IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units)

IDEA (Imprecise Data Envelopment Analysis) extends DEA so it can simultaneously treat exact and imprecise data where the latter are known only to obey ordinal relations or to lie within prescribed bounds. AR-IDEA extends this further to include AR (Assurance Region) and the like approaches to constraints on the variables. In order to provide one unified approach, a further extension also includes cone-ratio envelopment approaches to simultaneous transformations of the data and constraints on the variables. The present paper removes a limitation of IDEA and AR-IDEA which requires access to actually attained maximum values in the data. This is accomplished by introducing a dummy variable that supplies needed normalizations on maximal values and this is done in a way that continues to provide linear programming equivalents to the original problems. This dummy variable can be regarded as a new DMU (Decision Making Unit), referred to as a CMD (Column Maximum DMU).