Projections onto Efficient Frontiers: Theoretical and Computational Extensions to DEA

Abstract

Data Envelopment Analysis (DEA) has been widely studied in the literature since its inception in 1978 and is a key analytical technique used in Wharton's performance analysis for retail delivery systems. The methodology behind the classical DEA, the oriented method, is to hold inputs (outputs) constant and to determine how much of an improvement in the output (input) dimensions is necessary in order to become efficient. The authors extend this methodology in two substantive ways. First, a method is developed that determines the shortest projection from an inefficient DMU to the efficient frontier in both the input and output space simultaneously, and second, introduces the notion of the "observable" frontier and its subsequent projection. The observable frontier is the portion of the frontier that has been experienced by other DMUs, 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 example is used to illustrate the importance of these two methodological extensions.