On VEA, production trade-offs and weights restrictions

In this article we explore the relationship between Value Efficiency Analysis (VEA) and Data Envelopment Analysis (DEA) models including production trade-offs or weights restrictions. In particular, we show that the VEA model is equivalent to a DEA model including production trade-offs for which the trade-off coefficient vectors are equal to either (i) the negative of the input and output quantities of the Decision Making Units (DMUs) chosen as the Most Preferred Solution (MPS) in VEA, under constant returns to scale, or (ii) the deviations of all evaluated DMUs’ input and output quantities from those of the DMUs chosen as the MPS, irrespectively of the returns-to-scale assumption. These trade-offs are the dual forms of type II Assurance Region weight restrictions. We then show that a similar equivalence holds between pure output or input VEA and DEA models including trade-offs, if the above trade-offs are respectively considered only for outputs or only for inputs. In this case the trade-offs are the dual forms of type I Assurance Region weight restrictions.