Conventional data envelopment analysis (DEA) models require that inputs and outputs are given as crisp values. Very often, however, some of inputs and outputs are given as imprecise data where they are only known to lie within bounded intervals. While a typical approach to addressing this situation for optimization models such as DEA is to conduct sensitivity analysis, it provides only a limited ex-post measure against the data imprecision. Robust optimization provides a more effective ex-ante measure where the data imprecision is directly incorporated into the model. This study aims to apply robust optimization approach to DEA models with imprecise data. Based upon a recently developed robust optimization framework which allows a flexible adjustment of the level of conservatism, we propose two robust optimization DEA model formulations with imprecise data; multiplier and envelopment models. We demonstrate that the two models consider different risks regarding imprecise efficiency scores, and that the existing DEA models with imprecise data are special cases of the proposed models. We show that the robust optimization for the multiplier DEA model considers the risk that estimated efficiency scores exceed true values, while the one for the envelopment DEA model deals with the risk that estimated efficiency scores fall short of true values. We also show that efficiency scores stratified in terms of probabilistic bounds of constraint violations can be obtained from the proposed models. We finally illustrate the proposed approach using a sample data set and show how the results can be used for ranking DMUs.

1. 서 론
 2. 구간 데이터를 가지는 DEA 모형
 3. 로버스트 선형최적화
 4. 로버스트 DEA 모형
  4.1 승수모형에 대한 로버스트 최적화
  4.2 포락모형에 대한 로버스트 최적화
  4.3 DEA 모형에서 로버스트 최적화의 의미
  4.4 효율성 점수의 확률적 계층화
 5. 수치 예제
 6. 결 론
 Acknowledgement
 References

• 임성묵(동국대학교 서울캠퍼스 경영대학) | Sungmook Lim Corresponding Author