PROPORTIONAL PRODUCTION TRADE-OFFS IN DEA

Abstract

The "trade-offs Data envelopment analysis (DEA)" model is built by adding an extra axiom to the traditional production possibility set. The axiom introduces some replacement relations as production rules between inputs and outputs and leads to some extensions to the production possibility set. It provides more discriminatory power of decision-making units (DMUs) in DEA models, and the results are more adaptable to real conditions. In this paper, these variations are defined in proportional forms, which make the variation proportionate to DMUs' sizes. So we call them proportional trade-offs, and they offer some advantages in comparison with simple trade-off vectors, which depend on input or output units of measurements. First of all, the proportional trade-offs vectors can fairly consider the DMUs' abilities and their strengths in adapting to the proposed changes. Secondly, it will be seen that proportional trade-off vectors can be used as a generalization of usual returns to scales (RTS), and finally the proportional trade-offs models cover the basic DEA models and their related production possibility set (PPSs) as special cases.