Network DEA: Additive efficiency decomposition

In conventional DEA analysis, DMUs are generally treated as a black-box in the sense that internal structures are ignored, and the performance of a DMU is assumed to be a function of a set of chosen inputs and outputs. A significant body of work has been directed at problem settings where the DMU is characterized by a multistage process; supply chains and many manufacturing processes take this form. Recent DEA literature on serial processes has tended to concentrate on closed systems, that is, where the outputs from one stage become the inputs to the next stage, and where no other inputs enter the process at any intermediate stage. The current paper examines the more general problem of an open multistage process. Here, some outputs from a given stage may leave the system while others become inputs to the next stage. As well, new inputs can enter at any stage. We then extend the methodology to examine general network structures. We represent the overall efficiency of such a structure as an additive weighted average of the efficiencies of the individual components or stages that make up that structure. The model therefore allows one to evaluate not only the overall performance of the network, but as well represent how that performance decomposes into measures for the individual components of the network. We illustrate the model using two data sets.