This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale（RTS） of economic units with multiple inputs and outputs.It is frequently noticed that when we increase the input of a decision making unit（DMU） with a certain status of RTS,different status of RTS is observed.For example,when we increase the input of a DMU with constant RTS under the traditional method,a decreasing RTS is often observed instead of the expected constant RTS.We thus define the RTS of each DMU in both input expansion and contraction regions respectively.The research starts from transferring the production possibility set into the intersection form,by giving the explicit linear inequality representation of production frontiers.The RTS structural characteristics of DMUs＇ on the production frontier are described.Status of RTS of those DMUs on the production frontier include increasing RTS,constant RTS,decreasing RTS,saturated RTS and evidence of congestion.Necessary and suficient conditions for RTS evaluation are provided.The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.
This research proposes a new method to estimate returns to scale(RTS) of decision making units(DM Us) with multiple inputs and outputs.The state of return to scale includes increasing RTS,constant RTS,decreasing RTS and evidence of congestion.The method is based on the production possibility set in the intersection form given by a set of linear inequalities.We propose and prove the necessary and sufficient conditions for the RTS estimation.With the new procedure,to estimate the RTS of a DM U is simply to check the position of the DM U on the production frontiers.We point out that the procedure is particularly important for dealing with a large number of DM U s.Therefore,it can be regarded as a complementary to the data mining.
This paper considers the problem of evaluating efficiency of Decision Making Units （DMUs） with network structures of divisions by the Data Envelopment Analysis （DEA） model. All divisions in the network are under a decentralized authority organiza- tion. That is, each division in a decision making unit has its own authority to adjust its input and output. By incorporating the division operations in the DEA model, we discuss the sufficient and necessary conditions for a DMU to be network efficient in series structure and general structure respectively.
