程包含前後兩項子流程，子流程之間有多項之中間指標。從實體的角度單獨來看第一子流程時，流入之多項投入指標與流出的多項中間指標，分別被視為望小與望大指標；單獨來看第二子流程時，流入之多項中間指標與流出的多項產出指標，分別被視為望小與望大指標。由此可見兩階段子流程之中間指標，定位產生矛盾的現象，分別被兩端子流程視為望大與望小指標。文獻中顯示，若同時評量兩子流程時，此一矛盾之現象嚴重影響評量的結論。本研究窮舉出各中間指標分為望大指標及望小指標全部可能的組合，利用CCR模型計算所有的組合下各DMU的績效。以每個DMU在所有的組合下之績效，將其歸類為強高效群、半高效群、或全低效群，共三群。另外本研究提出每個DMU選擇一組中間指標屬性的最佳組合，這樣的方法能有效地解決大部分模型無法判斷中間指標屬性的缺點，並且在決定了中間指標屬性後，訂定各DMU主觀之各項投入、中間、及各項產出指標之權重，可以更進一步地去詳加探討每個DMU子流程之績效值和各指標的投影點與改善量。

Data Envelopment Analysis (DEA) has been widely employed to assess decision-making units (DMUs) that convert inputs to outputs. DMUs are then classified into two groups: efficient and inefficient. This research is dealing with the process contains two stages. In the first stage, the inputs are converted to a set of intermediate items. Then, they are converted to outputs in the second stage. The intermediate items respectively are treated as outputs and inputs in the first and second stages. In this research, the characteristic of each intermediate item could be treated as either an input or an output in the model for analyzing the system that aggregated two stages. We enumerated all the possible characteristic combinations of intermediate items. DMUs are assessed under each combination. According to the efficiencies evaluated under the combinations, each DMU is classified into all-efficient, mixed-efficiency and all-inefficient. Further, for each DMU, comparing the evaluations results under all the combinations, the most-favorable combination is selected. Therefore, the target of the DMU is identified as well as the set of indices weights are determined.