A "calculus" for data envelopment analysis

DEA models are not amenable to differential arguments for extreme efficient units. Consequently, function representations of the approximating technology are not differentiable in the usual sense. Dually, this nondifferentiability is manifested by multiple optima to the Charnes et al. (Eur J Oper Res 2:429-444, 1978) DEA problem. This paper shows how a "calculus" can be applied to DEA, and, in particular, how this "calculus" resolves the resulting weight choice problem uniquely. The "calculus" is based on the concept of willingness to pay and well-known results in the convex analysis literature (Rockafellar, Convex analysis, 1970) for directional derivatives and their associated superdifferentials.