Construction of all data envelopment analysis efficient surfaces of the production possibility set under the Generalized DEA model

In this paper, we study the structural properties of Data Envelopment Analysis (DEA) efficient surfaces of the production possiblity set under the Generalized Data Envelopment Analysis (GDEA) model introduced by Yu, Wei and Brockett. The GDEA model contains the following well-known DEA models as its special cases: the CCR model by Charnes, Cooper, and Rhodes; the BCC model by Banker, Charnes and Cooper; the FG model by Färe and Grosskopf; and the ST model by Seiford and Thrall. The relationships among Decision Making Units (DMUs) can be found by solving the GDEA model with prediction cone description. Using these relations to identify relative positions of the DMUs on the DEA efficient surface, we devise an efficient algorithm for constructing all the DEA efficient surfaces. Through further analysis, we show properties of DEA-efficient surfaces under several important subclasses of DEA models. Analytical expressions for the DEA efficient surfaces are obtained, which are useful in analyzing the structure of DEA efficiencies and in strategic group classifications. Results from this paper suggest important applications in constructing Pareto solutions (or nondominated solutions) and in analyzing structural properties of Pareto solutions in multiobjective programming.