Research On Directional Congestion And Directional Returns To Scale Of DMUs With Undesirable Outputs

Congestion and returns to scale are two concerned problems in the process of resource reallocation,which can help managers to expand or reduce the size of the organization to improve the efficiency.In the case of complex multi-input to multi-output systems,directional congestion and directional returns to scale can be used to measure congestion and returns to scale in all directions including the radial direction,which makes the analysis results more close to the actual situation.At present,the studies of directional congestion and directional returns to scale mainly focus on evaluating production units without undesirable outputs.However,undesirable outputs are inevitable in the actual production activities.Undesirable outputs are destructive to the organizational efficiency,and dispose of them need additional costs.Hence,it is important to including these factors in the adjustment of the scale of the organization.This paper mainly uses documentation method,mathematical modeling method and empirical research method.We first review the concepts of directional congestion and directional returns to scale,and analyze their kernel thoughts.Then,for the production systems with undesirable outputs,the definitions of directional congestion and directional returns to scale are proposed.Then corresponding data envelopment analysis models are proposed.Finally,the proposed data envelopment analysis models are applied to the empirical analysis of analyzing the directional congestion and directional returns to scale of the thermal power industry in 30 regions in china.The results show that,for an effective decision making units,when inputs and outputs vary in different proportions,the results of congestion and the returns to scale can be different.Furthermore,the former is influenced by the changing direction of undesirable outputs only,while the latter are influenced by the changing direction of inputs,desirable and undesirable outputs.In order to find the best decision scheme,it is necessary to analyze the congestion and the returns to scale in different directions when the production scale of the system with undesirable outputs is adjusted.