For the main DEA models, adding a Perfect Object—that is, a virtual object that has the smallest inputs and greatest outputs—to a collection of actual objects permits obtaining solutions analytically. The paper derives formulas for the solutions and demonstrates that computations with them comprise simple operations with ratios of inputs and outputs while avoiding the use of linear programming (LP) algorithms. A numerical example illustrates the utility of the approach.
Vaninsky, A. DEA with a Perfect Object: Analytical Solutions. Communications in Mathematics and Applications. 2(1), 1 – 13, 2011.