Projections onto efficient frontiers: Theoretical and computational extensions to DEA

Data Envelopment Analysis (DEA) has been widely studied in the literature s ince its inception in 1978. The methodology behind the classical DEA, the o riented method, is to hold inputs (outputs) constant and to determine how m uch of an improvement in the output (input) dimensions is necessary in orde r to become efficient. This paper extends this methodology in two substanti ve ways. First, a method is developed that determines the least-norm projec tion from an inefficient DMU to the efficient frontier in both the input an d output space simultaneously, and second, introduces the notion of the "ob servable'' frontier and its subsequent projection. The observable frontier is the portion of the frontier that has been experienced by other DMUs (or convex combinations of such) and thus, the projection onto this portion of the frontier guarantees a recommendation that has already been demonstrated by an existing DMU or a convex combination of existing DMUs. A numerical e xample is used to illustrate the importance of these two methodological ext ensions.