Super-Efficiency DEA Based on Directional Distance Function in the Presence of Infeasibility

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Project title

Code/計畫編號

MOST104-2410-H019-012

Translated Name/計畫中文名

建基於方向性距離函數無可行解時之DEA超級效率

Project Coordinator/計畫主持人

Hsuan-Shih Lee

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Shipping and Transportation Management

Website

https://www.grb.gov.tw/search/planDetail?id=11482224

Year

2015

Start date/計畫起

01-08-2015

Expected Completion/計畫迄

31-07-2016

Bugetid/研究經費

938千元

ResearchField/研究領域

管理科學

2011年我們在EJOR上發表了一篇文章處理無可行解時之輻射狀超級效率。次年，2012年我們在同一期刊上延續先前之研究，進一步處理數據為0時之超級效率。在2013年，Chen等人在Omega提出了一個以方向性距離函數為基礎之超級效率模式。該模式避免了受評單位產出調整後產生負數的問題，另外該模式也解決了投入出現0的資料產生無可行解的問題。可是當0的資料出現在產出時，仍有可能會發生無可行解的問題。此外，Chen等人之模式必須先決定兩個複雜的參數。最近，2014 年，Lin及Chen在JORS提出了一個新模式，解決了出現0資料無可行解的問題，以及受評單位產出調整後為負數的問題。可是在Lin及Chen在他們的模式引進了每一項投入之最大值，而此常數會掩蓋受評單位投入的影響，主導最後評估的結果。因此本研究將發展一個建基於DDF的新超級效率模式，避免Chen等人模式及Lin and Chen模式的缺點。當0資料出現時，避免無可行解。當所有資料為正數時，我們的模式會等同於傳統的DDF超級效率模式。此外我們亦將新發展的模式應用在預測與麥氏指數上。Abstract: We have published a paper in EJOR to deal with the radial super-efficiency in the presence of infeasibility in 2011. Later, in 2012, we publish another paper in the same journal, which extends the result to zero data. In 2013, Chen et al. propose a super-efficiency model based on directional distance function in Omega. There model avoids the infeasibility when zero data occur in inputs and also prevents the negative destination of the directional scaling. However, their model might be infeasible when zero data occur in outputs. Beside, their model relies on complex predetermined parameters. Recently, Lin and Chen (2014) propose a new model which prevents infeasibility and negative destination of the directional scaling in JORS. However, Lin and Chen’s method introduce a constant which would dominate the input of the evaluated DMU. To overcome the drawbacks of the models proposed by Chen et al. and Lin and Chen, we will develop a new super-efficiency model based on DDF, which prevents infeasibility when zero data occur and working the same as original super-efficiency based on DDF when all data are positive. We will apply our new model to forecasting and the Malmquist productivity index.

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Super-Efficiency DEA Based on Directional Distance Function in the Presence of Infeasibility

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