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Multiple Variable Proportionality in Data Envelopment Analysis

Data envelopment analysis (DEA) provides an optimization methodology for deriving an efficiency score for each member of a set of peer decision-making units. Under the original DEA model it was assumed that there is constant returns to scale (CRS). This idea was later extended to the more general case that allowed for variable returns to scale (VRS). In both of these structures, it is assumed that the returns to scale (RTS) classification, consistent with the classical definition, applies to the entire (input, output) bundle. In many settings it can be the case that the output bundle can be separated into distinct subsets or business units wherein an RTS-type behavior may be different for one subgroup than for another. We refer to such situations as involving multiple variable proportionality (MVP). Examples of MVP can occur when there are different product subgroupings in a company, different wards in hospitals, different programs in a university, and so on. Identification of such differential behavior can provide management with important insights regarding the most productive proportionality size (MPPS) in each of those subgroups. In the current paper we introduce DEA-based tools that address those situations where MVP exists.