Restricting virtual weights in data envelopment analysis

The consequences of the use of absolute weights restrictions (i.e. restricting the multipliers) on the efficiency score and targets of a DEA model have been explored elsewhere; the same is not true for the use of restrictions on the virtuals (i.e. the product of the input/output factor by its multiplier). In this paper, a reflection on the uses of virtual weights restrictions is presented. The reasons for using virtual weights restrictions instead of absolute weights restrictions, in particular cases, are explained. Following a critique of Wong and Beasley's first proposed method for constraining the virtuals in DEA, a new classification scheme for virtual weights restrictions is presented, which brings the concept of assurance regions into virtual weights restrictions. It is shown that the use of simple virtual restrictions and virtual assurance regions are preferable to the use of the more generally advocated WB's proportional virtual weights restrictions. In recognition of levels of decision making at the unit, and external to the unit, the use of the terms unit of assessment (UOA) and controller is proposed. It is concluded that the use of virtual assurance regions applying to the target UOA can be a natural representation of preference structures and translate established patterns between the input–output divide. Also, the meaning of the efficiency score and targets in this approach most approximate traditional DEA. Alternatives to using virtual weights restrictions are considered, namely using absolute weights restrictions with a virtual meaning. Finally, an empirical example is offered.