Performance evaluation and quota allocation for multiple undesirable outputs based on the uniform frontier

Abstract : The zero sum gains data envelopment analysis (ZSG-DEA) models and thecorresponding uniform frontier method are widely applied for performance evaluationand resource/quota allocation in practice. Nevertheless, assuming variablereturns-to-scale (VRS) and a situation with multiple ZSG inputs/outputs, the existingZSG-DEA models may have no feasible solution for some efficient decision makingunits (DMUs) and hence the uniform frontier cannot always be determined. In this study,two improved ZSG-DEA models are proposed, one assuming constant returns-to-scale(CRS) and the other VRS. Then, a general iterative algorithm is developed forresource/quota allocation based on the uniform frontier. We prove that the proposedmethod can always allocate multiple resources/quotas under both CRS and VRSassumptions, which extends the existing uniform frontier method research. Anapplication to environmental performance evaluation and quota allocation for 30administrative regions in China is presented to elucidate the main ideas.