Improvement methods for data envelopment analysis (DEA) cross-efficiency evaluation

Data envelopment analysis (DEA) cross-efficiency evaluation has been widely applied for efficiencyevaluation and ranking of decision-making units (DMUs). However, two issues still need to be addressed: nonuniquenessof optimal weights attached to the inputs and outputs and non-Pareto optimality of the evaluationresults. This thesis proposes alternative methods to address these issues. We first point out that the crossefficiencytargets for the DMUs in the traditional secondary goal models are not always feasible. We then givea model which can always provide feasible cross-efficiency targets for all the DMUs. New benevolent andaggressive secondary goal models and a neutral model are proposed. A numerical example is further used tocompare the proposed models with the previous ones. Then, we present a DEA cross-efficiency evaluationapproach based on Pareto improvement. This approach contains two models and an algorithm. The models areused to estimate whether a given set of cross-efficiency scores is Pareto optimal and to improve the crossefficiencyscores if possible, respectively. The algorithm is used to generate a set of Pareto-optimal crossefficiencyscores for the DMUs. The proposed approach is finally applied for R&D project selection andcompared with the traditional approaches. Additionally, we give a cross-bargaining game DEA cross-efficiencyevaluation approach which addresses both the issues mentioned above. A cross-bargaining game model is proposedto simulate the bargaining between each pair of DMUs among the group to identify a unique set of weights to beused in each other’s cross-efficiency calculation. An algorithm is then developed to solve this model by solvinga series of linear programs. The approach is finally illustrated by applying it to green supplier selection. Finally,we propose a DEA cross-efficiency evaluation approach based on satisfaction degree. We first introduce theconcept of satisfaction degree of each DMU on the optimal weights selected by the other DMUs. Then, a maxminmodel is given to select the set of optimal weights for each DMU which maximizes all the DMUs’satisfaction degrees. Two algorithms are given to solve the model and to ensure the uniqueness of each DMU’soptimal weights, respectively. Finally, the proposed approach is used for a case study for technology selection.