Simpler Transformations to a Linear Programming Equivalent and Redundancy of Assurance Region (AR) Conditions in AR0IDEA (Imprecise DEA)

Abstract

기존 DEA(Data Envelopment Analysis)에서는 모든 자료(data)가 정확한 값으로 주어져야 하는 반면, IDEA(Imprecise DEA)의 개발은 정확한 값을 가진 자료뿐만 아니라 불완전한 자료 처리를 가능하게 하였다. AR-IDEA는 IDEA의 확장으로써 IDEA에 확신영역(Assurance Region, AR)을 첨가한 것이다. 또한 비선형계획모델인 IDEA 및 AR-lDEA를 동일한 해를 갖는 선형계획모델로 전환하는 방법도 개발되었다. 본 전환방법은 주어진 자료의 척도변환(scale transformations)과 변수변환(variable alterations)을 거쳐야하며, 때로는 가변수(dummy variables)의 도입이 필요함으로 복잡하다고 할 수 있다. 본 논문에서는 이러한 복잡한 과정을 거치지 않고 오직 변수변환만을 통하여 선형계획모델을 얻을 수 있는 간략한 전환방법을 개발한다. 또한 특수한 (그러나 현실에 자주 등장하는) 유형의 확신영역 제약식이 AR-IDEA모델에 개입되었을 경우에 효율성점수(effciency ratings)에 전혀 영향을 미치지 않는다는 퇴화성질(redundancy)을 발견한다.

While assuming exact data in the ordinary data envelopment analysis (DEA), the development of imprecise data envelopment analysis (IDEA) permits us to deal with imprecise data as well as exact data in DEA. It has been extended to the incorporation of assurance region (AR) and cone-ratio envelopment approaches to DEA, referred to as AR-IDEA. These developments have also shown how to transform the IDEA and AR-IDEA models into ordinary linear programming equivalents via scale transformations and variable alterations plus, in some cases, introducing dummy variables. In the present paper, we show one simpler approach for achieving linear programming equivalents only by variable alterations without rescaling as well as introducing dummy variables. We also provide findings in the use of imprecise data and AR conditions in DEA. This points out that some AR conditions are redundant in effecting the efficiency ratings under AR-IDEA.

While assuming exact data in the ordinary data envelopment analysis (DEA), the development of imprecise data envelopment analysis (IDEA) permits us to deal with imprecise data as well as exact data in DEA. It has been extended to the incorporation of assurance region (AR) and cone-ratio envelopment approaches to DEA, referred to as AR-IDEA. These developments have also shown how to transform the IDEA and AR-IDEA models into ordinary linear programming equivalents via scale transformations and variable alterations plus, in some cases, introducing dummy variables. In the present paper, we show one simpler approach for achieving linear programming equivalents only by variable alterations without rescaling as well as introducing dummy variables. We also provide findings in the use of imprecise data and AR conditions in DEA. This points out that some AR conditions are redundant in effecting the efficiency ratings under AR-IDEA.