Efficiency Measurement of Multistage Processes: Context Dependent Numbers of Stages

An important area of research involving the benchmarking methodology data envelopment analysis (DEA), concerns the modeling of multistage situations. In the usual multistage settings, it is generally assumed that all decision-making units (DMUs) have the same number and configuration of stages. However, in many real-world examples, this assumption does not hold. Consider, for example, a supply chain setting where for some DMUs, products are shipped directly from a supplier to a retailer (single-stage), while for other DMUs, products can be transshipped through distribution centers (two or more stages). In the current paper, we investigate an efficiency measurement situation where the DMUs exhibit a mix of single and two-stage setups. The particular case examined involves a set of high technology firms that can be thought of as falling into two groups; those firms where the output of interest is the annual revenue generated, and those that not only generate revenue, but as well invest a portion of that revenue in R&D. Firms in the first group can be viewed as being single-stage DMUs while those in the other group are of the two-stage type. The modeling complication here is that the set of DMUs do not explicitly form a homogeneous set of units. We develop a DEA-style model aimed at measuring efficiency in the presence of such nonhomogeneous two-group structures.