Probabilistic Bounds on the Virtual Multipliers in Data Envelopment Analysis: Polyhedral Cone Constraints

The paper is concerned with the incorporation of polyhedral cone constraints on the virtual multipliers in DEA. The incorporation of probabilistic bounds on the virtual multipliers based upon a stochastic benchmark vector is demonstrated. The suggested approach involves a stochastic (chance constrained) programming model with multipliers constrained to the cone spanned by confidence intervals for the components of the stochastic benchmark vector at varying probability levels. Consider a polyhedral assurance region based upon bounded pairwise ratios between multipliers. It is shown that in general it is never possible to identify a center-vector defined as a vector in the interior of the cone with identical angles to all extreme rays spanning the cone. Smooth cones are suggested if an asymmetric variation in the set of feasible relative prices is to be avoided.