整合型模糊資料包絡分析模式

Abstract

資料包絡模式自1978年發展至今，於實際應用中遍及各領域，為一實用性非常高的經營分析方法，但於現實生活中有些投入或產出項難以用明確數值表示，而當其為口語化或模糊數值時，此資料包絡分析模式即延伸為模糊資料包絡分析模式，此模式更能反映出真實世界所發生的問題。

在過去模糊資料包絡分析的一些研究中，大多利用在不同α水準下之模糊參數提出兩個明確資料包絡模式，為分別求算在不同α水準下模糊效率值之上下限，但具模糊性之效率值不易表達出實質上之含意，最後還是必須尋求適合該模式之模糊排序方法去模糊化，且其受評單位之效率排序會受到模糊排序方法設定而會有不同排序的結果，為了克服這樣的問題，因此本研究中在各不同α水準下代入一未知偏好於受評單位之模糊投入項與模糊產出項之上下限中，經由偏好調整模糊投入項與模糊產出項之上下限之整合，透過整合可產生一條明確之效率前緣，並將線性規劃模式轉換成對偶模式，則可求出一明確效率值，由此管理者不必再經過模糊排序則可由此模式中得知受評單位之相對效率。

本文最後以Leon et al. (2003)之簡例來做模式之驗證工作，在效率分析中得知本研究之模式相對具判別能力，且能對於差額分析來進行研究，說明如何進一步求算出相對無效率之DMU與其評價對象之差，並進行在一特定水準下其模糊投入與模糊產出上下限之調整，以達到改善其相對效率之目的。並以35家國道客運公司為應用實例進行本研究模式之施行。

Data envelopment analysis (DEA) proposed by Charnes et al. (1978) has been extensively applied to performance evaluation of the organizations in many fields. However, in some cases, input and output can not be measured crisply. Thus, a fuzzy DEA model can more realistically and flexibly represent real-world problems and then further enhance the applicability of conventional (crisp) DEA models. Numerous fuzzy DEA models have been proposed. However, most of them employed two crisp DEA models to separately determine the evaluation results for the upper and lower bound of under a specific α-cut level. After repeated applications of the models under a sufficient large number of different α-cut levels, the evaluation result is represented by a re-formulated fuzzy number. At last, a fuzzy ranking method will be required to rank the fuzzy performances of various decision making units (DMU). To overcome abovementioned complex procedure and inconsistent results may be obtained by two separately DEA model, this study aims to propose an integrated fuzzy DEA model to optimize both upper and lower bound of a α-level simultaneously and to delivery a crisp efficient frontier without the need of additional fuzzy ranking method. The core logic of the model is to combine both bounds in the objective function or constraints by introducing self-determined weights under various α-cut levels. Therefore, the proposed model enables decision makers to obtain the relative efficiency of DMU directly without using any fuzzy ranking method. The mathematical formulation of the proposed model has been carefully derived. To investigate the properties and applicability of the proposed model, a numerical example and a real case study on 35 intercity bus operators are conducted. Additionally, comparisons to the results obtained by the model proposed by Leon et al. (2003) are also made. The results show that the proposed model can surely delivery a crisp evaluation result and exhibit higher benchmarking power than the Leon et al.’s model. Improvement strategies for the intercity bus operators are also proposed based on slack values determined.