Multistage network DEA: Decomposition and aggregation weights of component performance

Data envelopment analysis (DEA) is a technique for measuring the performance of peer decision making units (DMUs) that have multiple performance metrics. If the performance is viewed as efficiency, then the DEA frontier can be viewed as a production function along with the performance metrics characterized as inputs and outputs. However, DEA can be used as a benchmarking tool where the DEA frontier represents best practice frontier. A significant body of work has been directed at problem settings where the DMU is characterized by multistage or network processes. The current paper first examines weighted additive performance of two-stage process and then extends the methodology to examine general network structures. Under the condition of isolating the impact of stage weights on the overall performance, we propose a new overall performance as convex linear combination of multi-stage performance and prove that the existence of maximum score for the resulting new overall performance. We illustrate our findings through numerical and empirical data sets.