Multiple solutions identification in Data Envelopment Analysis

This paper addresses the problem of analyzing the results of a benchmarking process in which the efficiency of a set of Decision Making Units (DMUs) is evaluated via Data Envelopment Analysis (DEA). Because of the special structure of DEA linear programs, degeneracy often occurs and optimal solutions are not necessarily unique. This lack of uniqueness does not affect the efficiency evaluation of DMUs, but it may play a critical role in the interpretation of additional information provided by DEA models. Focussing on virtual inputs and outputs analysis, we suggest in this paper a two stage linear programming approach which allows the detection of some particular alternative optimal solutions. The proposed analysis may be useful to accurately model the “production technology” of each DMU, identifying real strengths and weaknesses and isolating specialized behaviors, according to the evaluation of a suitably defined equilibrium index.