Efficiency measurement in dynamic two-stage network structures with flexible intermediate materials

Data envelopment analysis (DEA) is a nonparametric method for evaluating the relative efficiency of decision making units (DMUs) described by multiple inputs and multiple outputs. Since DEA was introduced in the 1970s, it has been widely applied to measure the efficiency of a wide variety of production and operation systems, including two-stage production systems with a series or parallel structure. The outputs from the first stage to the next stage are called intermediate factors (or measures). In some real applications, an intermediate material or some part of it can become the final output or input to the second stage of production. Previously existing models cannot be employed directly to measure the efficiency of such systems. The authors introduce a dynamic DEA model that identifies the structure of flexible intermediate factors to maximise the measure of overall system efficiency.