Network DEA: A new approach for determining component weights

Data envelopment analysis (DEA) has a brilliant history in measuring the relative efficiency of organizational units called decision making units (DMUs). However, in traditional applications of DEA, a DMU is treated as a black box, the internal structure of which is generally ignored. Some serial processes in the DEA literature have examined closed systems in which the outputs of a stage are passed on to the next stage to progress the process of completion. Neither input nor output enters or leaves the process. In other situations, DMUs have network structure. The current paper scrutinizes some open multistage processes in which an output of a stage may leave the system and an input can enter at any intermediate stage. An output may even possibly go back and re-enter as an input to the previous stage. We then extend a methodology in which the weights of components are measured by the ratio of the total weighted output of the individual component to the total weighted output of all the components. The proposed model facilitates measuring the efficiency of components along with the overall efficiency of DMUs in the presence of rework in network multistage processes. A numerical example addresses the applicability of the proposed model.