Management Science · 1999 · 482 citations · 23 references
Mathematical ProgrammingEngineeringBusiness IntelligenceIndustrial EngineeringPrescriptive AnalyticsData PreparationData-driven InnovationBusiness AnalyticsMultiple-criteria Decision AnalysisOperations ResearchProductivityTrade-off AnalysisData ScienceManagementEconomic AnalysisSystems EngineeringData IntegrationData-driven Decision SupportImprecise DataAssurance RegionStatisticsQuantitative ManagementParametric ProgrammingAr-idea ModelInformation ManagementBusinessData TreatmentData Envelopment AnalysisData Modeling
DEA evaluates the relative efficiency of decision‑making units using multiple inputs and outputs, but traditionally assumes precise numerical data, whereas many real‑world applications involve imprecise data expressed as bounds or ordinal relations. The authors extend DEA by developing the Imprecise Data Envelopment Analysis (IDEA) method, which converts mixed precise and imprecise data into standard linear programs, and further introduce AR‑IDEA, which replaces variable‑level assurance region constraints with data‑level transformations, thereby integrating cone‑ratio envelopments. The resulting AR‑IDEA model unifies imprecise data handling, assurance region constraints, and cone‑ratio envelopments within a single DEA framework.
Data Envelopment Analysis (DEA) is a nonparametric approach to evaluating the relative efficiency of decision making units (DMUs) that use multiple inputs to produce multiple outputs. An assumption underlying DEA is that all the data assume the form of specific numerical values. In some applications, however, the data may be imprecise. For instance, some of the data may be known only within specified bounds, while other data may be known only in terms of ordinal relations. DEA with imprecise data or, more compactly, the Imprecise Data Envelopment Analysis (IDEA) method developed in this paper permits mixtures of imprecisely- and exactly-known data, which the IDEA models transform into ordinary linear programming forms. This is carried even further in the present paper to comprehend the now extensively employed Assurance Region (AR) concepts in which bounds are placed on the variables rather than the data. We refer to this approach as AR-IDEA, because it replaces conditions on the variables with transformations of the data and thus also aligns the developments we describe in this paper with what are known as cone-ratio envelopments in DEA. As a result, one unified approach, referred to as the AR-IDEA model, is achieved which includes not only imprecise data capabilities but also assurance region and cone-ratio envelopment concepts.
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