Optimal weights in DEA models with weight restrictions

Abstract

According to a conventional interpretation of a multiplier DEA model, its optimal weights show the decision making unit under the assessment, denoted DMUo, in the best light in comparison to all observed DMUs. For multiplier models with additional weight restrictions such an interpretation is known to be generally incorrect (specifically, if weight restrictions are linked or nonhomogeneous), and the meaning of optimal weights in such models has remained unclear. In this paper we prove that, for any weight restrictions, the optimal weights of the multiplier model show DMUo in the best light in comparison to the entire technology expanded by the weight restrictions. This result is consistent with the fact that the dual envelopment DEA model benchmarks DMUo against all DMUs in the technology, and not only against the observed DMUs. Our development overcomes previous concerns about the use of weight restrictions of certain types in DEA models and provides their rigorous and meaningful interpretation.