Explicit Representation of the Two-Dimensional Section of a Production Possibility Set

Technical and scale efficiencies of Data Envelope Analysis are associated with a two dimensional section (a convex set) representing the amounts by which the input and output vectors of a reference decision making unit may be scaled and still lie in the production possibility set. We describe a simple algorithm, closely resembling the simplex algorithm of linear programming, to traverse the boundary of this set. Given the output of our algorithm, the scalar efficiency measures and return-to-scale characterization are trivially determined. Moreover, the set may be graphically displayed for any problem in any number of dimensions with only a minimum of additional computing effort.